ECOMORPHOLOGICAL STRUCTURE OF BAT COMMUNITIES:
ALTERNATIVE MODELS AND ENVIRONMENTAL GRADIENTS
by
RICHARD D. STEVENS, B.S.
A THESIS
IN
ZOOLOGY
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE
Approved
May, 1996
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ACKNOWLEDGMENTS
This thesis represents the culmination of effort of many people. In fact, if one
were to tabulate all of the contributions towards its completion, mine would, by far, be
in the minority compared to those of others.
I would like to fu-st thank my major professor. Dr. Michael Willig, for his
friendship, criticism, enthusiasm, encouragement, emotional and financial support, and
direction. I specifically thank Mike for instilling in me the desire to improve upon my
weaker idiosyncrasies and to capitalize on the stronger ones. Moreover, I am greatly
indebted to him for constant funding, which allowed me teaching-free support
throughout the entire time I pursued my master's.
I would like to thank Dr. Clyde Jones, Dr. Daryl Moorhead, and Dr. Robert
Owen for serving on my committee as well as for their interaction and direction. I
would especially like to thank Dr. Jones for allowing me to be a not-so-honorary
member of his lab, and for ensuring that I truly appreciate what it means to be a
mammalogist. I certainly gained a lot from interaction with and stimulation by him and
his students.
Many fellow graduate students have aided in the conceptual and methodological
development of this thesis. First, and certainly foremost, is the contribution of Alec B.
Shaner. Without Big Al's computer wizardry and mathematical adroitness, my ideas
would have simply remained questions. Maryann Lynch and Kate Lyons provided
much criticism when I lacked forethought, and much support and encouragement
during times of self-doubt. Dianne Hall was exceedingly helpful not only through her
editorial reviews, but also through sharing her wisdom during the latter stages of this
thesis and reassuring me that many of the emotions I was experiencing were quite
normal. Pragna Patel, Maryann Lynch, Kate Lyons, and Dianne Hall were invaluable
in proofing of data and tables. Dr. Charles Werth, Dr. Robert Hollander, Dr. Gerardo
ii
Camilo, Dr. Michael Gannon, Dr. Rick Manning, Brian Croyle, Javier Alvarez,
Elizabeth Sandlin, Steven Cox, Steven Presley, Michael Cramer, Michele Secrest,
Franklin Delano Yancey, II, Michelle Wallace, Burhan Gharaibeh, Johnny Peppers,
Celia Lopez-Gonzales, Justin Jones, Jeff McMillen, Cakky Brawley, and Gary
Greenstreet, all provided much appreciated direction, friendship, and support.
I owe thanks to many faculty members from Texas Tech, as well as other
institutions. Dr. Mark McGinely provided me with much direction in my early pursuit
of community ecology. Dr. Richard Strauss provided statistical expertise regarding
PCA and simulation analyses. Dr. Elgene Box, from the University of Georgia, and
Dr. Michael Rosenzweig, from the University of Arizona, provided direction regarding
primary productivity and evapotranspiration.
Various people and agencies have paid my salary during the time I pursued my
master's degree. Dr. John Zak as director of The Institute for Environmental Sciences
at Texas Tech University provided funding from 1992-1994. Dr. Jorge Saliva and the
U.S. Fish and Wildlife Service provided funds for two summers studying bats in
Puerto Rico. Finally, Dr. Tony Krzysik and the U. S. Army Corps of Engineers
provided funding during the latter stages of this thesis, not to mention insight as to
statistical methods for achieving more accurate density estimates, an appreciation of
ecological phenomena at landscape scales, and many good times in the Mojave Desert.
Several museums have provided specimens for examination. These include:
the Field Museum of Natural History; museums at the University of Kansas and
Louisiana State University; the Smithsonian Institution and United States National
Museum; the American Museum of Natural History; the Carnegie Museum of Natural
History; and The Museum, Texas Tech University. I especially want to thank the
curatorial staff at each of these institutions for their hospitality and patience during my
visits. More specifically, I want to thank Thor Holmes from the University of Kansas
m
for not forgetting his humble beginnings and providing shelter, food, and hospitality to
a poor traveling graduate student.
I would like to state my appreciation to the late Dr. J. Knox Jones, Jr. It was
unfortunate that Dr. Jones was unable to directiy influence a majority of my graduate
career. Nonetheless, Drs. Knox and Clyde Jones are responsible for my initial
involvement in mammalogy, and my subsequent development certainly will be lessened
by the absence of Dr. J. Knox Jones, Jr.
This thesis has probably been my most selfish undertaking, and I would like to
end by thanking my family. Not only has my family been very patient regarding my
lack of interaction, but they have always provided unconditional support and
encouragement. For this I am most thankful. I especially want to thank my mother and
father for their bravery in allowing me the freedom to pursue what I wanted regardless
of the avenue, and can only hope that my winding road will lead to something
comparable to their expectations.
IV
TABLE OF CONTENTS
ACKNOWLEDGMENTS ii
LIST OF TABLES viii
LIST OF FIGURES x
CHAPTER
I. INTRODUCTION 1
Objectives 5
Methodological Considerations 5
Literature Cited 8
II. THE RELATIONSHIP BETWEEN ABUNDANCE AND MORPHOLOGICAL DISSIMILARITY: A MODEL OF COMMUNITY STRUCTURE 12
Abstract 12
Introduction 13
The Model 15
Competitive Scenarios 17
The Community 18
Results 20
Discussion 20
Literature Cited 26
III. COMMUNITIES, INTERACTIONS, AND COMPETITIVE EXCLUSION: A SYNOPTIC EVALUATION OF SIZE ASSORTMENT 37
Abstract 37
Introduction 37
Methods 39
Feeding Guilds 39
Morphological Structure 40 V
Species Pools 41
Results 43
Principal Components Analyses 43
Minimum Spanning Trees 44
Discussion 44
Literature Cited 49
IV. COMMUNITIES, INTERACTIONS, AND THE LACK OF COMPETITIVE EXCLUSION: A SYNOPTIC EVALUATION OF DENSITY COMPENSATION 76
Abstract 76
Introduction 78
Methods 80
Communities 80
Feeding Guilds 80
Morphological Structure 81
Null Hypotheses 83
Results 85
Discussion 86
Literature Cited 90
V. GRADIENTS IN THE STRUCTURE OF NEW WORLD
BAT COMMUNITIES 100
Abstract 100
Introduction 101
Metiiods 104
Selection of Communities 104
Characterization of Community Structure 104
Morphological Structure 105
Numerical Structure 106 vi
Environmental Characterization 108
Principal Components Analysis 109
Multiple Regression and Correlation Analyses 110
Results 114
Environmental Axes 110
Principal Components Analyses I l l
Axes of Structure 112
Multiple Regression Analyses 113
Correlation Analyses 114
Discussion 115
Literature Cited 120
VL SYNTHESIS 148
Literature Cited 151
APPENDICES
A. LOCATION AND ANNOTATED DESCRIPTION OF
BAT COMMUNITIES 152
B. DESCRIPTION OF FEEDING GUILDS 157
C. DESCRIPTION OF MORPHOLOGICAL CHARACTERS 159
D. STRUCTURE OF FIFTEEN BAT COMMUNITIES 160
E. SIMULATION PROGRAM TO EVALUATE DENSITY COMPENSATION 203
F. SIMULATION PROGRAM TO EVALUATE SIZE ASSORTMENT 209
vu
LIST OF TABLES
2.1 Structure of the nocturnal granivore guild from the Sonoran Desert community 31
3.1 Eigenvalues and percent variation accounted for by the fu-st two principal components (PC) in analyses conducted on morphological characters of species in each guild, separately 53
3.2 Factor loadings for the first and second principal components for each of the five feeding guilds 54
3.3 Pearson product-moment correlations of each of seven ecomorphological characters with the first and second principal components derived for each of the feeding guilds 55
3.4 Results from simulation analyses evaluating whether the mean MST segment length from an actual feeding guild was indistinguishable from those under the null hypothesis of stochastic guild assembly 56
3.5 Results from simulation analyses evaluating whether the variance of MST segment lengths from an actual feeding guild was indistinguishable from those under the null hypothesis of stochastic guild assembly 61
3.6 Results of Fisher's test of combined probability for overall significance regarding mean MST lengths from each of fifteen bat communities 66
3.7 Results of Fisher's test of combined probability for overall significance of variance of MST lengths from each of fifteen bat communities 68
3.8 Results of Fisher's test of combined probability determining overall significance of mean MST lengths from each of five feeding guilds 70
3.9 Results of Fisher's test of combined probability determining overall significance of variance of MST lengths from each of five feeding guilds 71
4.1 Results from simulation analyses evaluating nonrandom patterns in abundance within fifteen bat communities 95
4.2 Results of Fisher's test assessing overall deterministic structure of bat communities when probabilities from all feeding guilds are combined 98
4.3 Results from Fisher's test assessing overall, deterministic structure of each of five feeding guilds when probabilities are combined for all locations 99
5.1 Bat communities used to evaluate gradients of structure 125
viii
5.2 Environmental parameters and their associated acronyms in parentheses ..126
5.3 Latitudinal (" N or S) and precipitation (mm/mo-^ attributes of nine locations of New World bat communities 128
5.4 Attributes of temperature (° C) of each of nine locations of New World bat communities 129
5.5 Attributes of productivity (g/m ) of each of nine locations of New World bat communities 130
5.6 Eigenvalues and percent variation explained by principal components used to characterize environmental gradients 131
5.7 Factor loadings for all climatic variables on the first four environmental principal component axes 132
5.8 Pearson product-moment correlations of each climatic variable with four environmental principal component axes 133
5.9 Eigenvalues (Eigen) and percent variation (%Var) accounted for by significant principal components characterizing the relationship among eleven measures of structure for communities and each guild, separately.. 134
5.10 Factor loadings (Eigen) and degree of association as determined by Pearson product-moment correlation coefficients between each of the measures of structure and each principal component (CPC) 135
5.11 Results from stepwise multiple regression analysis determining the degree to which measures of structure are a linear function of environmental gradients 140
5.12 Results from Kendall rank correlation analyses evaluating the degree of association between environmental variables and measures of structure 141
D. 1 Species composition, abundance, and morphological attributes of bat communities 161
ix
LIST OF FIGURES
2.1 Theoretical expectations of the relationship between morphological distance and abundance 32
2.2 Graphical representation of the distribution of r-values generated by chance (Ho) and the location of the rejection region dictated by the alternate hypothesis of deterministic structure 33
2.3 Three competitive scenarios based on considerations of morphology and abundance 34
2.4 Results from simulation analyses that evaluate each of three competitive scenarios for deterministic structure 35
3.1 Graphical representation of a minimum spanning tree (MST) 72
3.2 Graphical representation of faunal pools 73
3.3 Graphical representation of the null hypothesis regarding mean minimum spanning (MST) tree segment lengths 74
3.4 Graphical representation of the null hypothesis regarding the variance of the minimum spanning tree (MST) lengths 75
5.1 Scattergram of the relationship (r = 0.761) between numerical structure for frugivores (CPC 3) and variability of temperature (EPC 2) 143
5.2 Scattergram of the relationship (r = 0.782) between morphological structure characterized by mean interspecific distance (CPCl) within the gleaning animalivore guild and the relative variabiUty of productivity (EPC4) 144
5.3 Scattergram of the relationship (r = 0.766) between numerical structure (CPC 3) of the gleaning animalivore guild and the absolute variabihty in precipitation and productivity (EPC 1) 145
5.4 Scattergram of the relationship (r = -0.908) between numerical structure (CPC 2) of the nectarivore guild and variability in temperature (EPC2)....146
5.5 Scattergram of the relationship (r ndaii = -0.674) between morphological structure characterized by the mean interspecific distance within the aerial insectivore guild and relative variability in precipitation and productivity.. 147
A. 1 Graphical representation of the approximate location of each bat community evaluated 159
CHAPTER I
INTRODUCTION
The morphological, biogeographic, and taxonomic radiation of the Chiroptera
is one of the most conspicuous characteristics of the class Mammalia. Bats are the
second largest order of mammals, and include two suborders, 18 families, 186 genera,
and 986 species (Nowak, 1991). Chiropteran diversity is organized into a well-
documented latitudinal gradient, whereby species richness increases with decreasing
latitude (Findley, 1993; Lyons, 1995; Willig and Lyons, in lit.; Willig and Sandlin,
1991; Willig and Selcer, 1989; Wilson, 1974). Furthermore, the latitudinal gradient
in bat species richness is so strong that it is the principal component inducing the
latitudinal gradient in species richness for mammals as a whole (Findley, 1993;
Wilson, 1974; however, see Kaufman, 1995). A considerable effort over the last 50
years has focused on distinguishing and understanding causal factors of the latitudinal
gradient. Increases in species richness with decreasing latitude are facilitated by an
increase in the number of species within ecological communities in tropical areas
(Begon et al., 1990). Thus, understanding the factors that affect community
composition are of interest from a biogeographical, as well as ecological, perspecitve.
A community is defined as a group of species that co-occur in space and time
(Begon et al., 1990). Entire communities often represent hundreds if not thousands of
species, and as such, may be complex from an ecological perspective (Simberloff and
Day an, 1991). Communities commonly are categorized into feeding guilds, which
often represent more germane study units than do entire communities (Bonaccorso,
1975; Findley, 1993; Hawkins and MacMahon, 1989; Simberloff and Dayan, 1991;
Willig, 1982; Willig and Moulton, 1989). Feeding guilds are groups of potentially
interacting species that consume similar resources in a similar fashion (Root, 1967).
1
Traditionally, it was believed that biotic interactions, primarily competition, mediate
the co-existence of species within feeding guilds and ultimately structure
communities (Robinson et al., 1993; Brown, 1989; Davidson et al., 1984; Fleming,
1984). As a result, competition theory provides much of the historical foundation of
contemporary animal community ecology.
An important assumption in community ecology is that the consumption of
resources is dependent on the size and shape of trophic apparati, and thus, the ecology
of an organism is reflected in its morphology (Bonaccorso, 1975; Brown and
Lieberman, 1973; Findley and Black, 1983; Findley and Wilson, 1982; Freeman,
1981, 1984, 1988, 1992; Hespenheide, 1973; Mares, 1976; Smartt, 1978). If
morphology reflects ecology, and competition mediates the structure of feeding
guilds, then there must be a limit to how similar two species can be and still coexist in
the same community (Abrams, 1983; MacArthur and Levins, 1967). If two species
are too similar, then they will experience such intense interspecific competition that
either one or both will diverge morphologically or be driven to extinction at the local
level. Thus, character displacement and competitive exclusion within feeding guilds
should produce patterns of morphology that are more overdispersed than would be
expected due to chance alone (Brown and Wilson, 1956; Gause, 1934; Hardin, 1960).
Indeed, this has been widely documented, not only for mammals, but for a number of
other vertebrate taxa as well (Simberloff and Boeklen, 1981).
Hyperdispersion of morphologies within feeding guilds alternately could be
the result of stochastic processes. Throughout the 1980s, community ecologists
employed null models to demonstrate the artifactual nature of many morphological
patterns (Bowers and Brown, 1982; Connor and Simberioff, 1979; Simberloff, 1984;
Simberloff and Boeklen, 1981; Strong and Simberioff, 1981; Willig and Moulton,
1989). As a result, evidence regarding competition and its influence on the
ecomorphological structure of communities is equivocal.
Two important oversights potentially obscure the role of competition in
structuring communities. First, patterns of morphology may not be the only
indicators of deterministic structure. Nonetheless, contemporary null models,
designed to detect hyperdispersed morphologies within communities, are incapable of
evaluating other manifestations of competitive interactions. For example, if resource
consumption is determined by morphology, then pairs of morphologically similar
species should exhibit more intense competition than do pairs of species that are less
similar. As a result, a negative correlation should exist between morphological
similarity and abundance within feeding guilds; the ultimate local extinction of a
species is but a consequence of this process.
Second, competition need not structure all communities in all situations to be
important. In fact, competitive interactions should not be expected to manifest in all
situations. For example, climatically unpredictable or unstable environments impose
greater density-independent mortality than do stable environments (Andrewartha and
Birch, 1954; MacArthur, 1972; Zeveloff and Boyce, 1988). As a result, populations
may never reach density-dependence, and never experience intense interspecific
competition. Conversely, more stable envkonments allow populations to approach
density-dependence and interspecific competition should become more intense; in
some cases, intense enough to induce deterministic structure. Hence, gradients in the
degree to which communities are deterministically structured by density-dependent
biotic interactions should coincide with axes characterizing environmental variability.
In isolation, single community studies offer littie insight into this scenario. Moreover,
general conclusions on the structure of communities and the causal factors of
structure are tenuous when only one community is evaluated. Studies involving many
communities must be conducted to assess the generality of hypotheses.
Bat communities represent exceptional systems by which gradients in
structure can be investigated. Bats numerically dominate many communities
(Robinson, 1971; Handley, 1966), are species rich in both tropical and temperate
areas, and occur in all terrestrial biomes except tundra (Nowak, 1991). Furthermore,
several bat communities are well-documented and have been the focus of intensive
ecological investigations (Findley, 1993).
Predictable patterns exist regarding the composition of bat communities
(Findley, 1993). In general, bat communities are composed only of aerial insectivores
at higher latitudes. As one goes toward more tropical environs, species richness
increases within communities (Findley, 1993). Moreover, as structural and resource
diversity increase, so does the number of feeding guilds, from one (aerial insectivore)
to no less than seven guilds (aerial insectivore, frugivore, gleaning animalivore,
molossid insectivore, nectarivore, piscivore, sanguinivore). Consistent morphological
patterns within communities are discernible as well. Most communities are
dominated by a group of morphologically similar species that form a core, whereas
the morphological periphery harbors fewer species of higher morphological disparity
species (Findley and Black, 1983; Fleming, 1986). Few studies have attempted to
negate that observable patterns, such as this, could be a product of chance (Willig and
Moulton, 1989). Moreover, no studies have determined variation in the strength of
patterns, or whether some extrinsic component of the environment influences the
degree to which communities are structured by deterministic processes.
Objectives
Herein, I statistically evaluate 15 bat communities in the New World to
determine whether their structure may be the product of deterministic processes (see
Appendix A). In Chapter n, I develop a model that evaluates community structure
based on patterns in abundance. In Chapter IE, I utilize a null model developed by
Willig and Moulton (1989) to determine whether nonrandom morphological patterns
are pervasive in the fifteen communities. In Chapter IV, I evaluate the ubiquity of
patterns in abundance. Finally, in Chapter V, I evaluate environmental characteristics
associated with each community to determine if the degree to which patterns are
nonrandom is dependent on climatic variables. Specifically, I evaluate whether
gradients exist regarding bat community structure.
Methodological Considerations
Although ecological communities can be defined operationally, they are often
nebulous entities. The boundaries of some communities (e.g., pond-fish community,
herbivores on bracken fern) strongly correspond to physical boundaries (Schluter and
Ricklefs, 1993). However, this may only be true for taxonomically defined
communities representing less mobile organisms. Bats are highly vagile and two or
more plant communities may be traversed within a night's foraging by some species
(Willig and Mares, 1989). As a result, bats may perceive different plant associations
as habitat patches. Discretion must be used to ensure that an appropriate area, large
enough to comprise all interacting species that co-occur, is sampled when evaluating
bat community structure. Conversely, sampling from too great an area may include
species from more than one community, leading to the inclusion of information on
species that have no potential to interact. Special care must be taken when selecting
the areal extent from which to sample communities.
5
In the ensuing investigation, several criteria were utilized to select bat
communities. Data collection must have been from more than one particular locality
(e.g., stock tank, specific trail), but the area that comprises samphng localities must
be limited so that information likely was from a single bat community. This criterion
was fairly subjective. Finally, sampling must have been conducted on a regular basis,
in all seasons during which bats were active, for at least one year. This minimizes the
possibility of missing rare species, and increases the accuracy of relative abundances.
Feeding guilds also can be defined operationally and, like ecological
communities, may be methodologically nebulous. Feeding guilds represent
taxonomic subsets of the community that consume similar resources in similar ways
and, consequentiy, are most likely to compete (Root, 1967). When addressing the
importance of competition in structuring communities, examination of groups of
species with little potential to compete will bias conclusions. Thus, communities
should be decomposed into feeding guilds (Bonaccorso, 1975; Findley, 1993, Willig
1982; Willig and Moulton, 1989). I decomposed each community into seven feeding
guilds (see Appendix B for a description of each): (1) aerial insectivore, (2)
frugivore, (3) gleaning animalivore, (4) molossid insectivore, (5) nectarivore, (6)
piscivore, and (7) sanguinivore (see Appendix B). A species was assigned to a
feeding guild based upon food items that composed the bulk of its diet (e.g., blood,
fish, fruit, animal, nectar). For example, the diet of Artibeus jamaicensis. in most
places, is primarily fruit. Although this species sometimes consumes nectar and
insects, it would be placed in the frugivore guild. Additionally, insectivores were
categorized into one of three guilds based on where and how they foraged.
Other classifications have been suggested to categorize bat communities into
feeding guilds. Bonaccorso (1975) suggested categorizing frugivores into canopy and
sub-canopy frugivores. However, included in the spatiotemporal spectrum of
6
communities that I evaluated are more than one community that lacks a distinction
between canopy and sub-canopy, yet those species believed to be canopy specialists
(stenodermatines) and those believed to sub-canopy specialists (caroliines) coexist.
Canopy and sub-canopy frugivores may be valid designations; however, to make
comparisons of frugivores across all locations where they exist, a more general
designation was necessary. In this investigation, all bats that consumed fruit as the
major component of their diet were included in the frugivore feeding guild.
Moreover, it is commonplace to distinguish gleaning insectivores and gleaning
carnivores. In this study, both of these groups were combined as gleaning
animalivores. There is insufficient evidence to suggest that carnivores exhibit
camivory through all seasons of the year (Willig et al., 1993). Moreover, in many
places, bats that would be designated as carnivores exhibit omnivory (Willig et al.,
1993). Thus, my operational definition of a gleaning animalivore is any species that
consumes principally animals (whether they be vertebrates or invertebrates) that are
gleaned from surfaces. Information on dietary composition of species was obtained
either directly from documents describing the bat community or from other literature
sources.
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Willig, M. R., G. R. Camilo, and S. J. Noble. 1993. Dietary overlap in frugivorous and insectivorous bats from Edaphic Cerrado habitats of Brazil. Journal of Mammalogy 74: 117-128.
Wilson, J. W., m . 1974. Analytical zoogeography of North American mammals. Evolution 28: 124-140.
Zeveloff, S. I., and M. S. Boyce. 1988. Body size patterns in North American mammal faunas. Pages 123-146 in: M. S. Boyce, Editor. Evolution of life histories of mammals: theory and pattern. Yale University Press, New Haven, Connecticut.
11
CHAPTER n
THE RELATIONSHIP BETWEEN ABUNDANCE AND MORPHOLOGICAL
DISSIMILARITY: A MODEL OF COMMUNITY STRUCTURE
Abstract
The role of interspecific competition in structuring communities has been a
highly debated issue for the last two decades. The deterministic nature of
morphological patterns within communities has been at the center of this debate. Null
models, designed as a more rigorous statistical means to evaluate the effects of
competition on the morphology of coexisting species, have failed to provide adequate
resolution. Furthermore, null models addressing community-wide dispersions in
morphology may be based on too restrictive assumptions (e.g., competitive
exclusion), and consequently, lack power to detect deterministic structure in many
communities. Other manifestations of the effects of competition on community
structure should be explored. Morphological uniqueness may allow species to escape
intense competitive pressure and exhibit increased densities. Thus, a positive
relationship should exist between the relative morphological dissimilarity of species
and their abundances. Species may not uniformly impose competitive effects on all
others within a feeding guild, however. Different competitive scenarios that consider
subsets of species in feeding guilds that potentially experience more intense
interactions should be evaluated specifically. Herein, I introduce a suite of models
that evaluate patterns in abundance from a diversity of morphological perspectives
Moreover, I apply these analyses to an ecological community (nocturnal desert
rodents) for which the effects of competition on community structure are well
established. Simulation analyses indicate that these models are powerful enough to
detect nonrandom patterns in abundance at the feeding guild level. Moreover, these
12
models reveal deterministic abundance patterns from all morphological perspectives.
These models are powerful tools to explore factors influencing the role of competition
in community structure.
Introduction
A considerable amount of theory and empirical evidence exists regarding the
role of interspecific competition in the structure of natural communities (Cody and
Diamond, 1975; Diamond and Case, 1986; Kikkawa and Anderson, 1986; Strong et
al., 1984). Nonetheless, competition remains one of the most controversial issues in
ecology. Patterns in the morphology of co-occurring species have been a popular
means to examine competitive interactions and, ultimately, community organization
(Bowers and Brown, 1982; Brown and Bowers, 1985; Case et al., 1983; Dayan and
Simberioff, 1994; Diamond and Case, 1986; Mares, 1976; Moulton, 1985; Moulton
and Pimm, 1983, 1986a, 1986b, 1987; Schoener, 1984; Willig, 1982, 1986; Willig
and Moulton, 1989). An important assumption of this approach, consistent with
competition theory, is that the consumption of food resources is dependent on
morphology. Moreover, substantial evidence indicates that this assumption is
generally true (Bonaccorso, 1975; Brown and Lieberman, 1973; Dayan and
Simberioff, 1994; Findley and Black, 1983; Findley and Wilson, 1982; Freeman,
1979, 1984, 1988; Hespenheide, 1973; Smartt, 1978). If the morphologies of two or
more species are not sufficiently distinct, the resources that they consume likely will
be similar, and interspecific competition will ensue. With enough time and intensity,
competitive interactions should manifest as character displacement or competitive
exclusion (Brown and Wilson, 1956; Case and Sidell, 1983; Gause, 1934; Hardin,
1960). Ultimately, competition should give rise to a hyperdispersion of morphologies
within ecological communities.
13
Prior to the 1980s, demonstration of hyperdispersed morphologies implied
competitively-induced community structure (see Simberloff and Boeklen, 1981).
However, null models have demonstrated boldly that many of the patterns in
morphology originally believed to be the result of interspecific competition can be
generated by chance (Connor and Simberioff, 1979; Grant and Schluter, 1984;
Ricklefs and Travis, 1980; Strong et al., 1979). As a result, equivocal evidence exists
regarding the nature of morphological patterns within communities. Moreover,
competitively induced community structure, based on contemporary interpretations, is
not as common as once believed (Strong et al., 1979). Subsequently, many have
abandoned the notion that competition theory provides substantial insight into
understanding the structure of natural communities (Strong et al., 1984).
As much as null models have engendered critical and rigorous hypothesis
testing, they too have failed to provide incontrovertible evidence concerning the
importance of competition in structuring natural communities. These models make
two implicit assumptions that may limit their power: (1) interactions between nearest
neighbors structure communities, and (2) those interactions must lead to
morphological hyperdispersions to evince deterministic structure. To structure
communities, competition need not affect the dispersion of morphologies through
character displacement or competitive exclusion. Competitive interactions may affect
relationships between abundance and morphological similarity among species;
current null models, based on morphology alone, are incapable of addressing this
possibility.
Nonetheless, species experiencing more competitive pressure should exhibit
lower abundance and this may be another means to evaluate deterministic structure
(Lotka, 1932; Volterra, 1926). If morphological similarity is a viable surrogate for
ecological similarity, then those species that are morphologically dissimilar from
14
other species in the community should experience the least competitive pressure and
exhibit the highest abundance. Thus, a positive relationship should exist between the
morphological distance of a species with respect to potential competitors and
abundance; the strength of this relationship should be greater than that produced by
stochastic processes.
Ecological communities are often complex entities including hundreds, if not
thousands of species (Simberloff and Dayan, 1991). Furthermore, communities
comprise species from different feeding guilds (sensu Root, 1967) and trophic levels.
As a result, competitive interactions should not be expected to exist among all species
within a conmiunity; competitive interactions should be most important within a
trophic level, and especially within a feeding guild. Hence, the best place to begin
examining the manifestations of competitive interactions within communities, should
be within feeding guilds. Herein, I develop a suite of models, based on the
ecomorphological relationships of species, that is designed to detect nonrandom
patterns of abundance within feeding guilds.
The Model
My analyses are predicated on two assumptions. First, measures of
morphological dissimilarity within a guild are suitable surrogates for ecological
dissimilarity. Second, a species with high ecomorphological similarity to one or more
potential competitors should suffer reduced density as a result of interspecific
competition. As a consequence of such competitive effects, a quantitative
relationship should exist between the position of a species in ecomorphological space
and its density within a guild (Fig. 2.1).
I performed simulation analyses to determine if associations between
morphological dissimilarity and abundance within feeding guilds are non-random.
15
Morphological distances among species were calculated based on a Euclidean
distance. I used Pearson product-moment and Spearman rank correlation coefficients
to describe the magnitude of the association between abundance and morphological
distance. Traditional tests determining significance assume that data follow a
specified distribution. For example, hypotheses tests for both Pearson
product-moment and Spearman rank correlation analyses assume that random variates
follow a t-distribution (Sokal and Rohlf, 1995). If variates from the actual data do not
follow this distribution, traditional hypothesis tests may be inaccurate (Noreen, 1989).
Simulation analyses, however, are not subject to these biases. By randomizing the
actual data to yield a distribution to which the observed statistics are compared, such
assumptions are not necessary, and violations of assumptions cannot jeopardize the
accuracy of hypothesis tests (Noreen, 1989).
To evaluate deterministic structure, I compared correlation coefficients from
actual guilds to those of simulated guilds. While preserving the integrity of the
morphological relationships among species, random abundances were assigned to
each species, thereby yielding the structure of a simulated guild. A correlation
coefficient was then calculated between randomized abundances and actual
morphological distances of members within the simulated guild. One thousand
iterations of this process yielded a probability density function for subsequent
hypothesis tests. The correlation coefficient from the actual guild was compared to
the probability density function of simulated correlation coefficients. If the
coefficient for the actual guild occurred within the upper ten percent of the
distribution (p < 0.10), I concluded a non-random association between morphology
and abundance in the actual guild (Fig. 2.2).
Many factors influence the abundance of individual species (Andrewartha and
Birch, 1954, 1988; Begon et al., 1990). As such, strong positive correlations between
16
morphological distance and abundance caused by competition may be obscured by
autecological or other synecological processes (e.g., predation, mutualism).
Consequently, caution should be used to prevent falsely rejecting competition as an
important influence on community structure. To minimize the possibility of such a
Type I statistical error (rejecting a positive correlation between morphological
distance and abundance when it actually exists), I established the alpha level at p <
0.10 as the level of significance.
Competitive Scenarios
Community structure can be produced via a spectrum of possible interspecific
interactions, ranging from pairwise effects, to those based on all possible interactions
among guild members. Ecomorphological dissimilarity can be measured from a
variety of perspectives as well, corresponding to the spectrum of ways in which
competitive effects are manifest in a community. In general, if diffuse competition is
important in structuring communities, then the morphological distance of each species
to all others in a feeding guild primarily determines the density of each species. In
contrast, if interaction between a species and its nearest neighbors is the primary
factor acting on community structure, then the density of a species should be most
affected by its ecomorphological distance to its two nearest neighbors. I evaluated
three competitive scenarios along the spectrum of possibilities (Fig. 2.3). In the first,
the abundance of a given species is the product of its morphological relationships
with all other (n-1) species in the feeding guild. The Euclidean distance (Dt) for each
species represents the ecomorphological (Findley, 1976; Findley and Wilson, 1982;
Mares, 1976) distance of a species with respect to all other (n-1) guild members:
17
n-1 m
Dt=l(E(X,-x,)^)"''. < 2 " i=i j=i
where: n is the number of species; m is the number of morphological characters; Xij
represents morphological character j of species i; Xtj represents morphological
character j of species t.
In the second, interactions between a focal species and its most
morphologically distinct neighbor may be so weak as to have no effect on abundance.
Therefore, simulations were conducted in which the Euclidean distance included all
species in the feeding guild except the most morphologically different neighbor (n-2
of the species in the feeding guild):
n-2 m
Dt=I(I(X,rX,)^r. (2.2) i=l j=i
In the third, the abundance of species is not the product of diffuse
competition; the abundance of each species is the product of interactions with its two
nearest morphological neighbors. Thus, two nearest neighbors of a focal species were
the only members of the feeding guild included in calculations of ecomorphological
distance:
Dt=t(i(X,rX,/)'". (") i=l j=i
18
The Community
I evaluated the validity of this model using a rodent community from the
Sonoran Desert east of Tucson, Arizona. This community was selected based on a
variety of criteria. First, although communities have explicit textbook definitions,
they are often methodologically difficult to circumscribe. I chose this rodent
community because the sampled area was a well-defined system (creosote flat) that
contained all microhabitats necessary for the focal group of species (nocturnal desert
granivores). Second, considerable effort must be spent to ensure accurate relative
abundances. Brown's (1989) bi-monthly census protocol was conducted for two
years and suitably meets this criterion. Third, it was desirable to assess if this model
could detect patterns in abundance in a community whose organization has been
demonstrated to be mediated by interspecific competition (Brown, 1989).
Only one feeding guild from this community was evaluated (Table 2.1). It
included Dipodomys merriami. Perognathus amplus. Mus musculus. Peromyscus
maniculatus. P. eremicus. P. merriami. Chaetodipus penicillatus, and C. baileyi. and
represented nocturnal granivores. Spermophilus tereticaudus. Ammospermophilus
harisii. Neotoma albigula. Sigmodon arizonae. and Onychomys torridus were
excluded because they are either diurnal or the composition of their diet differs
greatly enough for them to be considered members of other distinct feeding guilds.
I utilized a suite of cranial and body characteristics to estimate the position of
each species in ecomorphological space. These included length of body, length of
foot, length of ear, greatest length of skull, greatest width of skull, length of maxillary
toothrow, and interorbital width. Morphological measurements were obtained for at
least four males and four females of each species from Hoffmeister (1986) or from
specimens deposited in The Museum, Texas Tech University.
19
Results
Relative abundance and ecomorphological distance of species in the nocturnal
granivore guild are variable, spanning almost two orders of magnitude for relative
density and approximately five-fold for morphology (Table 2.1). Simulation analyses
indicated a nonrandom, positive relationship between ecomorphological distances of
species and abundance (Fig. 2.4). Species that were more ecomorphologically
distinct from other guild members exhibited higher abundances. Moreover, this
pattern was detected under all three competitive scenarios. The relationship was
strongest for the analysis based on diffuse competition and weakest when each
species most distant neighbor was not considered in calculation of ecomorphological
distance.
Discussion
Previous research and analyses have documented that the Sonoran nocturnal
granivore guild is structured by competition (Brown, 1989). My model was
sufficiently powerful to corroborate these results and detect competitive effects for
each of three morphological scenarios. Consequently, it holds promise as a
quantitative tool for detecting competitive effects that do not manifest as
morphological hyperdispersions at the community level.
Including patterns of abundance in the evaluation of community structure has
definite advantages. The detection of deterministic structure does not necessitate
competitive exclusion or character displacement. Moreover, this approach need not
assume that populations or communities are at equilibrium. Competitive interactions
are believed to be strongest when environments approach saturation and constituent
species are at carrying capacity (Adrewartha and Birch, 1954, 1988; Chesson, 1988;
Lotka, 1932; Volterra, 1926). Thus, predictable environments that persist for long
20
periods of time should be the arena in which hyperdispersions in morphology
manifest. Of course these circumstances may not characterize many systems. A
variety of environmental perturbations or disturbances prevent populations from
reaching equilibrium (Adrewartha and Birch, 1954, 1984; Sale, 1977; Simberioff,
1984). Moreover, research on invertebrate communities has caused many ecologists
to question the existence of environmental equilibria (Resh et al., 1988; Power et al.,
1988). If communities are not at equilibrium, morphologically similar species may
still coexist in the absence of strong biotic interactions, rendering the interpretation of
hyperdispersions in morphology difficult. As long as species are not at such a state of
disequilibrium that no density-dependent effects occur, the effects of competitive
interactions can be assessed if one evaluates abundance.
A considerable amount of information is lost when investigators ignore
abundance and focus only on morphology. Many times, species are only seasonal
residents in communities when resource levels are high (Bonnaccorso, 1975). When
resources become scarce, competition becomes more intense and these species are
unable to persist. When addressing morphological dispersions, seasonal residents can
either be included in analyses and given the same status as full-time residents, or
excluded because of their transient nature. Although these species are seasonal
members of the community, they should still be considered community members, but
with different status. Contemporary null models addressing hyperdispersions in
morphology lack the flexibility to give unequal weight to different species. If
abundance data reflect year-long sampling (summed across sampling periods),
seasonal species likely will exhibit lower abundances than year-round residents, thus
demonstrating their inability to coexist through aU seasons of the year.
Similarly, it is commonplace to exclude rare species from analyses. If species
are abundant because of a lack of competitive pressure (Lotica, 1932; Volterra, 1926),
21
then studies concentrating only on common species may be unable to detect structure
that is the consequence of deterministic processes. As this model demonstrates, rare
species provide considerable information regarding community structure; their
omission from studies may contribute to an inability to detect nonrandom patterns,
and thus, obscure the effects of competition on community structure.
Models addressing abundance evaluate current competitive interactions and
are not complicated by historical and biogeographic effects. Simply demonstrating
that morphologies are hyperdispersed within communities is not enough to invoke
competition. Seemingly deterministic patterns in morphology could result from
random assembly (Simberloff and Boeklen, 1981). If historical phenomena have
affected the distribution of morphologies within faunal pools, then the random
assembly of species into communities may recapitulate a nonrandom distribution of
morphologies within those communities. Models addressing morphology alone must
take into account the distribution of morphologies from source species pools.
However, determination of appropriate faunal pools often represents a considerable
methodological problem (Colwell and Winkler, 1984; Graves and Gotelli, 1983;
Willig and Moulton, 1989).
Several guidelines should be followed to ensure the determination of not only
more accurate abundances, but also community structure. The proper scale should be
selected to ensure that, in actuality, a single and entire unit community is being
sampled. If unit communities are not sampled, considerable potential exists for
measures of abundance to be biased in either of two ways. First, by sampling a
regional fauna, abundance data for a species will be combined across more than one
community, possibly distorting the relationship between abundance and morphology
in any one of the real communities. Second, by sampling only microhabitats, the
actual abundances of species within the community will be misrepresented and
22
critical community members may be excluded, thereby distorting morphological
components of the model.
Scale has substantial implications at many levels of biological organization
(Allen and Starr, 1982; Eldridge, 1985; Levin, 1992; Minshall, 1988), and
communities are no exception. Although communities are easily defined in theory,
they are often nebulous entities from a methodological perspective. For example,
rodent community may not encompass the same aerial extent as a raptor community.
Raptors may perceive individual rodent communities as microhabitats or patches
which differ in resource quality and quantity. Consequentiy, each group should be
sampled at the level appropriate for the constituent taxon, and arbitrary boundaries
should be avoided. The area encompassed by community sampling units should be
fairly uniform, yet possess all of the microhabitats necessary for persistence of
community members. For example, many desert ecosystems can be characterized by
canyons, desert flats, riparian areas, and mountains. Within each of these exist places
under vegetation, places in rock crevices, and places in open areas used by small
mammals. It would be inappropriate to characterize the community only in open
microhabitats. Species that predominate under bushes and crevices possess the ability
to interact with species with open microhabitat affinities, and their exclusion would
bias conclusions. By the same token, it would be inappropriate to combine data
collected from both the riparian area and the desert flat to describe community
structure because species that have little potential for interaction will be included in
this sample. Errors such as these deleteriosly affect the ability of any methodology to
assess the relationship between abundance and morphology.
Measures of abundance should be the product of intensive, long-term
sampling. If species that are morphologically similar to other guild members are
more rare in communities, their membership may go undetected by incomplete
23
sampling. Preston (1948, 1962) demonstrated a general species-area curve whereby
the number of species asymptotically increases as one increases the size of samples.
Rare species contribute to this phenomenon. Moreover, the species area relationship
can be generalized to a species-effort curve or collector's curve (Arata and Vaughn,
1970; Coleman et al., 1982; Thomas, 1972). If sufficient effort (number of traps,
number of nights, etc.) is not expended to sufficiently sample a community, the
potential for poor estimates of the abundance of species or even the failure to detect
rare species is great.
Even if accurate relative or absolute measures of abundance are suspect, this
model allows analyses based on ranks. In analyses of the nocturnal granivore guild,
the Pearson product moment correlation coefficient (PPMCC) was consistently higher
than the Spearman rank correlation coefficient (SRCC), indicating that information is
lost by using a rank correlation coefficient when relationships are linear and
abundances are accurate estimates. Despite this loss of information, SRCC and the
PPMCC yielded similar results when utilized in simulation analyses and significance
tests. Under all three competitive scenarios, the actual correlation coefficient was of
greater magnitude than the vast majority of simulated correlation coefficients.
However, SRCC did lack the power to demonstrate clear significance under the N-2
competitive scenario.
Parametric correlation coefficients are more powerful at detecting linear
associations than are those based on ranks (Sokal and Rohlf, 1995); however,
parametric coefficients require absolute or relative measures of each variable. For
many organisms, the absolute or relative abundance of species within guilds is not
easily or accurately ascertained, rendering the efficacy of such analyses questionable.
Nonetheless, if one is capable of accurately assigning rank abundance to each species
in a guild, evaluation of deterministic guild structure based on rank-analyses is
24
possible, with little reduction in power. Hence, this methodology may have broad
applicability to a diversity of plant or animal communities.
This model has great potential as a means to make comparisons among
communities. If competition is unimportant in the structure of communities, species
abundances will be the product of other phenomena, and thus, species should not
exhibit a strong positive relationship between ecomorphological distance and
abundance. Deterministic structure is operationally defined by the probability of
obtaining the observed pattern by chance (p-value). Thus, deterministic community
structure can range from a probability of 0 (highly unexpected by chance) to 1 (highly
expected by chance). There is considerable consensus that competition is not
important in all communities under all circumstances (Begon et al., 1990; Cody and
Diamond, 1975; Diamond and Case, 1986; Kikkawa and Anderson, 1986; Polls,
1991; Strong et al., 1984, for reviews). If variation in the degree to which
competition structures communities exists, comparisons based on p-values can be
made. If other extrinsic factors influence the degree to which competition is
important, p-values describing the degree of deterministic structure should be a
function of extrinsic factors. If the circumstances under which competition is
important in community structure are to be truly understood, similar analyses should
be applied to a diversity of communities (see Chapter IV).
25
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Simberloff, D. 1984. Properties of coexisting bird species in two archipelagoes. Pages 234-253 in: Strong, D. R., D. Simberioff, L. G. Abele, and A. B. Thistle, Editors. Ecological communities: conceptual issues and the evidence. Princeton University Press, Princeton, New Jersey.
Simberloff, D., and W. Boeklen. 1981. Santa Rosalia revisited: size ratios. Evolution 35: 1206-1228.
Simberloff, D., and Y. Dayan. 1991. The guild concept and the structure of ecological communities. Annual Review of Ecology and Systematics 22: 115-143.
Smartt, R. A. 1978. A comparison of ecological and morphological overlap in a Peromyscus community. Ecology 59: 216-220.
Sokal, R. R., and F. J. Rohlf 1995. Biometry. W. H. Freeman and Company, New ' York.
Strong, D. R., D. Simberioff, L. G. Abele, and A. B. Thistle, Editors. 1984. Ecological communities: conceptual issues and the evidence. Princeton University Press, Princeton, New Jersey.
29
^.
Strong, D. R., L. A. Szyska, and D. S. Simberioff 1979. Tests of community-wide character displacement against null hypotheses. Evolution 33: 897-913.
Thomas, M. E. 1972. Preliminary study of the annual breeding patterns and population fluctuations of bats in three ecologically distinct habitats in southwestern Colombia. Dissertation. Tulane University, New Orleans, Louisiana.
Volterra, V. 1926. Variations in fluctuations of the numbers of individuals in animal species living together. Reprinted in 1931. in: R. N. Chapman, Editor. Animal Ecology. McGraw Hill, New York.
Willig, M. R. 1982. A comparative ecological study of Caatingas and Cerrado chiropteran communities: composition, structure, morphometries, and reproduction. Dissertation. University of Pittsburgh, Pittsburgh, Pennsylvania.
Willig, M. R. 1986. Bat community structure in South America: a tenacious chimera. Revista Chilena de Historia Natural 59: 151-168.
Willig, M. R., and M. P. Moulton. 1989. The role of stochastic and deterministic processes in structuring Neotropical bat communities. Journal of Mammalogy 70: 323-329.
30
Table 2.1.-- Structure of the nocturnal granivore feeding guild from the Sonoran Desert (after Brown, 1989). n-1, n-2, and 2 correspond to three competitive scenarios used in calculations of morphological distance, n-1 indicates all other species in the feeding guild (diffuse competition), n-2 indicates all others except the most distant morphological neighbor, and 2 indicates only two nearest morphological neighbors.
Relative Morphological Distance Species abundance n-1 n-2 2
Dipodomys merriami 71.80 4.26 3.53 0.89
Perognathus amplus 26.96 3.04 2.36 0.51
Mus musculus 0.57 2.47 1.74 0.29
Peromyscus maniculatus 0.29 2.27 1.62 0.23
Peromyscus eremicus 0.10 2.32 1.66 0.20
Peromyscus merriami 0.10 2.44 1.93 0.34
Chaetodipus penicillatus 0.10 2.64 2.17 0.48
Chaetodipus baileyi 0.10 2.64 2.00 0.27
31
\
MORPHOLOGICAL ATTRIBUTE 1
Figure 2.1.~ Theoretical expectations of the relationship between morphological distance and abundance. The sum of the lengths of the bars emanating from a sphere (species) represents the morphological distance of a focal species with respect to all other competitors in the guild. The size of a sphere represents the abundance of the focal species with respect to all other competitors in the guild. If competition is important in structuring guilds, then the larger the sum of the morphological distances, the larger the sphere representing relative abundance.
32
Fig. 2.2.~ Graphical representation of the distribution of r-values generated by chance (Ho) and the location of the rejection region dictated by the alternate hypothesis of deterministic structure. The curve represents the frequency distribution of correlation coefficients between morphological distances of species and random abundances. If the correlation coefficient between observed morphological distances of species and their relative abundances (dot) is > 90% of the randomly obtained correlation coefficients (as in the example), the observed guild is structured by deterministic processes.
33
\
Figure 2.3.-- Three competitive scenarios based on considerations of morphology and abundance. In the first scenario (above), the abundance of the focal species (square) is a function of its relationships with all of its neighbors (dots); Euchdean distances include all species in the feeding guild (N-1). In the second scenario (middle), the morphological relationship between the focal species and its most distant neighbor has no influence on the abundance of the focal species; all but each species' most morphologically distant neighbor are included in the calculation of Euchdean distance (N-2). In the third scenario (bottoni), only the two nearest neighbors influence the abundance of the focal species and only those species are included m the calculation of Euclidean distance (2).
34
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36
CHAPTER m
COMMUNITIES, INTERACTIONS, AND COMPETITIVE EXCLUSION:
A SYNOPTIC EVALUATION OF SIZE ASSORTMENT
Abstract
For at least a quarter of a century, community ecologists have grappled over
which factors are responsible for the structure of communities. Most endeavors
consider a single community and likely provide littie information regarding the process
of community organization in a heterogeneous world. Before generalizations regarding
the importance of phenomena on community organization are cast, the degree of
ubiquity of those phenomena across a gradient of locations must be determined.
Herein, I evaluate the ubiquity of competitively induced morphological overdispersion
in five feeding guilds from each of 15 bat communities from North, Central, and South
America. Overdispersion is detectable at ten of fifteen locations, and in four of five
feeding guilds. Although overdispersed morphological patterns do not exist in all
situations, competitive interactions should not be considered unimportant.
Morphological overdispersion is not the only way competitive interactions manifest at
the community level, and the ubiquity of other consequences should be explored.
Introduction
The search for urefutable, pervasive patterns that identify factors responsible
for the structure of communities has been in the mainstream of ecology for over a
quarter of a century. As a result, many processes such as competition, disturbance,
predation, and mutualism, to name only a few, are disputed as the factor responsible
for the composition of communities (see Cody and Diamond, 1975; Diamond and
Case, 1986; Gee and Giller, 1987; Kikkawa and Anderson, 1986; Polls, 1991;
Ricklefs and Schluter, 1993; Strong et al., 1984; for extensive reviews). Nonetheless, 37
equivocal evidence corroborating most, if not all, of these phenomena seems to be the
only pervasive result. Because no two communities are alike, single community
studies offer littie insight into teasing apart the most important influence from the grab-
bag of possibilities. The world is characterized by substantial temporal and spatial
heterogeneity (Brown, 1992). Moreover, environmental gradients mediate the degree
to which at least some of these phenomena operate (Andrewartha and Birch, 1954,
1988; Chesson, 1988). Lastly, co-occurring feeding guilds and trophic levels provide
additional ecological complexity (Bonaccorso, 1975; Findley, 1993; Simberloff and
Dayan, 1991; Willig, 1982; Willig and Moulton, 1989). Studies of a single community
offer no means of accounting for such heterogeneity. However, community ecologists
have been impulsive in discounting the importance of various phenomena based on data
from a paucity of communities. It would not seem surprising that the environmental
context of a feeding guild, trophic level, or ultimately community, has bearing on the
importance of phenomena that affect structure. Comprehensive, comparative studies at
many geographic locaUties that represent a variety of cUmatic and abiotic conditions
must be conducted before the influence of any factor on community structure can be
ascertained with confidence.
Morphological attributes are informative metrics for inferring the relationships
of species at the community level (Wainright and Reilly, 1994; and citations therein).
They correlate well with ecological characteristics and have been demonstrated to be
good predictors of resource utilization (Bonaccorso, 1975; Brown and Lieberman,
1973; Dayan and Simberloff, 1994; Findley and Black, 1983; Findley and Wilson,
1982; Freeman, 1981, 1984, 1988, 1992; Hespenheide, 1973; Smartt, 1978).
Consequentiy, morphologically similar species should compete more intensely than do
dissimilar ones. Hyperdispersions along resource axes can result from competitive
interactions among coexisting species in the form of character displacement or
38
competitive exclusion, and result in hyperdispersions along morphological axes
(Hutchinson, 1959; MacArthur and Levins, 1967).
Although morphological hyperdispersion is commonplace under a variety of
environmental conditions (see Simberloff and Boeklen, 1981), a comprehensive
account of the ubiquity of hyperdispersion has never been conducted within a particular
taxon. Herein, I evaluate morphological pattems within bat communities throughout
the New World and explore if hyperdispersion is ubiquitous. I address two questions:
(1) does morphological structure, consistent with competition theory, exist within bat
feeding guilds and communities, and (2) are the effects of competitive interactions
pervasive within bat communities throughout the New World?
Methods
I evaluated 15 bat communities from throughout North, South, and Central
America (Appendix A). Several criteria limited the number of communities included in
analyses. First, data must have been the product of regular sampling in all seasons that
bats were active. Second, sampling must have been at least one year in duration.
Tlurd, sampling must have been conducted in a well-delimited local area that
represented an actual community of species that, because of spatial proximity, had the
potential to interact. Faunas of geopohtically bounded areas were not acceptable
because it was difficult to be reasonably sure that only one community was sampled.
Feeding Guilds. Each community was categorized into seven feeding guilds
(sensu Root, 1967): aerial insectivores, frugivores, gleaning animalivores, molossid
insectivores, nectarivores, piscivores, and sanguinivores (see Appendix B for
definitions). The rigid, yet general, nature of this classification enables comparisons
from wide ranging spatial and habitat conditions. Guild associations were based on
designations published in the actual account of the community or on other published
information (Gardner, 1977; Wilson, 1975). 39
Sanguinivores and piscivores were omitted from analyses. At most, real
communities contained one piscivore, rendering detection of a hyperdispersion in
morphology impossible. Moreover, the species pool of sanguinivores could at most
include three (all extant members of the Desmodontinae), and consequentiy no selection
of species, no matter how deterministic, could be shown to be a rare occurrence (Willig
and Moulton, 1989). If a feeding guild at a particular site did not contain at least three
species, it was omitted from analyses.
Morphological Structure. I followed Koopman (1993) for a comprehensive list
of extant New World bats. Seven attributes were utiUzed to ecomorphologically
characterize each species. These include forearm length, greatest length of skull,
condylobasal length, width across the postorbital constriction, breadth of the braincase,
length of the maxillary toothrow, and breadth across the upper molars (see Appendix C
for definitions). Measurements were obtained from Swanepoel and Genoways (1979)
for most phyllostomids, and from museum specimens for others. In most cases, eight
individuals, 4 males and 4 females, contributed to the mean of each character.
Common logarithms of each character were utilized in analyses following
Ricklefs and Travis (1980). Log transformations enhance normality and equalize
variances (Sokal and Rohlf, 1995). Moreover, they minimize the possibility that
differences in larger characters may disguise ecologically meaningful differences in
smaller attributes. Finally, they minimize the distortion of multivariable space when
standardized for data reducing techniques (Ricklefs and Miles, 1994; Ricklefs and
Travis 1980).
Morphological relationships of species were determined for each guild
separately, as suggested by Moulton and Pimm (1986,1987) and Willig and Moulton
(1989), using Principal Components Analyses (PCA) (SAS program PRINCOMP;
Ray, 1982). This technique maintains the morphological relationships among species
by constructing a linear combination of original variables that eUminates redundancy of 40
• \
highly correlated characters. Consequentiy, the number of dimensions necessary to
illustrate relationships is less than the original number of characters (Ricklefs and
Miles, 1994; Ricklefs and Travis, 1980). Via extraction from a covariance matrix, two
principal components characterized relationships among species. Minimum spanning
trees were then calculated to determine the distance of species in two dimensions
(principal components 1 and 2). Minimum spanning trees choose the shortest N-1 line
segments to connect N species (Fig. 3.1). Thus, the length of the minimum spanning
tree reflects the magnitude of interspecific morphological differences. Two descriptive
statistics (mean and variance) were then calculated for minimum spanning tree segment
lengths.
K competition prevents morphologically similar species from coexisting within
communities, overdispersions in morphology should be evinced in one of two ways:
(1) mean segment lengths of actual minimum spanning trees should be greater than
would be expected due to chance, or (2) the variance of minimum spanning tree
segment lengths should be smaller than would be expected due to chance (Moulton and
Pimm, 1986; Willig and Moulton, 1989).
Species Pools. The demonstration of large means and small variances of
minimum spanning tree segment lengths is insufficient to invoke competition. Many
artifacts can give rise to large means and small variances. If some aspect of the history
of a particular taxon created a particular pattern in morphology within a fauna, then the
random assembly of species into a community may recapitulate that pattem. Moreover,
if the community contains morphologically sunilar species, small variance components
may not be unusual. Lastiy, a large mean describing minimum spanning tree segment
lengths may simply be the consequence of an extreme morphological outiier. For these
reasons, species pools representing faunal groups from which communities are
assembled must be utilized in analyses; comparing actual communities must be
compared to those assembled at random from a faunal pool. Simulation provides the 41
basis for an unbiased assessment of guild characteristics. Although the means or
variances of MST segment lengths may be nocuously influenced by morphological
extremes (such as outliers or sets of similar species), these species also are included in
faunal pools. As a result, outiiers should be selected often enough in the assembly of
random communities that hyperdispersions resulting from outiiers will not be unusual.
Thus, the relative magnitude of a certain statistic, as compared to a distribution created
randomly, becomes a more salient point of comparison.
Morphological pattems from each guild were compared to those randomly
drawn from each of seven faunal pools. Species were included in analyses if their
geographic distributions occurred within a particular faunal pool. Distribution maps for
bat species were prepared using Hall (1981) for North and Central America, and
Koopman (1982), Eisenberg (1989), and Redford and Eisenberg (1992) for South
America. The bounds of five of these pools were represented by concentric rings that
equaled 500, 1000, 2000,4000, and 8000 kilometers in diameter (Fig. 3.2). The first
pool represented only those species whose distribution overlapped the actual
community and the last pool represented all those of the New World. For each pool,
randomly drawn guilds were assembled using the algorithm of Moulton (1985),
Moulton and Pimm (1987), and Willig and Moulton (1989). If N species occur in an
actual guild and S is the number of species in a species pool from which random guilds
are drawn, then the number of different guild combinations (C) is given by
S!/{N!(S-N)!}. (3.1)
The number of possible combinations was often large. When C was > 500,1 randomly
selected 500 combinations to calculate random guild statistics. When C was < 500,1
utilized each combination only once to minimize redundancy. As a result, hypothesis
tests for these situations were based on sample sizes that were less than 500. Both sets
of descriptive statistics from randomly assembled guilds form distributions under the
null hypothesis (random guild assembly) to which descriptive statistics from the actual 42
feeding guild can be compared. If the mean segment length from an actual guild was
greater than 90 percent of the simulated values, or the variance of die spanning tree
lengths was smaller than 90 percent of the simulated values, I concluded that
nonrandom morphological combinations existed in the actual guild (Figs. 3.3 and 3.4).
Results
Principal Components Analyses. Results of the five principal components
analyses were similar (Table 3.1). Eigenvalues for the first and second principal
components ranged from 0.022 - 0.073 and 0.003 - 0.005, respectively. Percent
variation accounted for by the fu-st and second principal components ranged from 76.8
- 89.2 and 5.9 - 16.4, respectively. Factor loadings from each of the five covariance
matrices appear in Table 3.2.
Analyses were based on the same suite of morphological characters for all
feeding guilds. In all cases, principal components analyses reduced the seven
morphological characters into two components. Nonetheless, the possibility exists that
the contributions of each character to each principal component may be different
depending on feeding guild. I determined the Pearson product-moment correlation
coefficient between principal components and each of the morphological characters
within each feeding guild (Table 3.3). All characters, regardless of feeding guild, were
positively and significantly correlated with the fu-st principal component; it is hkely a
measure of overall size. With the exception of width across the post-orbital
constriction, no pattem exists among guilds regarding significant correlations between
variables and the second principal component. Shape differs among species in a
guild-specific fashion, and is likely a consequence of modification of structure to
enhance ecological efficiency. Moreover, feeding guild distinctions often correspond
with profound morphological and phylogenetic differences. Thus, it is not surprising
that differences in the relative contribution of variables to the second principal 43
component exist. Nonetheless, the first two principal components extracted from these
seven morphological variables accounted for 87.6 - 95.2 percent of the variation among
species witiiin a particular feeding guild (Table 3.1).
Minimum Spanning Trees. Simulation analyses strongly indicate that
nonrandom morphological pattems, consistent with competition theory, exist within bat
communities. Twelve of the fifteen locations, and three of the five feeding guilds
exhibited mean segment lengths that were significantiy greater than those derived from
random assembly (Table 3.4). Furthermore, segment length variances were
nonrandom at eight locations and in three feeding guilds (Table 3.5). This indicates
that when communities represent nonrandom faunal subsets, morphological pattems
most often manifest as greater distances between species in morphological space.
No conspicuous pattem exists as to which communities or feeding guilds
exhibited nonrandom morphological stmcture. I utilized Fisher's test (Sokal and
Rohlf, 1995) to combine probabilities from all feeding guilds within a community as
well as within feeding guilds across locations to determine whether communities or
feeding guilds in general exhibited nonrandom morphological pattems. Six
communities exhibited unusually high mean segment lengths overall (Table 3.6),
whereas four communities exhibited atypically small variances (Table 3.7). Aerial
insectivores, gleaning animalivores, and nectarivores exhibited unusually higher mean
segment lengths (Table 3.8), whereas frugivores exhibited significantiy smaller
variances of segment lengths (Table 3.9).
Discussion
Although seemingly hyperdispersed morphological pattems are not uncommon
within communities, recent statistical evaluations using neutral models have determined
that statistically nonrandom hyperdispersions are in the minority (Simberioff and
Boeklen, 1981). Recent evaluations of bat communities have corroborated tiiese 44
findings (Willig and Moulton, 1989). Nonetheless, my results identified numerous
instances in which species within feeding guilds exhibit statistically nonrandom
hyperdispersions that are consistent with competition theory. Moreover, in a few
cases, entire bat communities exhibited deterministic structure. Obviously, variation
exists regarding tiie degree to which feeding guilds and communities exhibit
hyperdispersed morphological pattems. Evaluating the stmcture of communities along
gradients may shed hght onto which environmental conditions foster the production of
non-random structure (Chesson, 1988; Chapter V).
Morphological overdispersion is not uncommon in the bat communities I
evaluated. Nonetheless, simply observing morphological overdispersion in a sample
(s^ < x) is not a sufficient demonstration of deterministic structure. Nonrandom
structure is indicated only when the sample variance is statistically smaller than the
mean (Sokal and Rohlf, 1995). To these ends, ascertaining the deterministic nature of
hyperdispersions by comparison with guilds created randomly from faunal pools is
necessary to warrant against wrongfully positing the operation of competitive
interactions on community organization. Nonetheless, the utilization of faunal pools to
evaluate statistical hyperdispersions is not an infallible means of evaluating
morphological pattems (Diamond and Case, 1986; Strong et al., 1984), and
interpretations of results from faunal pools must be conservative.
Faunal pools represent different biogeographic scenarios from which
communities are sampled and care must be taken in choosing their appropriate size
(Willig and Moulton, 1989). Knowledge of species distributions is incomplete
(Patterson, 1994). Moreover, temporal heterogeneity and rescue effects probably
impart a dynamic nature to distributional boundaries. Faunal pool 0 in these
simulations almost certainly includes potential invaders of contemporary feeding guilds.
Furthermore, faunal pools 1 and 2 probably correspond to potential pools occurring in
the ecological time of a contemporary community. From an ecological perspective, 45
^
however, species pools 3 and above probably are unrealistic and provide little insight
into contemporary sources of colonists. These pools undoubtedly contain species that,
because of biogeographic and ecological barriers, lack the potential to invade the
community. Nonetheless, the identity of the faunal pool that is the most appropriate
remains uncertain, and an exhaustive scheme most likely minimizes the possibility of
deriving false conclusions. Results from all pools regarding either communities or
feeding guilds were similar. In most cases, increasing the size of faunal pools
increases the number of candidate species for assembly into random communities, yet
no consistent trend in P-values with increased faunal pool size was detectable and little
change in P-values existed between the largest and smallest faunal pool.
Competitive interactions are density-dependent phenomena (Begon et al.,
1990). Moreover, environmental variability and stochasticity can prevent populations
from approaching carrying capacity, and thus mediate the degree of density-dependence
(Andrewartha and Birch, 1954, 1988; Chesson, 1988). To these ends, it is reasonable
that differences exist in the degree to which nonrandom morphological pattems occur
and these differences may be a product of climatic differences among sites. Although
deterministic structure occurred in all biomes sampled, no conspicuous pattems exist
regarding which were likely to give rise to deterministic stmcture.
Three feeding guilds (aerial insectivores, fmgivores, and nectarivores) exhibited
fairly ubiquitous deterministic structure at all locations, whereas the molossid
insectivore guild ubiquitously exhibited stochastic stmcture. Fmgivores exhibited
morphological pattems that were more even than were those in faunal pools, whereas
aerial insectivores, gleaning animahvores, and nectarivores were characterized by
statistically large segment lengths. Fmgivores never exhibited mean segment lengtiis
that were unusually large, and nectarivores never exhibited variances that were
unusually small. The morphological diversity of these groups may be constrained by
other phenomenon, and the assembly of species into these guilds is determined 46
consistentiy by only one attribute: either the mean distance or the variability of the
distances between species.
Despite the detection of deterministic stmcture in many situations, nonrandom
morphological pattems were not ubiquitous. The spatio-temporal circumstances in
which competitive interactions manifest as morphological pattems may be fairly
restrictive. For size assortment to be pervasive in a community, competitive
interactions must be strong, include most if not all species, and be persistent (Moulton
and Pimm, 1986). Considerable fluctuations in resource levels or climatic conditions
occur in many environments. If narrow spatio-temporal, climatic, or resource
conditions are necessary for the manifestation and persistence of size assortment, then
much of the observed lack of significance may indicate appreciable environmental
variability.
Morphological pattems within feeding guilds may be the result of either
adaptation by constituent species or evidence that community assembly has reached
equilibrium (Case and Sidell, 1983; Strong et al., 1979). The explanation for the
occurrence of both of these phenomena is usually based on an evolutionary time frame.
Bats are highly mobile organisms (Hill and Smith, 1984; Rayner and Norberg, 1987;
Thomas, 1987); they may be present in a community at one time but absent at others
(Bonaccorso, 1975). Morphological pattems may exist only when resource levels are
low, during which times competitive interactions are most intense, and only core
species persist within the community. At other times, when resources are bountiful,
competitive interactions may not be intense, and invading species may occur within
communities; when this occurs, deterministic pattems in morphology will not be
detectable. Evaluating community stmcture in a number of communities through many
years, as well as at various times of the year (such as during the dry season and wet
season), would be a good means to test this hypothesis.
47
Hyperdispersion in morphology was detectable in many situations, and was
pervasive in some feeding guilds and within some communities. Nonetheless, these
pattems lack ubiquity. Morphological pattems are not the only way in which
competitive interactions can be detected at the community level. Pattems regarding
other consequences of competitive interactions may appear in the absence of size
assortment, and may serve to be more consistent or informative metrics (see Chapter
IV).
48
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Figure 3.1.-- Graphical representation of a minimum spanning tree (MST). MSTs connect N points with N-1 line segments. Dots represent the centroid of species attributes in morphological space, whereas line segments represent the magnitude of the differences between nearest neighbors. PCI and PC2 are axes summarizing the morphological relationships of species in multidimensional space.
72
Figure 3.2.-- Graphical representation of faunal pools. The sohd dot represents the location of a hypothetical community. Faunal pool 0 corresponds to all species whose distributions overlap the hypothetical community. Faunal pools 1, 2, 3,4, and 5 correspond to the set of all species whose distributions fall in concentric rings 1, 2, 3, 4, and 5, respectively. Concentric rings 1, 2, 3,4, and 5 have diameters of 500, 1000, 2000,4000, and 8000 kilometers, respectively. Faunal pool 6 corresponds to all species of bats from the mainland of the New World.
73
Figure 3.3.~ Graphical representation of the null hypothesis regarding mean minimum spanning tree (MST) segment lengths. The probability density function represents a randomly generated distribution of means from 500 MSTs. If the observed mean (dot) in a feeding guild is larger than 90% of means from the randomly-generated distribution, then species in the feeding guild are ecomorphologically hyperdispersed and the feeding guild is stmctured by deterministic processes.
74
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Figure 3.4.-- Graphical representation of the null hypothesis regarding the variance of the minimum spanning tree (MST) segment lengths. The probability density function represents a randomly generated distribution of segment variances from 500 MSTs. If the observed segment variance (dot) in a feeding guild is smaller than 90% of variances from the randomly-generated distribution, then species in the feeding guild are ecomorphologically hyperdispersed and the feeding guild is stmctured by deterministic processes.
75
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CHAPTER IV
COMMUNITIES, INTERACTIONS, AND THE LACK OF
COMPETITIVE EXCLUSION: A SYNOPTIC
EVALUATION OF DENSITY COMPENSATION
Abstract
Ecomorphological approaches are a popular means of inferring resource
utiUzation, ecological interaction, and ultimately, the stmcture of natural
conmiunities. Traditionally, ecologists have explored hyperdispersed morphological
pattems as a means of identifying competitively induced deterministic stmcture.
Recent research, however, has been equivocal in identifying nonrandom
morphological pattems within communities. Alternative approaches for identifying
deterministic stmcture must be explored to assess if competitive interactions
consistently affect organization. Density compensation is the phenomenon whereby
the abundances of species depends upon morphological relationships with other taxa
in a feeding guild. Close competitors, evinced by morphological similarity, should
exhibit lower abundances because of increased competitive affects. As a
consequence, a statistical relationship should exist whereby the morphological
distance of species is positively correlated with its abundance. Density compensation
exists within bat feeding guilds and communities. Nonrandom pattems in abundance
and morphology were detected in seven conununities, in three feeding guilds, and for
three competitive scenarios. Nonetheless, density compensation is neither a pervasive
nor consistent attribute of community or guild organization. These data add to new
information suggesting that no one measure of stmcture pervades all communities.
Future studies should be directed at environmental gradients in order to understand
76
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the circumstances that promote or deter the production of nonrandom pattems in
community organization.
Introduction
Ecomorphological approaches in community ecology have become a popular
avenue to explore pattems that explain the coexistence of sympatric species (Findley,
1993, 1976; Findley and Black, 1983; Hespenheide, 1973; Mares, 1976; Ricklefs and
Miles, 1994; Smartt, 1978; Wainwright and Reilly, 1994). Reasons for their
popularity are numerous. The mensural nature of morphological attributes yields
quantitative data that can be scmtinized and manipulated from a statistical standpoint.
Thus, more quantitative tests of hypotheses ultimately provide more rigor in
evaluating variation within and among species (Blackith and Reyment, 1971; Rohlf,
1990).
Morphological variation is a populational attribute molded by natural selection
to produce phenotypic optimization (Darwin, 1859; Endler, 1986). As a result, the
morphological phenotype has become a standard metric to evaluate fitness and
ultimately the evolution of organisms (Clarke, 1995; Jones, 1987; Leary et al., 1984;
Palmer and Strobeck, 1986). Furthermore, morphology may be among the most
important phenotypic attributes relevant to the ecology of organisms (Wainright and
Reilly, 1994); implications are profound. A species ability to invade a community,
and hence occur in a given area, is dependent on its morphology (Brown, 1981;
Drake, 1990; Fox, 1989; Hutchinson, 1959; Law and Morton, 1993). Consequently,
morphological attributes of species play important roles regarding conmiunity
composition and stability, and ultimately affect community equilibria (Drake, 1990;
Fox, 1989; Huston, 1994; Hutchinson, 1959). As such, ecomorphological approaches
77
are integral in understanding higher order ecological phenomena (Findley, 1976;
Findley and Wilson, 1982; Mares, 1976; Wainright and Reilly, 1994).
At the center of theory addressing community organization lies the notion
that, via optimization, natural selection drives the morphological attributes of species
populations to diverge within communities (Case and Sidell, 1983; Cody and
Diamond, 1975; Hutchinson, 1959; MacArthur and Levins, 1967). Morphological
characteristics are important in the consumption of resources (Bonaccorso, 1975;
Brown and Lieberman, 1973; Dayan and Simberioff, 1994; Findley and Black, 1983;
Findley and Wilson, 1982; Freeman, 1981, 1984, 1988, 1992; Hespenheide, 1973;
Smartt, 1978), and for species to coexist, there should be a limit to morphological
similarity (Abrams, 1983; MacArthur and Levins, 1967). If two species are similar,
the resources they consume will be similar, and they should compete with such
intensity that interactions culminate in local extinction or morphological shifts of one
or both species. From a community perspective, morphological optimization occurs
when sympatric species exhibit hyperdispersed morphologies that minimize
interspecific competition (Cody and Diamond, 1975; Case and Sidell, 1983;
Hutchinson, 1959; MacArthur and Levins, 1967; Moulton and Pimm, 1986).
The documentation of hyperdispersions along putatively important
morphological axes is commonplace for many taxa in many contexts (see Simberloff
and Boeklen, 1981, for a review). Nonetheless, an equal mass of evidence fails to
support hyperdispersions (Connor and Simberloff, 1978, 1979; Simberloff and
Boeklen, 1981; Willig and Moulton, 1989). Such equivocal results could be the result
of either of two aspects of competitive interactions: (1) species within feeding guilds
do not compete at all locations, or (2) competitive interactions lack the intensity to
govern the central tendency of morphological attributes of species in all cases.
78
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Hyperdispersions probably manifest as population densities approach carrying
capacity. For example, to cause size assortment, competitive interactions must be
intensive enough to produce local extinction, extensive enough to affect all species
utihzing a limiting resource, and these effects must predominate at a specific locality;
no other influences, such as disturbance or predation, may supersede the importance
of competitive interactions (Moulton and Pimm, 1986). Nonetheless, many
populations never approach carrying capacity and density-dependent phenomena are
circumvented by factors such as environmental stochasticity, seasonality, parasatoids,
or predators (Andrewartha and Birch, 1954, 1988; Petraitis et al., 1989; Strong,
1984). Competitive exclusion may not occur in these communities.
Demonstration of hyperdispersions along morphological axes need not be the
only indication of stmcture induced by competition. Density compensation also may
exist within feeding guilds (Hawkins and MacMahon, 1989; Root, 1973). Density
compensation is the phenomenon whereby the total abundance of individuals of all
species within a feeding guild tends toward a maximum density set by the
environment. The distribution of abundances of constituent species, however, is
dependent upon their relationships with other guild members. Those species that
experience the greatest competitive pressure exhibit the lowest density.
Morphological attributes have been demonstrated to be good surrogates for
ecological relationships of many animal taxa, including bats (Bonaccorso, 1975;
Brown and Lieberman, 1973; Dayan and Simberloff, 1994; Findley and Black, 1983;
Findley and Wilson, 1982; Freeman, 1981, 1984, 1988, 1992; Hespenheide, 1973;
Smartt, 1978). Moreover, the position of species on resource axes are mirrored by
positions on morphological axes. Species that exhibit a high degree of morphological
similarity to other species within a feeding guild should experience the greatest
competitive effects, and exhibit lower abundances. Therefore, a positive relationship
79
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should exist between the morphological distance of species and their abundance, and
density compensation should be a predictable attribute of feeding guilds (Fig. 2.1).
Herein, I evaluate bat communities from North, South, and Central America, to
determine whether density compensation exists and is pervasive.
Methods
Communities. Fifteen bat communities from throughout the New World were
evaluated for evidence of density compensation (see Appendix A). A number of
criteria limited the number of communities selected for analyses. First, sampling
must have been conducted in a well-delimited local area that represented an actual
community of species that, because of their spatial proximity, exhibit the potential to
interact. Faunas of geopoliticsdly bounded areas were not acceptable because it was
difficult to be reasonably sure that only one community was sampled. Second,
sampling must have been continual for at least one year. This minimizes the failure
to detect rare species. Lastly, data must have been the product of regular sampling in
all seasons that bats were active. If density compensation occurs, it may manifest
through the absence of species during portions of the year when resources are rare.
By totaling abundance from all seasons, density compensation can be evaluated from
a yearly perspective.
Feeding Guilds. Each community was categorized into seven feeding guilds
(sensu Root, 1967): aerial insectivores, fmgivores, gleaning animalivores, molossid
insectivores, nectarivores, piscivores, and sanguinivores (see Appendix B for
definitions). Assignment of species to guilds was based on designations from the
original authors description of the community or from Wilson (1975) and Gardner
(1977). I only examined five guilds (aerial insectivores, fmgivores, gleaning
animalivores, molossid insectivores, nectarivores). The piscivore and sanguinivore
80
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guilds were not included in analyses because at least three species are necessary for
correlation analysis. Piscivores never met this criterion, sanguinivores did, but at
only one location.
Morphological Stmctore. Seven ecomorphological attributes characterized
each species. These were forearm length, greatest length of skull, condylobasal
length, width across the postorbital constriction, breadth of the braincase, length of
the maxillary toothrow, and breadth across the upper molars (see Appendix C for
definitions). Morphological measurements were obtained from museum specimens.
In most cases, the mean of each morphological character was based on eight
individuals, usually 4 males and 4 females. Special care was taken to select
specimens for measurement from geographic locations as close as possible to that of
each community. In most cases, specimens for each community were from the same
phytogeographic area within 700 km of the actual community. In all cases,
specimens were from the same subspecies as those found in the actual community.
Common logarithms of each character were used in analyses following
Ricklefs and Travis (1980). Log transformations enhance normality and
homoscedasticity (Ricklefs and Travis, 1980; Sokal and Rohlf, 1995). Moreover, log
transformations minimize the disparity in size among morphological characters of a
species, thereby reducing the propensity for differences in large characters to disguise
differences in small characters.
Community stmcture can be produced via a spectmm of interspecific
interactions, ranging from pairwise effects, to those based on all possible interactions.
Ecomorphological dissimilarity can be measured from a variety of perspectives as
well, corresponding to the ways competition could stmcture communities. If diffuse
competition pervades a feeding guild, than the abundance of a species will be the
product of its morphological relationship with all other species. This should be tme
81
when all guild members are fairly general in their dietary requirements and possess
resource spectra that in at least some way overlap among neighbors. In contrast,
interactions between a species and its most ecologically similar neighbors may be the
primary factor acting on community stmcture, and the morphological relationships
between a species and its nearest neighbors should most affect abundance. This
should be tme when species possess fairly narrow dietary requirements and resource
overlap involves few species in a feeding guild.
I evaluated three competitive scenarios along the spectmm of possibilities
(Fig. 2.2). In the first scenario, the abundance of a given species is the product of its
morphological relationships with all other (n-1) species in the feeding guild. The
Euclidean distance for each species represents the ecomorphological (Findley, 1976;
Findley and Wilson, 1982; Mares, 1976) distance of a species with respect to all other
(n-1) guild members:
n-1 m
Dt=I ( I (X , rX/ r . f ') i=l j=I
where: Dt represents the morphological distance of species t; n is the number of
species; m is the number of morphological characters; Xy represents morphological
character j of species i; and Xtj represents morphological character j of species t.
In the second scenario, interactions between a focal species and its most
morphologically distinct neighbor may be so weak as to have no effect on abundance.
Therefore, simulations were conducted in which the Euclidean distance included all
species in the feeding guild except the most morphologically different neighbor (n-2
of the species in the feeding guild):
82
\
n-2 m
Dt=i(i:(x,-x/r. <«) i=i j=i
In the third scenario, the abundance of species is not the product of diffuse
competition; abundance is a consequence of interactions with nearest morphological
neighbors. Thus, two nearest neighbors of a focal species were the only members of
the feeding guild included in calculations of ecomorphological distance:
2 m
Dt=I(I(X.i-X,/)'". («) i=l j=l
Null Hypotheses. Analyses are predicated on two assumptions. First,
measures of morphological dissimilarity within a guild are suitable surrogates for
ecological dissimilarity. Second, a species with high ecomorphological similarity to
one or more potential competitors should suffer reduced density as a result of
interspecific competition. As a consequence of such competitive effects, a
quantitative relationship should exist between the proximity of species in
ecomorphological space and density (Fig. 2.1).
I used Spearman rank correlation coefficients (SRCC) to describe the
magnitude of the relationship between morphological distance and abundance within
feeding guilds for many reasons. The association between morphological
dissimilarity and abundance may be nonlinear. I was most interested in the general
form of this relationship (does abundance increase as dissimilarity increases), and
thus utilized a rank coefficient to identify any monotonic association. Furthermore, it
is difficult to assess the abundance of bats with great accuracy based on contemporary
sampling techniques (Jones, 1965; Kunz and Kurta, 1988). SRCC provides for a
more appropriate analysis because the abundance of species need only be ranked
83
\
within feeding guilds from most abundant to least abundant; absolute measures of
abundance are unnecessary.
Although SRCC analysis is a nonparametric method, its traditional hypothesis
test assumes that variates follow a specified distribution (t-distribution). As a result,
the possibility exists that traditional hypothesis tests yield slightly inaccurate results
when assumptions regarding the distribution of data are not met (Noreen, 1989).
Assessment of significance based on simulation analyses, however, are not subject to
these inaccuracies. Simulation creates a unique distribution of Spearman correlation
coefficients for each null hypothesis. Moreover, the actual data are used to create this
distribution. No assumptions about the actual data are necessary, and hypothesis tests
are based on a distribution that is perfectly suited for the data (Noreen, 1989). Thus,
no violations of assumptions can jeopardize the accuracy of hypothesis tests.
To determine significance, I compared the correlation coefficients from each
actual guild to a distribution of correlations produced by the following stochastic
process. While preserving the integrity of the morphological relationships among
species, random abundances were assigned to each species. A correlation coefficient
was then calculated between randomized ranked abundances and actual
morphological distances of members within the simulated guild. One thousand
iterations of this process yielded a probability density function for subsequent
hypothesis tests. The correlation coefficient from the actual guild was compared to
the probability density function of simulated correlation coefficients. If the
coefficient for the actual guild occurred within the upper ten percent of the
distribution (p < 0.10), I concluded a nonrandom positive association between
morphology and abundance in the actual guild (Fig. 2.3). Many phenomena operating
totally independently of guild-wide competitive interactions, however, can influence
the abundance of species. Positive associations between abundance and
84
morphological distance, consistent with competition theory, may be obscured
partially by species experiencing autecological influences (i.e., differential response
to resources or disturbance) or by a plethora of other influences (i.e., predation,
mutualism) occurring at the community level. To safeguard against these possibilities
and wrongfully failing to reject the null hypothesis, I set alpha at 0.10.
Results
Density compensation was detected in seven communities (Table 4.1:
Guanacaste [LaVal and Fitch, 1977], Guanacaste [Fleming et al., 19721, Sherman,
Barro Colorado Island, Pern, Cerrado, and Caatinga) and in three feeding guilds
(Table 4.1: aerial insectivores, fmgivores, gleaning animahvores). Statistically
significant positive correlations between abundance and morphological distance
ranged from r = 0.42 to r = 1.00. Nonetheless, no community was strongly
characterized by deterministic stmcture in all its constituent feeding guilds, and no
feeding guild was deterministically stmctured at all locations. Obvious pattems as to
which communities or feeding guilds consistently exhibit deterministic stmcture are
unclear overall.
Despite a lack of statistical concordance, the possibility exists that when
results are combined, either across all locations for a particular feeding guild or across
all feeding guilds in a particular community, overall deterministic stmcture may be
revealed (Sokal and Rohlf, 1995). I used Fisher's exact test (Sokal and Rohlf, 1995)
to evaluate this possibility. Two communities (Guanacaste [LaVal and Fitch, 19771
and Sherman) exhibited deterministic stmcture overall (Table 4.2), whereas, none of
the feeding guilds exhibited deterministic stmcture overall (Table 4.3).
Density compensation was detected for each of three competitive scenarios
(Table 4.1). However, when nonrandom abundances occur within feeding guilds only
85
\
rarely do they pervade all three competitive scenarios. Moreover, density
compensation was detectable most often when only nearer neighbors were utilized for
the determination of competitive pressure. Only rarely were nonrandom pattems in
abundance the product of diffuse relationships with all other taxa in a feeding guild.
Discussion
Recenfly, the role of competitive interactions in stmcturing communities has
been questioned critically (Strong et al., 1984, and references therein), and the
importance of competition theory and its implications to community organization has
been discounted. At the heart of recent criticism have been questions conceming the
validity and ubiquity of morphological pattems. Many morphological pattems have
been shown to lack statistical vaUdity (Simberloff and Boeklen, 1981). Moreover, a
preponderance of reported morphological pattems come from vertebrate communities
and may not be a fair representation of the stmcture of all communities (Strong,
1984). Morphological hyperdispersions within bat communities have been evaluated
only recently (Chapter 3; Willig and Moulton, 1989). Although morphological
pattems are well-documented in bat communities (Findley, 1976; Fleming, 1986,
McKenzie and Rolfe, 1986; WiUig, 1986), hyperdispersions are not a consistent
attribute of stmcture (Chapter IE, this thesis; Willig and Moulton, 1989).
Morphological pattems, however, are not the only possible manifestation of
competitive interactions at the community level. Before the effects of competitive
interactions on community stmcture are discounted, the existence and ubiquity of
other manifestations (i.e., density compensation) should be explored.
Rejection of the null hypothesis of random pattems of abundance is highly
dependent on the morphological scenario under consideration. Every species in a
feeding guild need not intensely compete with all others to impose stmcture.
86
Contemporary morphological models implicitly assume that the competitive
interactions that stmcture communities occur only between nearest neighbors.
Although these interactions probably are most intense, my results indicate that
interactions that lead to stmcture can be more diffuse. A limited focus on only
nearest neighbors will likely lead to a limited understanding of community
organization. Moreover, exploring the breadth at which interactions operate may
provide added insight into the process of community organization.
The breadth of interaction may shed light on community characteristics as
well. If species compete along a single resource axis, such as fmit size, resource
spectmm will be unidimensional. In this case, species' nearest neighbors most likely
impose a preponderance of the competitive pressure realized by a particular species.
However, in feeding guilds or communities where resource utilization is
multispectral, pressures from more species may be the mle. For example,
omnivorous rodent species may compete and divide resources with regard to seed size
on one axis and chitin hardness of insects on another. If the positions of species are
not mirrored on both resource axes, combinations of close competitors from both axes
could be different, and a species' two nearest ecological neighbors could, in tum, be
different, depending on the axis. Thus, scenarios involving more than just nearest
neighbors would be necessary to understand competitive interactions.
Density compensation is not a pervasive attribute of communities or feeding
guilds. Nonetheless, it is an additional approach for characterizing the influence of
interspecific competition on community organization. Community ecologists have
been hasty to discount the validity of competition theory based on rejections of single
predictions. An approach like "strong inference" (Piatt, 1964) would be more
appropriate to evaluate the validity of competition theory. For example, one might
first evaluate morphological hyperdispersions within communities. Upon failure to
87
\
appropriate to evaluate the validity of competition theory. For example, one might
first evaluate morphological hyperdispersions within communities. Upon failure to
reject the null hypothesis of random morphological dispersion, one would then
evaluate a null hypothesis of no association between morphological distance and
abundance. Upon rejection of this null hypothesis, one might then evaluate another
putative manifestation of competitive interaction. Failure to reject single null
hypotheses should not be an end, but rather a beginning.
Interspecific competition is a density-dependent phenomenon (Begon et al.,
1990). Manifestations of competitive interactions may assume a hierarchical
organization, with levels corresponding to the degree to which populations approach
carrying capacity. For example, in environments where populations are at or near
carrying capacity, competitive interactions may be intense (strong enough to meet the
assumptions of size assortment), and capable of causing the extinction of species that
share much morphological similarity with one or more species; size assortment
pervades. In intermediate situations, population densities may be lower (relative to
resources), and competitive interactions may not be sufficiently strong to cause
extinction. However, lower species abundances may be the consequence of
interactions with similar community members. Lastly, competitive interactions may
be too weak to cause extinctions or manipulate abundances. Nonetheless, species
may maximize resource consumption by some behavioral attribute that allows them
competitor-free space or time (e.g., habitat or temporal segregation). Thus, density
compensation may be a manifestation of competitive interactions of intermediate
intensity.
These data partly corroborate those of James and Boeklen (1984), who found
little evidence that species abundance was associated with morphology in birds. It is
important to point-out that both studies address competitive interactions among
88
highly mobile organisms. More mobile organisms may simply leave a community
when local resources are low and thereby escape strong competitive effects.
Furthermore, more mobile species may easily recolonize when communities regain
sufficient resource levels. This may explain why some bat species are only seasonal
residents in some communities (Bonaccorso, 1975). Moreover, this may explain a
lack of ubiquity of density compensation. The lower mobility of organisms such as
plants, rodents, and lake fishes, may explain why such profound manifestations of
competitive interactions sometimes obtain (Brown, 1989; Brown et al., 1979; Fowler,
1986; Holbrook and Schmitt, 1992; Kodric-Brown and Brown, 1993; Price, 1986;
Robinson et al., 1993; Silvertown and Dale, 1991).
Considerable variation exists regarding the degree of density compensation
within feeding guilds and communities. Competitive interactions are not the only
constraints on the abundance of species. Other biotic factors, such as mutualism,
predation, and parasitism, along with abiotic influences such as environmental
productivity and climatic variability, influence abundance as well (Andrewartha and
Birch, 1954, 1988; Begon et al., 1990). These influences may modulate abundances
to such an extent that the effects of competitive interactions are obfuscated. Gradients
in the degree of alternative influences on community composition should correspond
with gradients in the degree to which competitive interactions stmcture communities.
Moreover, the exact circumstances that lead to competitively induced community
stmcture should be explored (Chapter V).
89
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94
Table 4.1.-- Results of simulation analyses evaluating nonrandom pattems in abundance within fifteen bat communities (Appendix A), n-1, n-2, and 2 represent three competitive scenarios; rs and ps represent the Spearman rank correlation coefficient and the probability that the observed correlation coefficient comes from a simulated distribution where rs = 0, respectively. Bold values indicate deterministic guild stmcture at p < 0.10 level.
Community Feeding guild
n-1 rs Ps
n-2 rs Ps rs Ps
Iowa
Aerial insectivore 0.228 0.298
Cahfomia
Aerial insectivore 0.167 0.348
Chiapas
Fmgivore
Gleaning animalivore
Molossid insectivore
0.154 0.304
-0.162 0.732
1.000 0.152
Guanacaste (LaVal and Fitch, 1977)
Aerial insectivore 0.729 0.008
Fmgivore
Gleaning animahvore
Molossid insectivore
Nectarivore
0.174 0.340
0.409 0.125
-0.200 0.607
0.400 0.371
Guanacaste (Fleming et al., 1972)
Aerial insectivore -0.419 0.834
0.228 0.336
0.190 0.336
0.156 0.347
0.071 0.422
0.113 0.365 -0.118 0.633
-0.105 0.632
0.866 0.836
-0.295 0.817
1.00 0.171
0.720 0.009 0.679 0.008
-0.087 0.547
0.443 0.122
-0.400 0.803
-0.087 0.520
0.298 0.206
-0.400 0.784
-0.600 0.846 -0.600 0.833
-0.419 0.836 -0.419 0.832
Fmgivore
Gleaning animahvore
;nas
Aerial insectivore
Fmgivore
0.407
-0.239
-0.009
-0.238 95
0.179
0.715
0.500
0.718
0.323
-0.037
-0.230
-0.238
0.207
0.571
0.711
0.750
0.503
-0.110
-0.426
-0.286
0.098
0.610
0.877
0.767
Table 4.1. Continued
Community Feeding guild
Nectarivore
Heredia
Aerial insectivore
Fmgivore
Gleaning animahvore
Nectarivore
Sherman
Aerial insectivore
Fmgivore
Gleaning animalivore
Rodman
Aerial insectivore
Fmgivore
Gleaning animahvore
Barro Colorado Island
Fmgivore
Gleaning animahvore
Zabehtas
Fmgivore
Gleaning animahvore
Nectarivore
Pance
Fmgivore
n-] rs
-0.200
-0.110
-0.047
-0.351
-0.638
0.464
0.258
-0.049
-0.632
0.314
-0.406
0.455
-0.498
0.211
0.091
0.100
-0.301
96
[
Ps
0.631
0.656
0.556
0.924
0.898
0.185
0.188
0.526
0.848
0.145
0.811
0.081
0.941
0.189
0.485
0.485
0.836
n-2 rs
-0.200
-0.245
-0.052
-0.316
-0.174
0.754
0.326
0.049
-0.632
0.388
-0.063
0.448
-0.402
0.179
-0.030
0.100
-0.329
1
Ps
0.653
0.791
0.590
0.916
0.668
0.032
0.117
0.438
0.835
0.118
0.556
0.079
0.905
0.255
0.567
0.465
0.856
2 rs
-0.429
-0.084
-0.333
-0.312
-0.667
0.493
-0.204
-0.025
-0.632
0.300
0.381
0.007
-0.411
-0.126
0.030
-0.300
-0.483
Ps
0.816
0.609
0.879
0.892
0.932
0.136
0.524
0.515
0.826
0.171
0.154
0.488
0.900
0.694
0.567
0.738
0.933
Table 4.1. Continued
Community Feeding guild
n-1 rs Ps
Pern
Aerial insectivore -0.474 0.933
Gleaning animalivore -0.215 0.780
Molossid insectivore -1.000 1.000
Nectarivore
Edaphic Cerrado
Aerial insectivore
-0.600 0.829
-0.198 0.702
Fmgivore 0.321 0.259
Gleaning animalivore 0.316 0.387
Molossid insectivore -0.500 0.821
Caatinga
Aerial insectivore -0.718 0.928
Fmgivore 0.179 0.374
Gleaning animalivore 0.683 0.047
Molossid insectivore -0.667 0.953
n-2 rs Ps rs Ps
Nectarivore -0.500 0.845
-0.460 0.931 -0.519 0.947
-0.109 0.636 0.415 0.055
-0.866 0.814 -1.000 1.000
-0.600 0.811 -0.600 0.818
-0.198 0.676 -0.126 0.586
0.250 0.308 0.036 0.461
0.949 0.040 0.949 0.040
0.000 0.486 -0.500 0.836
-0.718 0.943 -0.667 0.948
0.214 0.355 0.214 0.307
0.683 0.029 0.311 0.231
-0.667 0.942 -0.757 0.982
-0.866 0.828 -0.500 0.845
97
Table 4.2.-- Results of Fisher's test assessing overall deterministic stmcture of bat communities when probabilities from all feeding guilds are combined, n-1, n-2, and 2 represent three competitive scenarios. Boldfaced print indicates overall deterministic community stmcture at p < 0.10.
Communitv
Iowa
Califomia
Chiapas
Guanacaste (LaVal and Fitch, 1977)
Guanacaste (Fleming, 1972)
Puntarenas
Heredia
Sherman
Rodman
Barro Colorado Island
Zabelitas
Pance
Pem
Edaphic Cerrado
Caatinga
n-1
0.298
0.348
0.327
0.040
0.600
0.813
0.959
0.228
0.564
0.272
0.369
0.836
0.998
0.680
0.557
n-2
0.336
0.336
0.612
0.109
0.575
0.904
0.934
0.043
0.394
0.259
0.471
0.856
0.982
0.201
0.421
2
0.347
0.422
0.554
0.128
0.413
0.975
0.984
0.342
0.237
0.798
0.454
0.933
0.593
0.309
0.845
98
Table 4.3.-- Results from Fisher's test assessing overall deterministic stmcture of each of five feeding guilds when probabilities are combined for all locations, n-1, n-2, and 2 represent three competitive scenarios. No feeding guild exhibited deterministic stmcture (p > 0.10).
Feeding guild nA n-2
Aerial insectivore
Fmgivore
Gleaning animalivore
Molossid insectivore
Nectarivore
0.477
0.252
0.827
0.725
0.948
0.331
0.271
0.389
0.870
0.984
0.510
0.858
0.194
0.816
0.999
99
CHAPTER V
GRADIENTS IN THE STRUCTURE OF NEW WORLD
BAT COMMUNITIES
Abstract
One of the most debated issues in ecology is the importance of competitive
interactions in stmcturing communities. Ecologists only recently have begun to
consider that the density-dependent nature of competitive interactions sometimes make
predictions based on classical equilibrium theory invalid. More specifically,
coexistence within a community of competitors that would be unexpected under
equihbrial theory may be possible by virtue of unutihzed resources resulting from the
disequilibrial densities of populations. As a consequence, many ecologists have
abandoned equilibrial competition theory because it is unable to predict stmcture in
many situations. Determining the environmental conditions that mitigate the
consequences of competitive interactions on community stmcture would be an
important advance in theoretical ecology. Herein, I evaluate the degree to which
measures of the deterministic stmcture of bat communities and feeding guilds are
associated with mean measures of precipitation, productivity, and temperature; their
associated variability; and latitude.
Stmcture was evaluated from three perspectives. Numerical stmcture was
determined by the degree to which correlations between the abundance of a species and
its morphological distance with other competitors was nonrandom. The way that
competition produces hyperdispersed morphological pattems was evaluated in two
ways. Interactions may influence the mean or the variance of the distance between
species centroids. Thus, hyperdispersion was defined by the degree to which the mean
and variance of interspecific distances differed from random expectations.
100
Variation in the degree of competitively induced stmcture of feeding guilds
coincides with variation in environmental parameters; however, variation in overall
community stmcture does not. The overall response of bat communities may be
confounded by the unique response of each feeding guild to environmental variation.
Unique responses by feeding guilds suggest that species at higher trophic levels
respond to more complex characteristics, such as productivity and latitude, whereas
species at lower trophic levels respond to simpler factors such as temperature.
Measures of numerical stmcture were more sensitive to environmental characteristics
than were measures based on morphology alone. Nonetheless, these results
demonstrate that the environmental context of a community should be considered before
casting predictions regarding deterministic organization.
Introduction
A paradigm pervading modem ecology is that biotic, abiotic, and historical
processes act on hfe history attributes to determine the distribution and abundance of
species (Andrewartha and Birch, 1954, 1988; Begon et al., 1990). Consequently,
understanding the spatial and temporal scales, ecological levels, and circumstances
under which each of these processes prevail is a major thmst of contemporary ecology.
Competitive interactions often transpke within trophic levels, but are probably
most intense within feeding or other resource guilds (Cody and Diamond, 1975;
Diamond and Case, 1986; Gee and Giller, 1987; Hawkins and MacMahon, 1989;
Kikkawa and Anderson, 1986; Pimm, 1982, 1991; Polls, 1991; Ricklefs and Schluter,
1993; Simberloff and Dayan, 1991). Ultimately, interspecific competition mediates
community stmcture when populations are at or near equilibria (Begon et al., 1990;
Krebs, 1985; Ricklefs, 1979). An equilibrium is defined as the state at which the rate
of death of organisms equals the rate of birth (MacArthur and Wilson, 1967). More
101
operationally, however, equilibria refer to demographic states at which population
densities fluctuate only slightly about carrying capacity (Begon et al., 1990; Huston,
1994; Krebs, 1985). At equilibrium, limiting resources effectively are exhausted, and
the potential for competitive interactions is greatest. If two species are not sufficiently
different ecologically, their resource spectra will overlap to such an extent that both
species will consume and compete for the same resource (Abrams, 1983; Hutchinson,
1959; MacArthur and Levins, 1967). As a result of increased competition species
exhibiting ecological overlap should suffer reduced fitness, possibley stimulating
divergence with regard to utihzation of resources (Hardin, 1960; MacArthur and
Levins, 1967). Under equilibrial conditions, competitive interactions drive natural
selection in either of two directions: competitive exclusion or character displacement.
To these ends, repeatable, quantitative predictions regarding the coexistence of species
and ultimately the stmcture of communities are possible if populations within
communities are at equilibrium (Huston, 1994; Pielou, 1975; Ricklefs, 1979;
Vandermeer, 1969).
Equilibrial conditions may be unreasonable expectations for many systems.
Empirical confirmation of aspects of disturbance theory, as well as a focus away from
vertebrates, has demonstrated profoundly that many systems are not at equilibrium
(Power et al., 1988; Resh et al., 1988; Strong, 1984). Moreover, the predictions of
traditional competition theory are invahd and provide httle understanding conceming
coexistence under non-equilibrial conditions (Chesson, 1986; Strong et al., 1984). If
co-existing populations are not at equilibrium, the effects of density-dependent
interactions (e.g., competition) are variable and lead to potentially unpredictable
community stmcture. For example, species with inferior competitive ability can coexist
and competitive hierarchies may be dismpted when species are added under
nonequilibrial conditions (Armstrong and McGehee, 1976; Koch, 1974; Levins, 1979;
102
Park, 1954; Rotenberry, 1978). Nonetheless, competitive interactions may still
influence community organization despite nonequilibrial conditions. New theory
addressing the dynamics of density- or frequency-dependent phenomena under
nonequilibrial conditions may provide greater insight and suggest productive avenues
of future research in community ecology.
Predictions of community organization under non-equilibrial conditions have
been developed only recently, and are slow in development (Chesson, 1986; Levin,
1970; Levin and Paine, 1974; Weins, 1977). These models are quantitatively more
complex than equihbrial models, and result in outcomes that are difficult to interpret
because of nonlinearity (Chesson, 1986). Nonetheless, non-equilibrial population
dynamics probably occur in most species and their ramifications on community
organization should be examined from a variety of perspectives (Strong, 1984).
Furthermore, environmental change as a consequence of anthropogenic activity
continues to accelerate, resulting in increased destmction of habitat and ultimately an
increase in the number of populations experiencing disequihbrial population densities
(Wilson, 1988). The importance of understanding ecological phenomena under
nonequilibrial conditions becomes even more critical in this context.
Abiotic factors have considerable effects on demographic attributes of
populations (Andrewartha and Birch, 1954, 1988). These effects can influence
coexistence by modifying life history traits of species such as body mass, adult survival
rate, and age at parturition (Zammuto and Millar, 1985). Moreover, these effects on
populations can emerge at the community level by many avenues. Abiotic conditions
modify the potential intensity of biotic interactions at the community level (Dunson and
Travis, 1991). By affecting the composition of species pools from which communities
are assembled, environmental conditions also may dictate which species potentially
interact (Roughgarden and Diamond, 1986). Moreover, environmental fluctuations or
103
disturbances that indiscriminately lower population densities can result in diminished
competition, or in extreme cases, drive species to extinction (Sousa, 1984).
Nonequilibrial community organization might be better understood if the degree to
which abiotic factors, especially envkonmental variability, influence deterministic
stmcture is discemed.
Herein I evaluate whether variation in environmental parameters mediates the
degree to which competitive interactions manifest as deterministic stmcture at the level
of ecological guilds and communities. I predict that if environmental variabihty
decreases the degree of deterministic stmcture in bat communities, then gradients in
stmcture should coincide with environmental variability.
Methods
Selection of Communities. I evaluated gradients in the stmcture of bat
communities based on nine sites distributed throughout the New Word (Table 5.1).
Bat communities were selected for many reasons. Bats are distributed widely and in
sufficient numbers throughout the New World such that communities from many
different biomes could be represented in analyses. Moreover, bats are numerically
dominant in many systems and represent keystone species (Handley, 1966; Robinson,
1971). Lastly, bats occupy at least three trophic levels (primary, secondary, and
tertiary consumers) and seven feeding guilds (aerial insectivores, fmgivores, gleaning
animalivores, molossid insectivores, nectarivores, piscivores, and sanguinivores).
Thus, comparisons of the stmcture of bat communities are possible from a number of
ecological perspectives (Findley, 1993).
Characterization of Community Stmcture. Bats were categorized into feeding
guilds based on designations pubhshed in the actual account of the community, or on
other published information (Gardner, 1977; Wilson, 1975). Piscivore and
104
sanguinivore feeding guilds were not used in analyses because they comprise too few
species. The molossid insectivore guild was not included in analyses because it was
represented by sufficient numbers of species at only three locations, and thus does not
lend itself to regression analyses. Consequently, analyses were restricted to aerial
insectivores, fmgivores, gleaning animalivores, and nectarivores. Feeding guilds from
particular locahties were not included in analyses if they did not contain at least three
species. In general, I used two suites of Monte Carlo simulations to characterize the
degree to which communities exhibited stmcture with regard to morphology or density.
Morphological Stmcture. Deterministic, morphological stmcture occurs if a
feeding guild exhibits statistically hyperdispersed morphologies. Hyperdispersion may
manifest in either of two ways: species within feeding guilds may have larger mean
nearest neighbor distances than expected by chance, or the variance of the distances
between nearest neighbors may be smaller than expected by chance (Willig and
Moulton, 1989). I evaluated both scenarios. Significant hyperdispersions were
determined by comparing statistics from actual feeding guilds to those randomly
generated from faunal pools. Four faunal pools were used for comparison: all species
whose distributions overlapped the geographic location of the actual community, as
well as all species whose distribution fell within a circle centered at the location of the
community and had diameters of 500, 1000, or 2000 km (Fig. 3.2). Species were
randomly drawn from faunal pools in numbers equal to those of the actual community.
Seven morphological characters were used to characterize relationships among species
(Appendix C). Principal components analyses were used to reduce to two the number
of dimensions describing morphological relationships. The mean and variance of
interspecific morphological distances were then calculated between nearest neighbors.
This was iterated 500 times to yield a random distribution of each statistic. The
position of the actual mean and variance with regard to their respective random
105
distributions determined the degree to which stmcture was nonrandom. More in-depth
descriptions of these models of community organization are provided in Willig and
Moulton (1989) and in Chapter m.
Numerical Stmcture. Numerical stmcture was defined by the degree of
association between the morphological distance of species from other taxa and
abundance. A species with a high degree of morphological similarity to other members
of its feeding guild (low ecomorphological distance) should experience greater
interspecific competition, and consequently exhibit reduced density. Hence,
deterministic numerical stmcture exists if a nonrandom positive correlation was
detectable between morphological distance and abundance. Monte Carlo simulations
were used to evaluate the statistical significance of such correlations.
Morphological distance was evaluated from a number of perspectives
representing a range of ways in which competitive interactions influence abundance
(Fig. 2.1). In all cases, Euclidean distances characterized the morphological distances
among competitors. In the first approach, the calculated morphological distance for
each species was from the perspective of all other (n-1) guild members:
n-1 m
Dt=I(I (X, -X/ ) '" . (5.1) i=l j=l
where: Dt represents the morphological distance of species t; n is the number of
species; m is the number of morphological characters; Xy represents morphological
character j of species i; Xtj represents morphological character j of species t.
In the second approach, the calculation of morphological distance for a species included
all species in the feeding guild except its most morphologically distant neighbor (n-2 of
the species in the feeding guild):
106
n-2 m
D,= I(I(X,j-X,P'r. <5-2) i = l j=l
In the third scenario, the two nearest neighbors of each species were the only members
of the feeding guild included in calculations of ecomorphological distance:
2 m
Dt^IdCXg-X,/)"'. (5.3) i = l j = l
Distributions of random correlation coefficients were created to facilitate
detection of significance. To create null stmcture, abundance was randomized while
the morphological relationships of the species in the actual feeding guild were
maintained. A Spearman rank correlation coefficient was then calculated between
random abundance and morphological distance. This process was iterated 1000 times,
thereby yielding a distribution of random correlation coefficients. The position of the
correlation for an actual feeding guild with respect to this random distribution
determined the degree to which stmcture was nonrandom. More in-depth descriptions
of these models appear in Chapters n and IV.
In all, 11 measures (four regarding mean distance of species in morphospace,
four regarding the variance of distance between species in morphospace, three
regarding abundance pattems) characterized the stmcture of each feeding guild. A
composite value of each measure of stmcture was calculated from the P-values of each
feeding guild analyzed in a community. This composite P-value characterized the
overall stmcture in each community and was calculated as directed for Fishers test of
combined probability (Fisher, 1954; Sokal and Rohlf, 1995). Thus, 11 measures of
stmcture described each community as well.
For communities and each of five feeding guilds, separate principal components
analyses were conducted on all original measures of stmcture to produce more general
107
indices of organization. The 11 measures of stmcture from all locations were entered
into separate principal components analyses for each guild. The same is tme for
communities. Principal components analysis is a technique whereby a linear
combination of the original variables is selected that ehminates redundancy and reduces
the number of dimensions necessary to illustrate relationships (Tobachnick and Fidell,
1989). Thus, each derived principal component represents a unique axis characterizing
stmcture.
Environmental Characterization. I used seven descriptive statistics to
characterize the regime of each of three environmental variables (precipitation, r;
productivity, p; and temperature, t) for each community (Table 5.2). Measures
included the mean (M) of the mean monthly value of each environmental parameter
(MMD MMt» MMp; Table 5.2), as weU as six measures of variabihty. Variability was
evaluated fi"om a number of perspectives including both absolute and relative scales.
Relative variability (CV) was characterized using the coefficient of variation, whereas
absolute variabihty (V) was described by the variance.
Three measures describe absolute variabihty for each parameter. Variances
within years were averaged across all years to yield a measure of average absolute
within-year variability (Mvr, Mvt, Mvp; Table 5.2). Variance among years in the mean
of a parameter was calculated also (VMT, VMI* VMp; Table 5.2). Finally, the variability
among years regarding the within-year variance of a parameter was calculated (Vvr,
Vvt, Vvp; Table 5.2).
Similarly, three measures of relative variabihty characterized each community.
The relative variabihty within years was described by the within-year coefficient of
variation averaged across years (Mcvr» Mcvt. Mcvp; Table 5.2). Year-to-year relative
variabihty was determined using the coefficient of variation of the mean across years
108
(CVMH CVMI, CVMp; Table 5.2). Lastly, the variability across years of the
within-year, relative variability was calculated (Vcvr, Vcvt, Vcvp; Table 5.2).
Environmental data (mean monthly temperature and precipitation) for each
community were obtained from weather stations in the same phytogeographic region
and from no more than 150 km from the actual site (U. S. Department of Commerce,
1966, 1979, 1989). These criteria likely provide data that are sufficiently similar to that
of the focal sight so that comparisons among widely distributed (spatially as well as
phytogeographically) sites are possible.
Net, above-ground, primary production (NAPP) in grams per square meter can
be calculated from actual evapotranspiration (AE) following the recommendations of
Rosenzweig (1968) as:
NAPP= 1.66(logAE) - 1.66. (5.4)
Unfortunately, AE was not available for any of the sites from which bat communities
were studied. Consequently, I quantified the relationship between NAPP and both
temperature and precipitation based on AE, temperature, and precipitation data from 48
other sites (Thomthwaite and Associates, 1964) distributed throughout the biomes from
which bat communities were obtained. Data for AE were used to predict NAPP for the
48 sites. Stepwise multiple regression analysis (SPSS, 1990) identified the best
relationship between temperature and precipitation to estimate NAPP. The algorithm
derived from this analysis was then used to estimate productivity for each bat
community based on temperature and precipitation data.
Principal Components Analvsis. I used principal components analysis to
delineate important environmental gradients based on 21 chmatic characters (Table 5.2).
Conducting multiple bivariate correlations between raw environmental variables and
measures of stmcture would greatly enhance experiment-wise error rate. Moreover,
many of the envu-onmental parameters I measured were highly correlated with one or
109
more variables. Instead of using all 21 environmental variables in subsequent analyses,
principal components analyses enabled measures that are highly correlated to be
integrated into fewer composite environmental gradients (i.e., the principal
components). Original environmental variables that were correlated highly with a
principal component elucidate the identity of that composite gradient.
Multiple Regression and Correlation Analyses. The degree to which
deterministic stmcture was a linear function of composite environmental gradients was
evaluated by stepwise multiple regression analysis (SPSS, 1990). Nonetheless, the
response of stmcture to environmental parameters may not be linear. Hence, I used
Kendall's rank correlation analysis to determine if sUncture changed in a consistent
direction along each environmental gradient. To protect from inflated experiment-wise
error rate associated with conducting numerous bivariate correlations, I decreased
comparison-wise error rate of each correlation based on Bonferroni's sequential
adjustment (Rice, 1989). Nonetheless, many phenomena acting independently of
density-dependent competitive interactions possibly influence the stmcture of
communities (e.g., predation, mutualism, parasitism). As a consequence, associations
between stmcture and environmental parameters may be obscured. To safeguard
against this, I set alpha at 0.10 in multiple regression and correlation analyses.
Results
Environmental Axes. The sites of the ten bat communities differed greatly with
regard to both climatic variables and latitude (Tables 5.3-5.5). Among-site variation
in temperature was consistently lower than that for precipitation or productivity,
whether assessed by central tendency or absolute and relative variability. For example,
means for precipitation, as well as productivity, differed among sites by two orders of
magnitude, whereas means for temperature were much less variable (e.g.,
110
< 1/2 order of magnitude). Among-site variation in absolute measures of variability
(Vvr» Vvt, Vvp) were greater than that for corresponding relative measures of
variability (CVMF, CVMI, CVMp).
Multiple regression analysis identified the best algorithm to estimate
productivity (P) based on mean monthly temperature and precipitation as:
P = -61.9 -I- 9.39 [temperature] + 7.52 [precipitation] (5.5)
it accounted for a highly significant proportion of the variation in productivity (R =
0.795, p < 0.001).
Principal Components Analysis. Principal components analysis of the 21
environmental characters accounted for 93.4% of the variation among the ten
communities (Table 5.6). Four environmental gradients were extracted (Table 5.7).
Eigenvalues for the first four significant principal components (PCs) ranged from 1.35
to 10.94.
PCI was correlated highly with MvpVMr. Vvr, Vj p, and Vvp (Table 5.8).
PCI constitutes an axis of absolute variabihty in precipitation and productivity.
Locations on the negative portion of this axis represent areas of low absolute
variabihty, whereas locations on the positive end represent areas of high variability of
these parameters. This axis essentially depicts a gradient from dry to wet habitats. Wet
tropical areas experience high precipitation and productivity, but a pronounced dry
period as well. This results in high average rainfall as well as high variability. On the
other hand, deserts experience little rainfall, and as a consequence experience httle
absolute variabihty.
PC2 was highly correlated with Mvt, Mcvt, Vvt. and Vcvt (Table 5.8). It
represents an axis of the variabihty of temperature. Locations on the negative portion
of this axis experience low variability, whereas locations on the positive end experience
111
high variability. PC2 recapitulates the latitudinal gradient in temperature, whereby
mean monthly temperature increases toward the equator and variability decreases.
PC3 was highly correlated with measures of the relative variability of rainfall
and productivity (CVMF, Vcvr, and CVMp: Table 5.8). Locations on the negative
portion of this axis represent areas of low relative variability, whereas locations on the
positive end represent areas of high variability.
PC4 was correlated highly with Mcvp (Table 5.8), representing an axis of the
within-year variability in productivity. Locations on the negative end of this axis are
characterized by low relative variability in productivity, whereas areas on the positive
end of this gradient are characterized by high degrees of variabihty.
Axes of Stmcture. Results from principal components analyses for communities
and each of the four feeding guilds were similar (Table 5.9). In most cases, PCA
extracted three gradients of stmcture. Eigenvalues for the first principal component
ranged from 4.9 to 8.6, and the amount of variation ranged from 44.1 to 78.1 %. PC2
accounted for variation ranging from 15.0 to 38.2%; eigenvalues ranged from 1.65 to
4.2. A third principal component was extracted for three of the feeding guilds and for
communities. Nectarivores were examined at too few locations for extraction of a third
principal component. Variation accounted for by PC3 ranged from 10.6 to 15.5%, and
eigenvalues ranged from 1.32 to 1.71.
Axes representing overall community, aerial insectivore, and fmgivore stmcture
were similar. Measures of morphological stmcture regarding the variance of the
interspecific distance in a feeding guild were most highly correlated with PCI (Table
5.8). Measures of morphological stmcture regarding the mean distance between
species within feeding guilds were most highly correlated with PC2. Lastly, measures
of numerical stmcture were most highly correlated with PC3. The farther in the
112
positive dkection on each principal component, the weaker is the degree of
deterministic stmcture.
For gleaning animalivores, the three types of stmcture were segregated on
distinct axes, however their identity was different from those of communities, aerial
insectivores, and fmgivores (Table 5.10). The first principal component represented an
axis in morphological stmcture defined by the mean differences between species. The
second principal component represented an axis in stmcture regarding the variance of
interspecific differences. Finally, principal component three represents an axis in
numerical stmcture. The farther in the positive direction on each principal component,
the weaker is the degree of deterministic stmcture.
Principal components analyses extracted only two axes of stmcture for
nectarivores (Table 5.10). The first principal component characterized morphological
stmcture regarding the variance in interspecific morphological distances, whereas the
second principal component characterized numerical stmcture. On the first axis,
deterministic stmcture decreases as one moves to the right, whereas deterministic
stmcture increases as one moves to the right on the second axis.
Multiple Regression Analyses. The stmcture of three feeding guilds statistically
were affected by combinations of environmental attributes (Table 5.11, Fig. 5.1). The
numerical stmcture of the fmgivore guild was positively related to temperature
(R = 0.761, p = 0.047). As the mean temperature decreased and its variabihty
increased, the degree to which this guild exhibited deterministic stmcture decreased.
Fmgivores exhibited more deterministic stmcture in areas with warmer and less
variable temperatures (e.g., Guanacaste, Rodman, Sherman).
The stmcture of the gleaning animalivore guild was affected by two
environmental gradients (Table 5.11, Figs. 5.2 and 5.3). Morphological stmcture
regarding the mean distance of species within a feeding guild was a significant function
113
of the relative variability in productivity (R = 0.782, p = 0.038). As the relative
variability of productivity increases, the degree to which morphological stmcture is
deterministic decreases (e.g., Guanacaste, Sherman, Caatinga). Numerical stmcture,
however, was dependent on the absolute variabihty of productivity and precipitation (R
= 0.776, p = 0.044). As variability increased, the degree to which the gleaning
animalivore guild was stmctured deterministically decreased. In general, gleaning
animahvores exhibit more deterministic stmcture in areas of less variable productivity
and precipitafion (e.g., Guanacaste, Heredia, Sherman).
Numerical stmcture of the nectarivore guild was related to the mean and
variability in temperature (R = -0.908, p = 0.092; Table 5.11, Fig. 5.4). The N-2
scenario essentially defined the stmcture axis, and was oriented such that stmcture
increases as one moves to the right. Moreover, the relationship between stmcture and
the temperature axis was negative. Thus, stmcture of the nectarivore guild was more
deterministic in areas with less variability in temperature (e.g., Heredia).
Gradients in the stmcture of communities in general, and the aerial insectivore
guild in particular, did not coincide with environmental axes in a linear fashion. None
of the environmental attributes significantly predicted the stmcture of these
organizational units.
Correlation Analyses. Correlation analyses identified two measures of stmcture
in two feeding guilds that were associated with environmental gradients (Table 5.12,
Fig. 5.5). Morphological stmcture regarding the mean interspecific difference of the
aerial insectivore guild was negatively associated with the relative variability of
productivity and precipitation (r = -0.674, p = 0.004). Deterministic stmcture occurred
in areas of greater variability. Fmgivores exhibited a positive association between
numerical stmcture and the gradient of mean and variabihty of temperature (rKendaii =
114
0.683, p = 0.017). As the mean temperature increases and its variabihty decreases,
numerical stmcture becomes more deterministic.
Discussion
In 1959, Hutchinson published his pioneering work on food webs, community
stmcture, and diversity. Although various facets have come under scmtiny (Simberloff
and Boeklen, 1981), his work certainly provided order and direction for much of
contemporary ecology. Coupled with consequences of quantitative models of
competitive interactions (e.g., Lotka-Volterra), Hutchinson's mle (species should differ
by a ratio of 1.3 linear units) set the stage for quantitative considerations of competitive
exclusion, limiting similarity, and much of the subsequent theoretical advancement
regarding biotic interactions (Huston, 1994).
Nonetheless, ecology might have advanced more quickly over the last 30 years
if there had been less acceptance of the dogma that density-dependent phenomena, such
as competition, are pervasive and substantial determinants of pattems of diversity and
community stmcture, and more attention had been directed to a lesser known
publication by Hutchinson (1961). Hutchinson (1961) attributed the high diversity of
plankton to the circumvention of equilibrial processes. He contended that
envkonmental variability enhanced the number of available niches, resulting in higher
diversity, and demonstrated that coexistence could be a nonequilibrial phenomenon.
The world is a heterogeneous and variable place (Brown, 1992). Even in supposedly
stable environments, such as tropical rainforests, environmental variability may be
pronounced. Areas that exhibit high degrees of environmental stability and invariability
(prerequisites for density-dependent outcomes) probably are in the minority.
Nonetheless, the assumption that populations are operating at equilibrium is implicit to
much of contemporary theory in ecology (Huston, 1994). If most populations or
115
communities do not experience equilibrial dynamics, then nonequilibrial approaches
must be employed to model community organization.
Bat communities do not exhibit deterministic stmcture in a ubiquitous fashion
(Chapters in and IV). However, the degree to which feeding guilds and communities
exhibit nonrandom stmcture, as predicted by competition theory, is dependent on
environmental parameters. In a majority of situations, variability with regard to
precipitation, productivity, or temperature, was an important influence on the degree of
deterministic stmcture.
Because of morphological and behavioral variabihty, bats are functionally
diverse, and occupy many feeding guilds and trophic levels (Findley, 1993; Fleming,
1988; Willig, 1982, 1986). As a consequence, it is not surprising that results differed
among feeding guilds. The variance of interspecific morphological differences
accounted for a majority of the variation in stmcture among locations regarding the
aerial insectivore, fmgivore, and nectarivore guilds (44.1% to 78.1%). However,
gleaning animalivores responded differently; the mean interspecific difference
accounted for a majority of variation among sites (57.9%). All feeding guilds did
respond similarly, however, in that numerical stmcture accounted for the least amount
of variation among locations.
Four feeding guilds exhibited significant associations with environmental
parameters, however, feeding guilds did not respond in the same manner. Aerial
insectivores and gleaning anunahvores were responsive to variability of productivity
and precipitation, whereas fmgivores and nectarivores responded to variability in
temperature. Because of the diminution of matter and energy moving from lower to
higher levels, more primary productivity is necessary for the sustenance of higher
trophic levels (Connell and Orias, 1964; Rosenzweig, 1977, 1995). Thus, it is not
surprising that animalivores and insectivores responded to variability in productivity.
116
Nonetheless, primary consumers too are affected by levels and variability of primary
productivity, and there is no explanation as to why fmgivores and nectarivores do not
respond in the same fashion.
Temperature has been shown to control photosynthesis, plant growth rates, and
the timing of phenological states (Jones, 1992; Podolsky, 1984). Variabihty of
temperature affects fmit phenology as well (Jones, 1992). Most tropical bats are
precise thermoregulators with fakly invariant body temperatures, yet do not utilize
bouts of torpor or rely on fat reserves to enhance increased metabolic rates during
colder conditions (Fleming, 1988). Thus, bats probably must forage nightly to
overcome an energeticaUy precarious metabolic situation. In more variable
environments, energy balance is probably a more critical consideration than in less
variable environments. To these ends, both direct and indirect effects of variability in
temperature probably has important imphcations regarding fitness, and ultimately
survival for fmgivores and nectarivores. Nonetheless, the same may be said for
insectivores and animalivores; their resources are probably dependent on fmit
phenology, and temperature probably has similar ramifications to their fitness and
survival. These two differences probably are important distinctions underlying the
stmcture of feeding guilds at these two trophic levels.
Stmcture at the community level did not exhibit a significant response to
envu-onmental parameters. Many biotic (e.g., competition, mutualism, parasitism,
predation) as well as abiotic factors (e.g., variation in nutrients, climatic fluctuations,
disturbance) operate simultaneously at the community level. Communities represent an
amalgam of feeding guilds and trophic levels, all of which respond differentially to
biotic and abiotic gradients. Thus, differences in the way feeding guilds respond to
each environmental gradient (i.e., insectivores and animalivores versus fmgivores and
nectarivores) probably confounds any consistent association between communities and
117
environmental parameters. This reason, among others, highlights the importance of
focusing on guilds when evaluating ecological phenomena.
Although stmcture regarding the variance of morphological distances accounted
for a majority of the variation among sites in all but one feeding guild, it did not
respond to any environmental gradients. This does not necessarily mean that this form
of stmcture is uninformative. Species morphologies are constrained by phenomena
occurring over their entire geographic ranges (Ricklefs and Travis, 1980). Moreover,
functional, phylogenetic, and physiological phenomena also constrain the ways
morphology may vary. Either stmcture regarding interspecific variance of morphology
is controlled by some other factor, such as biogeographic or evolutionary constraints on
the variability of morphology, or it is not sensitive to extrinsic attributes of the
community.
Numerical stmcture was most sensitive to environmental parameters. The
abundances of species are probably much more malleable in ecological time than are
morphological attributes. Differential extinction and invasion of morphotypes, or
morphological evolution, must occur to influence the morphological stmcture of a
community (Case and SideU, 1983). Moreover, competitive interactions leading to the
elimination of species probably need be of greater intensity and longer duration than
those that eliminate individuals and alter numerical stmcture. Numerical stmcture, on
average, probably manifests more rapidly than does morphological stmcture. This may
be inferred by its sensitivity to environmental variation. If this were tme, community
organization may be better understood if considered from two time frames. Processes
occurring in evolutionary time, such as size assortment and size adjustment, may set the
stage for the coarse-grained stmcture of a community. In concert, numerical
adjustments occurring over ecological time may be a means of fine-tuning stmcture.
When selection from abiotic environmental variation supersedes that due to biotic
118
interactions, deterministic stmcture may not obtain. The degree to which
morphological or numerical relationships deviate from expectations of competition
theory should be a function of selective forces associated with environmental
variability.
119
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124
Table 5.1.-- Bat communities used to evaluate gradients of stmcture. A, F, G, and N refer to the aerial insectivore, fmgivore, gleaning animalivore, and nectarivore feeding guilds, respectively.
Community
Cahfomia
Iowa
Guanacaste
Guanacaste
Heredia
Puntarenas
Sherman
Rodman
Pem
Caatinga
Country
USA
USA
Costa Rica
Costa Rica
Costa Rica
Costa Rica
Panama
Panama
Pem
Brazil
Reference
Supemant, 1977
Kunz, 1973
Fleming et al., 1972
Laval and Fitch, 1977
Laval and Fitch, 1977
Laval and Fitch, 1977
Fleming et al., 1972
Fleming et al., 1972
Ascorra, in litt
Willig, 1982
Feeding guilds examined
A
A
A,F,G
A, F, G, N,
A, F, G, N
A,F,N
A,F,G
A, F,G
A, G, N
A, F, G, N
125
Table 5.2.— Environmental parameters and their associated acronym in parentheses.
Latitude
Centr2d Tendency
Mean of Mean Monthly Precipitation (MMF)
Mean of Mean Monthly Temperature (MMI)
Mean of Mean Monthly Productivity (MMp)
Within Year Variabihty
Average Across Years of the Within Year Absolute Variability of Precipitation (Mvr)
Average Across Years of the Within Year Absolute Variability of Temperature (Mvt)
Average Across Years of the Within Year Absolute Variabihty of Productivity (Mvp)
Average Across Years of the Within Year Relative Variability of Precipitation (Mcvr)
Average Across Years of the Within Year Relative Variabihty of Temperature (Mcvt)
Average Across Years of the Within Year Relative Variability of Productivity (Mcvp)
Among Year Variabilitv
Absolute Variability Across Years of the Yearly Average Precipitation (VMT)
Absolute Variability Across Years of the Yearly Average TemperaUire (VMI)
Absolute Variability Across Years of the Yearly Average Productivity (VMp)
Relative Variability Across Years of the Yearly Average Precipitation (CVMT)
Relative Variabihty Across Years of the Yearly Average Temperature (CVMO
Relative Variabihty Across Years of the Yearly Average Productivity (CVMp)
126
Table 5.2 Continued
Within Year Variabihty Across Years
Variabihty Across Years of the Within Year Absolute Variability of Precipitation (Vvr)
Variability Across Years of the Within Year Absolute Variability of Temperature (Vvt)
Variability Across Years of the Within Year Absolute Variability of Productivity (Vvp)
Variability Across Years of the Within Year Relative Variabihty of Precipitation (Vcvr)
Variability Across Years of the Within Year Relative Variabihty of Temperature (Vcvt)
Variability Across Years of the Within Year Relative Variabihty of Productivity (Vcvp)
127
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Table 5.6.-- Eigenvalues and percent variation explained by principal components used to characterize environmental gradients. EPCl - EPC4 refer to the first four gradients extracted from the 21 climatic variables.
Principal
component
EPCl
EPC2
EPC3
EPC4
Eigenvalue
10.94
4.37
2.93
1.35
Percent
variation
52.1
20.8
14.0
6.5
Cumulative
variation
52.1
72.9
86.9
93.4
131
Table 5.7.-- Factor loadings for all climatic variables on the first four environmental principal component axes. EPCl - EPC4 refer to the four gradients extracted fromthe suite of climatic variables. Productivity values were calculated minus the intercept (61.9). Variable acronyms are defined in Table 5.2.
Variable
MMT
Mvr
McVr
VMr
CVMT
Vvr
Vcvr
MMt
Mvt
Mcvt
VMt
CVMt
Vvt
Vcvt
MMP
Mvp
Mcvp
VMP
CVMP
Vvp
Vcvp
EPCl
0.067
0.161
0.021
0.153
-0.002
0.201
0.008
-0.017
0.022
0.024
0.004
0.026
0.031
0.040
0.065
0.167
0.126
0.145
0.084
0.199
0.073
EPC2
0.022
0.001
-0.114
0.025
-0.077
0.027
-0.017
-0.014
0.173
0.177
-0.045
0.142
0.201
0.220
0.011
0.007
0.041
0.025
-0.025
0.028
0.082
EPC3
-0.081
-0.008
0.211
0.042
0.246
0.082
0.204
-0.152
-0.020
-0.028
-0.037
-0.038
-0.068
-0.133
0.046
-0.006
-0.044
0.040
0.246
0.083
0.148
EPC4
-0.117
0.191
0.292
-0.014
-0.452
0.116
-0.032
0.036
-0.039
-0.027
0.309
0.153
-0.015
0.064
-0.111
0.189
0.579
-0.033
0.009
0.108
-0.026
132
Table 5.8.-- Pearson's product-moment correlations of each climatic variable with the four environmental principal component axes (EPCl - EPC4). Boldface represents those variables that dominate each principal component. Variable acronyms are defined in table 5.2.
Variable
MMT
Mvr
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VMr
CVMT
Vvr
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MMt
Mvt
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Vvp r
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EPCl
0.752
0.823
-0.427
0.933
-0.204
0.975
-0.239
0.226
-0.203
-0.204
-0.421
-0.371
-0.159
-0.116
0.742
0.850
-0.086
0.919
0.167
0.970
0.049
EPC2
-0.305
-0.330
-0.082
-0.159
0.087
-0.102
0.341
-0.841
0.932
0.943
-0.020
0.802
0.978
0.984
-0.350
-0.307
0.154
-0.159
0.213
-0.095
0.647
EPC3
-0.470
-0.315
0.714
-0.037
0.957
0.080
0.890
-0.369
0.268
0.240
0.100
0.133
0.097
-0.078
-0.466
-0.305
-0.264
-0.037
0.927
0.090
0.739
EPC4
-0.327
0.100
0.481
-0.251
-0.092
-0.077
-0.054
0.011
-0.011
0.009
0.566
0.325
0.029
0.079
-0.317
0.090
0.908
-0.276
0.098
-0.087
-0.099
133
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Variability of Temperature
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143
0
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Relative Variability of Productivity
Figure 5.2~Scattergram of the relationship (r = 0.782) between morphological stmcture characterized by the mean interspecific distance (CPC 1) within the gleaning animalivore guild and the relative variability of productivity (EPC 4).
144
0 u S
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145
u S
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Variability of Temperature
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146
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Figure 5.5~Scattergram of the relationship (randan = -0.674) between morphological stmcture characterized by the mean interspecific distance within the aerial insectivore guild and relative variability in precipitation and productivity.
147
CHAPTER VI
SYNTHESIS
Traditionally, community ecologists have pursued single processes to explain
the organization of natural communities (for a review, see Polls, 1991). Competitive
interactions often have been implicated for inducing the observed morphological
pattems that characterize stmcture. Nonetheless, throughout the 1970s and 1980s
morphological pattems came under intense scmtiny. Many supposedly deterministic
pattems were shown to be more likely the product of chance (Simberloff and Boeklen,
1981). Moreover, as ecologists switched their focus from vertebrates to invertebrates,
especially those living in streams, the fact that competitive interactions do not stmcture
a majority of animal communities became obvious (Power et al, 1988; Strong, 1984).
The expectation that a single factor (i.e., competition) stmctures all communities is
unrealistic. Furthermore, competitive interactions have the potential to operate through
a number of avenues. Consequently, decisions may have been hasty regarding the
frequency at which competitive interactions stmcture communities.
Density compensation is a demonstrable means whereby competitive
interactions give rise to deterministic stmcture. This is tme not only for rodent
systems, where the effects of competitive interactions on community organization are
well understood, but also for bats. In the absence of morphological hyperdispersion
produced by either size adjustment or size assortment, species that are morphologically
similar to other competitors in a feeding guild sometimes exhibit lower relative
abundance because of greater competitive pressure.
Nonetheless, morphological hyperdispersions and density compensation are not
consistent attributes of die organization of bat feeding guilds and communities. Simple
bat communities composed of only the aerial insectivore guild consistentiy exhibit
deterministic stmcture, as predicted under a scenario of size assortment, whereas 148
results from more complex communities are equivocal. The aerial insectivore guild
consistentiy exhibited size assortment in temperate areas, whereas in tropical areas,
stmcture was equivocal. Deterministic morphological stmcture for fmgivores involved
only the variance of interspecific differences, whereas deterministic stmcture for
nectarivoresonly involved the mean interspecific difference. Lastiy, molossid
insectivores consistentiy exhibited stochastic stmcture.
Environmental conditions play an important role in providing the context for the
induction of deterministic stmcture. In fact, the degree to which fmgivores, gleaning
animalivores, and nectarivores exhibited deterministic stmcture was differentially
predictable based on environmental parameters. The specific spatiotemporal context of
environmental factors experienced at a location determines the extent to which
competitive interactions manifest.
This has many implications. First, the role played by competitive interactions,
and probably all other influences on stmcture, is not consistent across sites, and
therefore not pervasive. Nonetheless, this should not discount the relevance of
understanding the ways in which competitive interaction influences community
organization. Moreover, no one determinant of stmcture should be expected to
dominate in all situations. Second, it should not be assumed that phenomena that give
rise to stmcture act independently of other biotic and abiotic influences. Interactions
between causal factors may obscure any consistent indication of deterministic stmcture.
Accordingly, these interactions must be considered before tiie role of a given
phenomenon is dismissed. Lastly, as suggested by Weins (1984), tiie organization of
all communities should not be thought of as dichotomous (deterministic versus
stochastic), but probably is better viewed from the perspective of a continuum from
deterministic to stochastic.
Altiiough tiie predictions of competition theory may have limited apphcability to
all communities, they do provide a template from which communities may be viewed. 149
Environmental parameters such as productivity, precipitation, temperature, and latitude
are only a few of the additional factors that influence the significance of competitive
interactions. Moreover, many other factors such as morphological constraints and
biogeographic radiations of congeners probably serve to modulate the role of
competition in community assembly and ultimately species coexistence. The basis of
coexistence should be viewed from the perspective of equilibrial competition theory.
However, a complete understanding probably necessitates appreciation of abiotic
factors that influence equilibrium. In an invariable worid, there is no disturbance,
population densities may mildly oscillate around carrying capacity, and limiting
similarity defines which species coexist. Nonetheless, the worid is not invariant.
Disturbances do exist and variability does induce density-independent mortality
(Andrewartha and Birch, 1954,1988). These factors, and more, determine a
communities position on a continuum describing stmcture.
150
Literature Cited
Andrewartha, H. G., and L. C. Birch. 1954. The distribution and abundance of animals. The University of Chicago Press, Chicago, Illinois.
Andrewartha, H. G., and L. C. Birch. 1988. The ecological web: more on the distribution and abundance of animals. The University of Chicago Press, Chicago, Illinois.
Pohs, G. A., Editor. 1991. The ecology of desert communities. The University of Arizona Press, Tucson, Arizona.
Power, M. E., R. J. Stout, C. E. Gushing, P. P. Herper, F. R. Hauer, W. J. Mathews, P. B. Moyle, B. Statzner, and I. R. Wais de Badgen. 1988. The role of disturbance in stream ecology. Joumal of the North American Benthological Society 7: 456-479.
Simberloff, D., and W. Boeklen. 1981. Santa Rosedia reconsidered: size ratios and competition. Evolution 35: 1206-1228.
Strong, D. R., Jr. 1984. Exorcising the ghost of competition past: phytophagous insects. Pages 28-41 in: D. R. Strong, D. Simberloff, L. G. Abele, and A. B. Thistie, Editors. Ecological communities: conceptual issues and the evidence. Princeton University Press, Princeton, New Jersey.
Weins, J. A. 1984. On understanding a non-equilibrium world: myth and reality in community pattems and processes. Pages 439-437 in: D. R. Strong, D. Simberloff, L. G. Abele, and A. B. Thistle, Editors. Ecological communities: conceptual issues and the evidence. Princeton University Press, Princeton, New Jersey.
151
APPENDIX A
LOCATION AND ANNOTATED DESCRIPTION OF
FIFTEEN BAT COMMUNITIES
1. IOWA: Boone County, Honey Creek and its adjacent areas.
42°0'N, 94°0'W. This community occurred in primary and secondary
deciduous forest along two tributaries of the Des Moines River: Honey Creek
and Pease Creek (Kunz, 1973).
2. CALIFORNIA: Inyo County, Surprise Canyon, 5 km East of Ballarat.
36°0'N, 117°15'W. Located at Chris Wicht Camp, in the Panamint Mountains,
just west of Death Valley. Habitat is described as typical of that of the Mojave
Desert. Larrea tridentata and Atriplex sp. are conspicuous vegetative
components (Supemant, 1977).
3. MEXICO: Estado de Chiapas, La Selva La Candona, Reserva de la Biosfera
Montes Azules. 16''6TSf, 90°57'W. Habitat described as lowland humid
rainforest. Conspicuous floral components consist of Talauma sp., Licania sp.
Brosimum sp., Swietenia sp., Dialium sp., and Ficus spp (Medellin, 1993).
4. COSTA RICA: Provincia de Heredia, 1 km upstream from Puerto Viejo.
10°30'N, 84°0'W. Tropical wet forest, in the Caribbean lowlands (LaVal and
Fitch, 1977).
5. COSTARICA: Provincia de Puntarenas, near the town of Monteverde on the
Pacific slope of the Cordillera deTilleran. lO'SO'N, 84°45'W. Premontane
moist and wet tropical forests (LaVal and Fitch, 1977).
6 COSTARICA: Provincia de Guanacaste, 4 km Northwest of Canas. 10°28'N,
8 5 " 9 ^ . Habitat described as tropical dry forest. This community was
sampled during two time periods (Fleming et al., 1972; LaVal and Fitch, 1977).
152
7. PANAMA: Canal Zone, Fort Sherman Military Reservation, 3 km West of
Cristobal. 9^201^, 79°57'W. Habitats sampled were riparian, swamp, and
secondary growth tropical forests (Fleming et al., 1972).
8. PANAMA: Canal Zone; Lake Gatun, Barro Colorado Island. 9°10TSf, 79''51'W.
Habitat described as tropical moist forest (Bonaccorso, 1975).
9. PANAMA: Canal Zone, Rodman Naval Ammunition Depot, 8 km West of
Balboa. 8''57'N, 79°37'W. Habitats sampled were riparian, swamp, and
secondary growth tropical forests (Fleming et al., 1972)
10. COLOMBIA: Departmento Del Valle, El Topacio Farm, 2 km South of Pance.
4''30'N, 76°45'W. Habitat characterized as secondary subtropical forest
(Thomas, 1972).
11. COLOMBIA: Department del Valle, near the village of Zabelitas. 4°30'S,
76''30'W. Habitat was tropical rainforest (Thomas, 1972).
12. PERU: Departmento de Loreto; Provincia de La Requena, Centro de
Investigacciones Janero Herrera, 140 km South Southwest of Iquitos.
4*'55'S, 73°45'W. Vegetation characterized as low-terrace broadleaf tropical
rain forest (Ascorra, in litt).
13. BRASIL: Municipio de Crato, Ceara, in the Floresta Nacional Araripe-Apodi'.
7''14'S, 39° 23IV. Vegetation characterized as sclerophyllous and semi-
diciduous (Edaphic Cerrado; Willig, 1982).
14. BRASIL: Municipio de Exu, Pemambuco. 7''35'S, 39°40'W.
Described as a xerophytic flora with members of the Cataceae and
Euphorbiaceae conspicuous components (Caatinga; Willig, 1982).
153
Liturature Cited
Bonaccorso, F. J. 1975. Foraging and reproductive ecology in a community of bats in Panama. Dissertation. University of Florida, Gainesville, Florida.
Fleming, T. H., E. T. Hooper, and D. E. Wilson. 1972. Three Central American bat communities: stmcture, reproductive cycles, and movement pattems. Ecology 53:555-569.
Kunz, T. H. 1973. Resource utilization: temporal and spatial components of bat activity in central Iowa. Joumal of Mammalogy 54: 14-32.
Laval, R. K., and H. S. Fitch. 1977. Stmcture, movements, and reproduction in three Costa Rican bat communities. Occasional Papers of the Museum of Natural History 69: 1-28.
Medellin, R. A. 1993. Estmctura y diversidad de una comunidad de murcielagos en el tropico humedo Mexicano. Pages 333-354 in: R. A. Medellin and G. Ceballos, Editors. Avances en el estududio de los mamiferos de Mexico. Asociacion Mexicana de Mastazoologia, Mexico City.
Suprenant, H. R. 1977. Noctumal activity pattems in a bat fauna of southem Califomia with comments on the physiological ecology of Pipistrellus hespems. Thesis. Califomia State University, Fullerton.
Thomas, M. E. 1972. Preliminary study of the annual breeding pattems and population fluctuations of bats in three ecologically distinct habitats in southwestern Colombia. Dissertation. Tulane University, New Orleans, Louisiana.
Willig, M. R. 1982. A comparative ecological study of Caatingas and Cerrado chiropteran communities: composition, stmcture, morphometries, and reproduction. Dissertation. University of Pittsburgh, Pennsylvania.
154
Figure A. 1.-Graphical representation of the approximate location of each community evaluated.
155
APPENDDC B
DESCRIPTION OF FEEDING GUILDS
Aerial Insectivore -Those bat species that principally consume insects which are
obtained from the air while in flight. Members of the families
Mormoopidae, Emballonuridae, Furipteridae, Thyropteridae, and
Vespertilionidae are commonly associated with this mode of feeding.
Fmgivore -Those bat species that primarily consume fmit. Members of the
phyllostomid subfamilies CaroUiinae, Stenodermatinae, and Brachyphyllinae
are commonly considered fmgivores.
Gleaning animalivore —Those bat species that principally consume invertebrates as
well as vertebrates that are gleaned from surfaces, such as the ground, leaves,
and the bark of trees. Members of the nominal subfamily of the
Phyllostomidae are commonly considered gleaning animalivores.
Molossid insectivore —Those bat species that principally consume insects that are
obtained from high altitudes (30-300 m). Most members of the family
Molossidae obtain resources in this fashion.
Nectarivore -Those bat species that principally consume nectar and pollen from
flowers. Members of the subfamilies Lonchophyllinae, Phyllonycterinae, and
Glossophaginae (Phyllostomidae) commonly are nectarivores.
Piscivore -Those bat species that principally consume fish. Noctilio leporinus
(Noctilionidae) and Myotis vivesi (Vespertilionidae) are representatives of this
feeding guild.
156
Sanguinivore -Those bat species that primarily consume blood. Desmodus
rotundus. Diamus voungi. and Diphylla ecaudata are representatives of this
feeding guild.
157
APPENDDC C
DESCRIPTIONS OF MORPHOLOGICAL CHARACTERS
Forearm length - Distance between the most distal edge of the elbow and
wrist.
Greatest length of skull - Distance between the anterior most point on the
rostmm and the most posterior point on the skull.
Condylobasal length — Distance between the anterior most edge of the
premaxillae and the posterior most edge of the occipital condyles.
Postorbital constriction - Least width of the skull between the orbits.
Breadth of the braincase - Greatest width of the braincase between the parietals.
Breadth across the upper molars Greatest distance between the widest set of upper
molars.
Length of the maxillary toothrow — Length from the anterior edge of the first tooth
present in the maxillae to the posterior edge of the last molar.
158
APPENDDC D
STRUCTURE OF FIFTEEN BAT COMMUNITIES
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202
APPENDIX E
SIMULATION PROGRAM TO
EVALUATE DENSITY COMPENSATION
203
#include <iostream.h> #include <string.h> #include <correlation.h> #include <quicksort.h> #include <console.h> #include <time.h> #include <math.h> #include <stdlib.h>
#defme NUM.SIMS 1000
void Morph_Dif(int a,int b,int d, double sumLength[l, double morph[l);
void main(void) {
char File l[50],File2[50]; FILE *fp; int numSims; //number of times to run simulation int numSp; //number of species in community int numCh; //number of morphological characters int x,y,count; //looping variables double PearsonAb; //Pearson correlation for abundance double SpearmanAb; //Spearman correlation for abundance
//get input data c o u t « "Enter name of input file: "; cin.getline(Filel,52); c o u t « "How many times to run simulation:"; cin » numSims;
//start the timer unsigned int begin = clock();
/ * * * * * • * * * * * * * * * * * • * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Read species abundances,morphological data, and weights * * * • * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /
if ((fp=fopen(Filel,"r"))=NULL) { printf("Cannot open file\n"); exit(l);
fscanf(fp,"%d\n",&numSp); fscanf(fp,"%d\n",&numCh); cout « "Number of species = " « numSp « endl; c o u t « "Number of morphological characters = " « numCh « endl;
//create new arrays to hold abundances, morphological data double* actualAb = new double[numSp]; int index = numSp*numCh; double* morph = new double [index!;
204
double sumAb = 0.0;
//read abundance and morphological data double dist; for (x=0; x<numSp; x-H-)
fscanf(fp,"%Lf',&actualAb[x]); //read abundance sumAb -1-= actualAb[xl; //record abundance sum for (y=0; y<numCh; y-f-f-) {
index = numCh*x + y; fscanf(fp,"%Lf,&dist); morph[indexl = loglO(dist);
}
fclose(fp);
Transform abundances into percentages
for (x=0; x<numSp; x++) actual Ab[x]=100.0*actualAb[x]/sumAb;
//create dynamic arrays for storing simulation info double* abundance = new double[numSp]; double* sumLength = new double[numSpl; double* pearsonAb = new double[numSimsl; double* spearmanAb = new double[numSims];
Begin cycle for three methods of calculating distances
for (int m=0; m<3; m-H-)
double PearAbProb=0.0; double SpearAbProb=0.0;
//Calculate sums of morphological distances Morph_Dif(m,numSp,numCh,sumLength,morph);
//Calculate Pearson and Spearman correlation coefficients //for actual abundances PearsonAb = Pearson(actualAb,sumLength,numSp); SpearmanAb = Spearmans_Rank(actualAb,sumLength,numSp);
Assign random abundances and convert to percentages * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /
205
double maxAb = 100.0-numSp*0.1;
//set the random seed with the current time int s = (unsigned int) clockO; srand(s);
for (count=0; count<:numSims; count-H-)
sumAb=0.0; for (x=0; x<numSp; x++)
abundance[xl=100.0*rand()/32767.0; sumAb-i-=abundance[x];
}
double convertToPercent=maxAb/sumAb;
for (x=0; x<numSp; x++) {
abundance[x]=abundance[x]*convertToPercent-i-0.1; }
Calculate Pearson and Spearman correlation coefficients for simulated abundances, and calculate p's ^h ^p ^F ^F ^h ^ ^F ^h ^h ^^ ^ ^p ^ ^h ^ ^ ^F ^h ^h ^ ^h ^h ^ ^F ^h ^ ^h ^h ^ ^h ^n ^ ^P ^h ^ ^h T * ^F • P *!* ^ ^ ^ "I* ^h ^h •!* "F ^ * l* *n • I * ^F "P ^ •P * l* /
pearsonAb [count] = Pearson(abundance,sumLength,numSp); if (pearsonAb[count]>=PearsonAb) PearAbProb-»-=l/(double)
numSims;
spearmanAb[countl = Spearmans_Rank(abundance,sumLength,numSp);
if (spearmanAb[countl>=SpearmanAb) SpearAbProb-i-=l/(double) numSims;
}
Sort simulated correlation coefficients
quicksort(pearsonAb,0,numSims-1); quicksort(spearmanAb,0,numSims-1);
Determine name of output file * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /
strcpy(File2,Filel);
206
Determine name of output file
strcpy(File2,Filel); switch (m) {
case 0: strcat(File2,".n-l"); break;
case 1: strcat(File2,".n-2"); break;
case 2: strcat(File2,".n-(n-2)"); break;
}
Write simulation data to output file with tab delimiters
if ((fp=fopen(File2,"w"))==NULL) { printf("Caimot open file\n"); exit(l);
} fputs("Actual Data\n",fp); fputs("Species ",fip); j^utsfSum Dist. ",fp); fputs("% Density\n",fp); for (x=0; x<numSp; x-H-) {
fprintf(fp,"%d ",x); ft)rintf(fp,"%lf ",sumLength[x]); fprintf(fp,"%lAn",actualAb[x]);
} fiputs("\n",fp); fputs("%Density\n",fp); fputsf Pearson ",fp); fputs("Spearman\n",fp); fputs("r ",fp); fprintf(fp,"%Lf ",PearsonAb); fprintf(fp,"%Lf\n",SpearmanAb); fputs("p '\fpy, fprintf(fp,"%Lf ",PearAbProb); fprintf(fp,"%Lf\n",SpearAbProb); fputs("\n",fp); fputs("SIMULATION\n",fp); fputsr%Density\n",fp); fputsfPearson ",fp); fputs("Spearman\n",fp); for (count=0; count<numSims; count-H-) {
^rintf(^,"%Lf ",pearsonAb [count]); 207
unsigned int elapsed = (clockQ - begin)/CLOCKS_PER_SEC; cout « "Time to run simulation: " « elapsed « endl;
}
void Morph_Dif(int m, int numSp, int numCh, double sumL[], double morph[]) {
double distance; //store total distance between two species double theLargest; //store the largest distance for a species double smaller; //store the 2nd smallest distance double smallest; //store the smallest distance double sumDifSqr; //use for calculating distance int x,y,z; //looping variables int fix_index; //index of fixed species int rel_index; //index of iterative species
for (x=0; x<numSp; x-H-) {
theLargest=0.0; smallest=100000.0; smaller=1000000.0; sumL[x] = 0.0; for (y=0; y<numSp; y-H-) {
sumDifSqr=0.0; for (z=0; z<numCh; z-H-)
fixjndex = x*numCh -i- z; rel_index = y*numCh + z; sumDifSqr+=pow((morph[fix_index] -
morph[rel_index]),2.0); } distance=sqrt(sumDifSqr); sumL[x] += distance; if (theLargest < distance) theLargest = distance; if(y!=x)
if (distance < smallest)
smaller=smallest; smallest=distance;
else if (distance < smaller)
smaller=distance; }
}
if (m==l) sumL[x] -= theLargest; if (m==2) sumL[x] = smaller + smallest;
} }
208
APPENDK F
SIMULATION PROGRAM TO EVALUATE SIZE ASSORTMENT
209
#include <iostream.h> #include <fstream.h> #include <stdlib.h> #include <stdio.h> #include <string.h> #include <math.h> #include <time.h> #include "general.h" #include "write_file.h" #include "spanningtree.h" #include "constants.h"
struct name { char filename[40]; name* next;
} ;
double fact (int); void combination (int,int,int,cell[],char[]); voidrandom_combination(int,int,cell[],char[]); voiddistance_matrix(int,int,cell[],cell[]);
void main() {
c o u t « "Welcome to the MST Simulation Center" « endl;
ifstream Input; //input stream charfilename[40]; //input file name double c; //calculated number of combinations int pools; //number of species pools to use int s; //size of real community int n; //number of species int v; //number of variables measured char outfile[40]; //output file name
//get input file name from user c o u t « "Enter input file name:"; cin » ws; cin.getline(filename,42);
//start time int start = (unsigned int) clock();
//try to open specified file, exit if error occurs Input.open(filename,ios: :in); if(!Input)
cerr « "This file cannot be opened or does not exist"; exit(l);
}
//read in specs 210
endl;
Input» s; Input» n; Input» v; Input» pools; c o u t « "The file indicates that" « s « " species comprise the community," «
c o u t « "there are " « n « " species in the pool," « endl; c o u t « "there are " « v « " variables," « endl; c o u t « "and there are " « pools « " pools." « endl;
//read in output file names //Input» ws; name* outlist = new name; name* tempname = outlist;
for (int i = 0; i < pools; i-H-) {
tempname->next = new name; Input»tempname->next->filename; tempname = tempname->next;
} int* pool = new int[pools-i-l]; //array to hold pool size for each
range cell* variables = new cell[n-i-l]; i = l ;
of pool number
//array of lists containing variables //counter to keep track
matnx
//read in morphological data for (int count=l; count < (n-»-l); -H+count) {
int current_pool; Input» current_pool; variables[count].next = new cell; cell* temp = variables [count].next; for (int X = 0; X < v; -H-x) {
Input»temp->var; temp->next = new cell; temp = temp->next;
} if (current_pool > i)
pool[i] = count-1; -H-i;
} } pool[i] = n; Input.closeO;
//calculate the morphology difference matrix cell* dist = new cell[n-»-l];
distance_matrix(n,v,variables,dist);
211
//list to contain distance
//iterate through the pools and generate combinations //this block will lead to the minimum spanning tree calculations tempname = outlist; for (1=1; i<(pools-l-l); -H-i) {
//determine output file name tempname = tempname->next; strcpy(outfile,tempname->filename); c o u t « "Current outfile is: " « outfile « endl; int m = pool[i];
//calculate combinations c = fact(m)/(fact(s) * fact(m-s)); c o u t « "Number of combinations: " « c « endl; c o u t « "Cutoff point for combinations is currently " «
MAX_COMBINATIONS*2 « endl;
//if number of combinations is too large, use random set, otherwise use //all combinations if (c > MAX_C0MBINATI0NS*2) {
c o u t « "Simulated distributions will be generated randomly " « MAX_COMBINATIONS « " times." « endl;
random_combination(s,m,dist,outfile); } else {
c o u t « "Simulated distributions will use all combinations" « endl;
}
combination (s,m, (int) c,dist,outfile); }
}
int elapsed = ((unsigned int) clock() - start)/CLOCKS_PER_SEC; c o u t « "Elapsed time was " « elapsed « " seconds" « endl;
//procedure distance_matrix //This procedure uses sum of squared distances of all variables for each // pair of species in the pool to construct a matrix //Parameters: // n - size of the species pool // V - number of variables // variables[] - array of lists containing measurements for each species
// dist[][] - array of morphological distances
void distance_matrix(int n,int v,cell variables[], cell dist[])
for(inti = 2;i<n-i-l;-H-i) {
dist[il.next = new cell; cell* d_temp = dist[i].next; for (int j = l;j<i;-i"HJ) {
double sum = 0.0; 212
cell* i_temp = variables[i].next; cell* j_temp = variables [j].next; for (int k=0; k<v; -H-k)
sum += pow((i_temp->var - j_temp->var),2); Ltemp = i_temp->next; j_temp = j_temp->next;
d_temp->var = sqrt(sum); if (j == (i - 1)) d_temp->next = NULL; else {
}
d_temp->next = new cell; d_temp = d_temp->next;
}
//function fact // function calculates the factorial of a number
double fact (int n) {
if (n< 2) return (1); else return (n * fact(n-l));
}
//procedure combination //This procedure finds all possible combinations of s numbers drawn from // a pool of n. It does not count the first combination (1 to s) because // that is assumed to be the "real" community. For each combination the // spanning tree function is called to build variance and mean arrays //Parameters: // s - size of community // n - size of pool // dist[] - morphological distance matrix //Calls // procedure spanning_tree // procedure write_to_file;
void combination (int s, int n, int c, cell dist[], char outfile[])
int* sp = new int[s+l]; //array containing the combination sequence double real_mean; //mean of spanning tree lengths for real community double real_variance; //variance of span, tree lengths for real community double mean; //variable to hold mean length for simulated
comm. double var; //variable to hold mean var for simulated
community
for (int X = 1; X < (s-i-1); -H-x) sp[x]=x; if (sp[s] == n)
213
c o u t « "only one combination" « endl-spanning_tree(sp,s,real_mean,real_variance,dist)-c o u t « ||Mean for real community:" « real.mean « endl; c o u t « Variance for real community:" « real_variance « endl;
//calculate spanning tree for real community spanning_tree(sp,s,real_mean,real_variance,dist);
int count = 0; double* means = new double[c]; double* variance = new double[c]; while (sp[l] !=(n-s-i-l))
int check = 0; inty = 1; while (y < (s-i-1) && check == 0) {
if((sp[y] + s-y)==n)
check = 1; ++sp[y-l]; inti = sp[y-l]; for (int z = y; z < (s-i-1); -H-Z)
++i; sp[z] = i;
} } -H-y;
} if (check == 0) -H-sp[s]; else check=0; spanning_tree(sp,s,mean, var,dist); means[count] = mean; variance[count] = var; -H-count;
} c o u t « "Through iteration, found " « count« " combinations different from
real"« endl; write_to_file(count,s,n,means,variance,real_mean,real_variance,"Actual",outfile); delete[] means; delete[] variance; delete[] sp;
}
//This procedure operates similar to combination() except it doesn't iterate through //all possible combinations, but calculates them randomly void random_combination (int s, int n,cell dist[],char outfile[]) {
double real_mean; //mean of sp. tree for real com.
double real_variance; //var of sp. tree for real com. 214
double mean; //mean of sp. tree for simulation ^
double var; //var of sp. U-ee for simulation
double means[MAX_COMBINATIONS]; //array of sp. tree means double vanance[MAX_COMBINATIONS]; //array of sp. tree variances int* randjist = new int[n-»-1 ]; //array to check for dupUcations int* sp = new int[sH-l]; //array containing
combinations int seed = (unsigned int) clock(); //seed for randomization
//use the seed to initialize randomization srand(seed);
//calculate spanning tree for real community for (int X = 1; X < (s-Hl); -H-X) sp[x]=x; spanning_tree(sp,s,real_mean,real_variance,dist);
//generate random combinations for (X = 0; X < MAX_COMBINATIONS; -H-x) {
for (int y = 1; y < (n-i-1); -H-y) rand_list[y] = 0; int count = 0; while (count < s) {
int value = n*rand()/RAND_MAX -i- 1; if (value <= n && rand_list[value] == 0) {
-H-count; sp [count] = value; rand_list[value]= 1;
} } spanmng_tree(sp,s,mean,var,dist); means[x] = mean; variancefx] = var;
write_to_file(MAX_COMBINATIONS,s,n,means,variance,real_mean,real_varian ce, "Random",outfile); }
//constants const MAX_COMBINATIONS = 500;
struct cell { double var; cell* next;
};
//prototypes void spanning_tree(int sp[],int s,double &mean, double &var,
cell dist[]);
215
' ' i i j i
/ /
// File: Spanning Tree / /
// Programmer: Alec Shaner //Date: 1/15/94 / /
// This file finds the minimum spanning lengths based on a distance // matrix. It returns (by reference) the mean and variance of the lengths
#include "general.h" #include "spanningtree.h" #include <MFSET.h> #include <stats.h>
struct edge {
int vl; int v2; double cost;
};
double find_cost(int,int,cell[]);
void sparming_tree(int sp[],int s,double &mean, double &var, cell dist[]) {
//initialize MFSET int* Parent = new int[s-f-l]; for (int X = 1; X < (s-J-1); -H-x) Parent[x] = -1;
//generate available edge list edge* avail = new edge[s*(s-l)/2]; //create mst edges double* mst = new double[s-l];
int count = 0; for(x= 1; x<s;-H-x) {
for (int y = x-f-1; y < (s+1); -H-y) {
avail[count].vl =x; avail[count].v2 = y; avail [count] .cost = find_cost(sp[x],sp[y],dist); -H-count;
} } //sort avail list for (x=0; x<count-l; -H-x) {
for (int y=x-i-l; y<count; -H-y) {
if (avail[x].cost > avail[y].cost) 216
{ inttl =avail[x].vl; int t2 = avail[x].v2; double tc = avail[x].cost;
avail[x].vl = avail[y].vl; avail[x].v2 = avail[y].v2; avail [x] .cost = avail [y].cost;
avail[y].vl =tl; avail[y].v2 = t2; avail[y].cost = tc;
}
count = 0; int i = 0;
//find edges in minimum spanning tree while (i<(s-l)) {
int V = avail[count].vl; int w = avail[count].v2; int pv = find(v,Parent); int pw = find(w,Parent); if (pv != pw ) {
mst[i] = avail [count] .cost; merge(pv,pw,Parent); -H-i;
} -H-count;
}
//calculate mean and variance for spanning tree mean = Calculate A verage(SumXdouble(s-l,mst),s-l); var = CalculatePVar(SumXdouble(s-l,mst),SuniX2double(s-l,mst),s-l);
//clean up delete[] Parent; delete[] avail; delete[] mst;
}
double find_cost(int i,int j,cell dist[]) {
int index; //indicates index of list int pos; //indicates position in list
i f ( i > j ) {index = i; pos =j;} else {index =j; pos = i;}
217
V.VS*
cell* d_temp = dist[index].next; int count = 1; while (count < pos)
-H-count; d_temp = d_temp->next;
return d_temp->var; }
//function prototypes void write_to_file(int c,int s,int n,double means [],double variance[],
double real_mean,double real_variance, char type[],char[]);
/ / * * * * * * : i c 4 : * * * * * * 4 ( 4 : * * 4 : * * * * * 4 : * * * * 4 : * * : | c * * * 4 : * * * 4 : * : i c * * * * 4 : 4 : * * 4 : * * 4 : * : | c * : i : : ) : : t : 4 : 4 : * * * : t : * * 3 ) :
* * * *
/ / // File: Write.File / / // Programmer: Alec Shaner //Date: 1/15/95 / / // Purpose: This procedure creates an output file containing the simulation // results with tab delimiters / /
* * * *
#include "write_file.h" #include <iostream.h> #include <fstream.h> #include <stdlib.h> #include <console.h> #include <quicksort.h>
void write_to_file(int c,int s,int n,double means[],double variance[], double real_mean,double real_variance, char type[],char outfile[])
{ FILE *fp; //ofstream Output; double p_means; double p_variance; char delimeter = Vt';
//sort the two arrays quicksort(means,0,c-1); quicksort(variance,0,c-1);
//calculate p-values by iteration 218
N.'—
inti = c-l; while (real_mean < means[i] && i >= 0) --i; p_means = (double)(c-i)/(double)c; i = 0; while (real_variance > variance[i] && i < c) ++'i; p_variance = (double)i/(double)c;
//write information to output file if ((fp=fopen(outfile,"w"))==NULL) {
printffCannot open file\n"); exit(l);
} fputs("Community ",fp); fprintf(fp,"%d\n",s); fputs("Pool ",fp); ^rintf(fp,"%d\n",n); fputs("Combinations ",fp); fprintf(fp,"%d\n",c); fputs("Type ",fp); fprintf(fp,"%s\n",type); fputs("\n",fp); fputs("Real Community\n",fp); fputs("Mean ",fp); fprintf(fp," %lf\n" ,real_mean); fputs(" Variance ",fp); fprintf (fp," %lf\n" ,real_variance); fputs("\n",fp); fputs("P-Values\n",fp); fputs("Mean ",fp); fprintf(fp,"%lf\n",p_means); fputs("Variance ",fp); fprintf(fp,"%lf\n",p_variance); fputs("\n",fp); fputs("Simulations\n",fp); fputs("Means ",fp); fputs("Variances\n",fp); for (int X = 0; X < c; ++x)
fprintf(fp,"%lf ",means[x]); fprintf(fp,"%lf\n",variance[x]);
} fclose(fp);
}
//function prototypes void swap (float [],int,int); int partition (float [],int,int); void quicksort (float[],int,int);
void merge (int i, int j , int Parent[]); int find (int i, int Parent[]);
#include <quicksort.h> #include <MFSET.h>
219
\r.Tm
/ / // File: MFSET / /
// Programmer: Alec Shaner //Date: 1/15/95 / / // This file contains simple merge-find set functions using an // array based set system. It utilizes weighted merges and // path compression so the Parent array must be initialized to // -1. Children index to their parent, roots index to the // negative of the number of children / / / / s i : * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
void merge (int i, int j , int Parent[]) {
int X = Parent[i] -I- Parent[j]; if(Parent[i]>Parent[j]) {
Parent[i]=j; Parent[j] = x;
} else {
Parent[j] = i; Parent[i] = x;
} }
int find (int i, int Parent[]) {
intj = i; while (ParentOl > 0) j = Parent[)]; int k = i; while (k !=j)
int t = Parent[k]; Parent[k]=j; k = t;
} return j ;
}
/ / * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
/ /
// File: quicksort / /
// Programmer: Alec Shaner*
// *: This is basically the quicksort routine from an example in Object // Oriented Programming Using C-H-, by Ira Pohl, with the code modified
220
// to work with an array based // implementation. / / / / * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
//Function wrong_order // This function takes as inputs an array, the indices from and to, and // an order value: 0 specifes check for 2-lex-precedes order and 1 // specifes 1-lex-precedes order. The function returns TRUE if the two // coordinates are out of lexiographic order
void swap (float v[],int from,int to) I
float temp = v[from]; v[from] = v[to]; v[to] = temp;
}
int partition (float v[],int from,int to)
int front = from-I-1; int back = to; float compare = v[from];
while (front < back)
//search forward for out of order element while ((front<back) && (compare > v[front])) {
-H-front;
//search backward for out of order element while ((front<back) && (compare <= v[back])) {
—back;
swap(v,front,back); }
//insert mid position comparison element if (compare >= v[front])
swap(v,from,front); return front;
} else
swap(v,from,front-1); return (front-1);
} }
221
void quicksort (float v[],int from, int to)
int mid;
if (from < to) { if (from == to - 1) //2 elements
if ( v[from] > v[to])
swap(v,from,to);
} else {
mid = partition(v,from,to); quicksort(v,from,mid-1); quicksort(v,mid-f-1 ,to);
} }
This is a general header for calculating simple statistics. It calculates the following statistics:
Mean Standard Deviation Variance Standard Error
NOTE: It also contains functions to sum and sum the squares of arrays. Two copies are provided, one for integer arrays and the other for double arrays.
All functions return float values.
float SumXint(int arraySize, int *Y); float SumX2int(int arraySize, int *Y); float SumXfloat(int arraySize, float *Y); float SumX2float(int arraySize, float *Y); float CalculateAverage(float SumX, int n); float CalculateSE(float SumX, float SumX2, int n); float CalculateSD(float SumX, float SumX2, int n); float CalculateVar(float SumX, float SumX2, int n); float CalculatePVar(float SumX, float SumX2, int n);
/ / * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* *
/ /
// File: Stats / /
// Programmer: Alec Shaner //Date: 1993 / /
// This file contains a set of statistical fiinctions used for descriptives 222
V . T l l
/ / / / * * * * * * * * * * * * * * * ; ^ ; ^ 5 ^ 5 ^ ^ j ^ j ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ _ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ _ ^ _ ^ ^ _ ^ ^ _ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^
* *
#include <math.h> #include "stats.h"
y * * * * * * * * * * * * * * 5 | e * * * * * * : ) c : ( : : | . : ( . 4 . 5 | ( s ) . ^ j ( , j ^ 5 , . ^ ^ j ^ j ^ ^ ^ j ^ ^ j ^ j ^ j ^ ^ j j , j ^ j j , j ^ j | , j j , j j j j | j j ^
Sum the values of an array of integers, return sum as a float * * * * * * * * * * * * * * * * * ^ 5 l . : ^ C 5 | j j J . : j 5 j , , j ^ 5 ^ j , j ^ j , j ^ j ^ j , j j ^ j ^ j j . j ^ ^ j | , ^ j ^ j j j j | j j ^ . j | , j ^ j | , j j . j j , j ^ j ^ j | j
float SumXint(int arraySize, int *Y)
int count; float SumX=0;
for (count=0; count<(arraySize); count-H-) { SumX-i-=*(Y-K:ount);
} return SumX;
}
/^ t ^ t ^ t ^ ^ ^ ^ ^# ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ -I)- ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ »X. -J,- ^^ .Jf. ^ ^ ^ ^ ^^ ||- ^^ -J^ ^^ ^ ^ ^^ ^^ J)- ^^ ( ^ ^ ^ ^ ^ >|- ^ ^ ^ - -J- ^^ ^ ^ ^ ^ ^^ ^ ^ ^U ^^ ^ ^ ^ ^ ^ ^ 4 ^ ^ ^ ^ ^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^* ^* ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ P ^^ P P ^^ P P ^p P p K ^p P P K p p ^p p p p ^p p ^» ^p p ^p p ^p ^^ P p ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ *T* ^^ ^^ ^^ ^^ ^^
Sum the squared values of an array of integers, retum sum as a float 3|C !|C 9|C 5|C «|C 3fC 3|C 9|C SfC SfC 3JC 3|C SfC 3|C 9|C 9|C 9|C 3|C 3)C 9)C 3|C 3|C 3|C 3|C 3|C 3|! 3|» SfC SfC 3|C 3|C 3|C 3|C 3|C !^ 3|C SfC 3f» S ^ 3|C 3|C j|C 9|C 9)C 3fC 3]C s|C 3|£ 3|C 3|C 3|C 3|C 3fC 3|C 3|C 3|C S|C SfC 3(C « ^ 9|C 3|C 9fC ^ 3 p 3 ^ ^ ^ /
float SumX2int(int arraySize, int *Y) {
int count; float SumX2=0;
for (count=0; count<(arraySize); count-H-) { SumX2-i-=pow(*(Y-i-count),2.0);
} retum SumX2;
}
/ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Sum the values of an array of floats, retum sum as a float * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /
float SumXfloat(int arraySize, float *Y) {
int count; float SumX=0.0; for (count=0; count<(arraySize); count-H-) {
SumX-f=*(Y-K:ount); } retum SumX;
}
/ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Sum the squared values of an array of floats, retum sum as a float * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /
float SumX2float(int arraySize, float *Y)
223
• — ^ ^ ^ ^ — ^ - ^ ^ —
)
int count; float SumX2=0.0;
for (count=0; count<(arraySize); count-H-) { SumX2-i-=pow(*(Y-i-count),2.0);
} retum SumX2;
y * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * : ( . : | . : | c : | c : ) t ; ( . : ^ : ( : 5 | s : ( . : j ( : ^ ; , . j ^ ^ : ^ ; ^ ; ^
CalculateAverage takes as its arguments a sum and the number of observations comprising the sum * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * : ( : : ( . : ( £ * * * * * * * * * * * * /
float CalculateAverage(float SumX, int n) {
float average,N=n;
average = SumX/N; retum average;
}
CalculateSD calculates the standard deviation, taking as its arguments a sum, a sum of squares, and the number of observations
float CalculateSD(float SumX, float SumX2, int n) {
float SD,N=n;
if (n>l) SD=sqrt((SumX2-pow(SumX,2.0)/N)/(N-1.0)); retum SD;
}
/ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Calculate Var calculates the sample variance, taking as its arguments a sum, a sum of squares, and the number of observations * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /
float CalculateVar(float SumX, float SumX2, int n) {
float Var,N=n; if (n>l) Var=pow(sqrt((SumX2-pow(SumX,2.0)/N)/(N-1.0)),2.0); retum Var;
} / * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
Calculate Var calculates the parametric variance, taking as its arguments a sum, a sum of squares, and the number of observations * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /
float CalculatePVar(float SumX, float SumX2, int n)
float Var,N=n;
224
if (n>l) Var=pow(sqrt((SumX2-pow(SumX,2.0)/N)/(N)),2.0); retum Var;
} / * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
CalculateSE calculates the standard error, taking as its arguments a sum, a sum of squares, the number of observations, and the average * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * /
float CalculateSE(float SumX, float SumX2, int n) {
float SE,N=n;
if(n>l){ SE=sqrt((SumX2-pow(SumX,2.0)/N)/(N-1.0))/sqrt(N); retum SE;
} else retum 0.0;
}
225
\:.:^ .^r^tAaMHCiiga
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