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POPULATION DYNAMICS OF THE AMAZONIAN PALM Mauritia flexuosa: MODEL DEVELOPMENT AND SIMULATION ANALYSIS
By
JENNIFER A. HOLM
A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
2007
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© 2007 Jennifer A. Holm
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To my family who encouraged me at a young age, to keep striving for academic knowledge, and to my friends
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ACKNOWLEDGMENTS
I gratefully thank my supervisory committee, Dr. Kainer and Dr. Bruna, and most
importantly my committee chair, Dr. Wendell P. Cropper Jr. for their time and effort. I
acknowledge the School of Natural Resources and Conservation, the School of Forest Resources
and Conservation, and the Tropical Conservation and Development Program, the United States
Forest Service, and the Fulbright Scholar Program for funding and guidance. Data collection in
Ecuador was conducted with the help from Dr. Christopher Miller, Drs. Eduardo Asanza and
Ana Cristina Sosa, Joaquin Salazar, and all the Siona people of Cuyabeno Faunal Reserve. Data
collected in Peru was conducted with the help from Weninger Pinedo Flores, Exiles Guerra,
Gerardo Bértiz, Dr. Jim Penn, and with the generosity of Paul and Dolly Beaver of the Tahuayo
Lodge. Lastly, I would like to thank my parents for their support through my education
experience, Heather, Chris, friends, and fellow graduate students.
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TABLE OF CONTENTS page
ACKNOWLEDGMENTS ...............................................................................................................4
LIST OF TABLES...........................................................................................................................7
LIST OF FIGURES .........................................................................................................................8
ABSTRACT...................................................................................................................................10
CHAPTER
1 INTRODUCTION ..................................................................................................................12
2 POPULATION DYNAMICS OF THE DIOECIOUS AMAZONIAN PALM Mauritia flexuosa: SIMULATION ANALYSIS OF SUSTAINABLE HARVESTING ......................14
2.1 Introduction...................................................................................................................14 2.2 Methods.........................................................................................................................17
2.2.1 Study Site ..........................................................................................................17 2.2.2 Study Species ....................................................................................................17 2.2.3 Data Collection .................................................................................................18 2.2.4 Matrix Model Development and Parameter Estimation....................................19
2.3 Results ...........................................................................................................................22 2.3.1 Density Dependence..........................................................................................22 2.3.2 Sustainable Harvest Scenarios ..........................................................................23
2.4 Discussion .....................................................................................................................25 2.4.1 Sustainable Harvest Scenarios ..........................................................................25 2.4.2 Implications for Management ...........................................................................26
3 GENETIC ALGORIHTM OPTIMIZATION FOR DEMOGRAPHIC PARAMETER CALIBRATION AND POPULATION TRAITS OF A HARVESTED TROPICAL PALM .....................................................................................................................................41
3.1 Introduction...................................................................................................................41 3.1.1 South American Palms and Consequences of Wild Harvesting .......................41 3.1.2 Matrix Modeling and Population Dynamics .....................................................42 3.1.3 Parameter Calibration........................................................................................43 3.1.4 Introduction to Genetic Algorithms ..................................................................44 3.1.5 Objectives..........................................................................................................45
3.2 Methods.........................................................................................................................45 3.2.1 Study Site: Ecuador...........................................................................................45 3.2.2 Study Site: Peru.................................................................................................46 3.2.3 Study Species Role in Peru ...............................................................................47 3.2.4 Palm Distribution and Matrix Model Development: ........................................48 3.2.5 GA Method Description....................................................................................48
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3.3 Results ...........................................................................................................................51 3.3.1 Genetic Algorithms ...........................................................................................51 3.3.2 Peru Size Class Distribution and Demographic Characteristics .......................54 3.3.3 Genetic Algorithm: Harvest History for Peru M. flexuosa Palm Population....55
3.4 Discussion .....................................................................................................................57 3.4.1 Genetic Algorithms ...........................................................................................57 3.4.2 Peru Size Class Distribution and Demographic Characteristics .......................59 3.4.3 Genetic Algorithm: Peru M. flexuosa Palm Population....................................60
3.5 Conclusions...................................................................................................................60
4 SUMMARY............................................................................................................................84
4.1 Applicability..................................................................................................................84 4.2 Future for M. flexuosa ...................................................................................................84 4.3 Future Research.............................................................................................................85
APPENDIX: PERU GARDEN DATA FOR Mauritia flexuosa ...................................................86
LIST OF REFERENCES...............................................................................................................89
BIOGRAPHICAL SKETCH .........................................................................................................96
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LIST OF TABLES
Table page 2-1 Observed size class distribution (based on height) of M. flexuosa ....................................29
2-2 M. flexuosa (Ecuador) transition matrix ............................................................................30
2-3 Size class distribution for density independent (DI) and density dependent (DD) models after 100 yr. ...........................................................................................................31
2-4 Adult (stage 5 & 6) M. flexuosa transition probabilities....................................................32
3-1 M. flexuosa population size class distribution in Ecuador and Peru..................................62
3-2 Optimal Ecuador seedling parameters and carrying capacity using observed demographic parameters.. ..................................................................................................63
3-3 Observed range of the 13 non-seedling demographic transition probabilities. .................64
3-4 Observed and optimal Ecuador transition matrices. ..........................................................65
3-5 Optimal Ecuador seedling parameters and carrying capacity using optimal demographic parameters. ...................................................................................................66
3-6 Demographic traits for the Peru population in size classes 3-6 (palms that have developed trunks)...............................................................................................................67
3-7 GA estimates of harvest regimes consistent with the observed size class distribution. ....68
3-8 Peru’s harvesting history found using separate GAs which uses the Ecuador optimal demographic parameters to reach Peru’s observed population distribution. .....................69
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LIST OF FIGURES
Figure page 2-1 Elasticity for the M. flexuosa matrix population model.....................................................33
2-2 Density dependent model for M. flexuosa simulated over 500 yr.. ...................................34
2-3 Four simulated harvesting scenarios with various harvest frequencies and intensities for M. flexuosa. ..................................................................................................................35
2-4 The average number of female palms the year before harvesting over a 100 yr harvest regime. ...................................................................................................................38
2-5 Harvesting 22.45 percent at a frequency of every 20 yr. ...................................................39
2-6 Two harvest scenarios (both 75 percent at a frequency of every 10 yr) with density independence (DI) and density dependence (DD). ............................................................40
3-1 Map of study site in Ecuador. ............................................................................................71
3-2 Map of study site in Peru. ..................................................................................................72
3-3 Ecuador Genetic Algorithm (GA) size class distribution and observed size class distribution after running a GA to find optimal seedling parameters (stasis and growth) and carrying capacity. Fitness score for this GA is 46.67....................................73
3-4 Ecuador GA size class distribution and observed size class distribution after running a GA using the observed transition parameters and evaluating how well it matches the observed population distribution. Fitness score for this GA is 67.03. .........................74
3-5 Genetic algorithm simulated and observed size class distribution of the Ecuador palm population for unconstrained, all values (UCAV) GA optimization. Fitness score for this GA is 14.14. ................................................................................................................75
3-6 Genetic algorithm simulated and observed size class distribution of the Ecuador palm population for unconstrained, no two-size class transitions (UCNT) GA optimization. Fitness score for this GA is 5.07........................................................................................76
3-7 Stasis and growth demographic points generated from a GA optimization for (A) an UCAV (unconstrianed, all value), and (B) an UCNT (unconstrained, no two size-class transitions).................................................................................................................77
3-8 Stasis and growth demographic points generated from CAV (constrained, all values) GA optimization.................................................................................................................78
3-9 Stasis and growth demographic points generated from a CNT (constrained, no two-size class transitions) GA optimization..............................................................................79
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3-10 Genetic algorithm simulated and observed size class distribution of the Ecuador palm population for CAV (constrained, all values) GA optimization. Fitness score for this GA is 6.29 ..........................................................................................................................80
3-11 Genetic algorithm simulated and observed size class distribution of the Ecuador palm population for CNT (constrained, no two-size class transitions) GA optimization. Fitness score for this GA is 7.69........................................................................................81
3-12 M. flexuosa population distribution for palm populations in a 1ha area in Peru and Ecuador. .............................................................................................................................82
3-13 Distribution of male vs. female palms and estimated, averaged fecundity values from Peru and Ecuador. ..............................................................................................................83
A-1 Average height(m) for M. flexuosa palms sampled in Peru (wild and gardens).
A-2 Comparison of average palm height and average number of petioles, for juvenile M. flexuosa located in gardens and wild populations (in Peru).
A-3 M. flexuosa palms in Peru homegardens. (A) Picture of juvenile (pre-reproductive) M. flexuosa palms in a homegardens. (B) Picture of dwarf, reproductive female palm in Peru.
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Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
POPULATION DYNAMICS OF THE AMAZIONIAN PALM Mauritia flexuosa: MODEL DEVELOPMENT AND SIMULATION ANALYSIS
By
Jennifer A. Holm
December 2007
Chair: Wendell P. Cropper Jr. Major: Interdisciplinary Ecology
The tropical palm Mauritia flexuosa has high ecological and economic value, but some
wild populations are harvested excessively by cutting the stem to retrieve the fruit. It is likely
that M. flexuosa harvesting in the Amazon will continue to increase over time. I investigated the
population dynamics of this important palm, the effects of harvesting, and suggested sustainable
harvesting regimes. Data were collected from populations in the Ecuadorian Amazon that were
assumed to be stable. I used a matrix population model to calculate the density independent
asymptotic population growth rate (λ = 1.046) and to evaluate harvesting scenarios. Elasticity
analysis showed that survival (particularly in the second and fifth size class) contributes more to
the population growth rate than does growth and fecundity. In order to simulate a stable
population at carrying capacity, density dependence was incorporated and applied to the seedling
survival and growth parameters in the transition matrix. Harvesting scenarios were simulated
with the density dependent population models to predict sustainable harvesting regimes for the
dioecious palm. I simulated the removal of only female palms and showed how both sexes are
affected with harvest intensities between 15 and 75% and harvest intervals of 1 to 15 years. By
assuming a minimum female threshold, I demonstrated a continuum of sustainable harvesting
schedules for various intensities and frequencies for 100 years of harvest. Furthermore, by
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setting the population model’s λ = 1.00, I found that a harvest of 22.45 percent on a 20 year
frequency for the M. flexuosa population in Ecuador is consistent with a sustainable, viable
population over time.
Demographic parameters of long-lived plants are difficult to accurately estimate with short
duration studies. Genetic algorithm (GA) optimizations have been used to calibrate the matrix
population model from populations sampled in Ecuador. Assuming that the observed population
was stable at carrying capacity, sampling error could explain that the estimated demographic
parameters (transition probabilities) do not project equilibrium population values that match the
observed size class distribution.
GA optimization of seedling parameters somewhat improved the match to the observed
size class distribution, but the optimal parameters were from a range of local optima. GA
optimization of non-seedling demographic parameters for the Ecuador population produced a
close fit to the observed population size class distribution. It was found that the technique of
constrained GA optimization produced models that closely matched the observed size class
distribution and were consistent with plot measurements. This study also compared the palm
size class distributions and demographic characteristics between Peru and Ecuador populations.
Unlike in Ecuador, palm populations in Peru are heavily harvested, with reduced numbers of
adult females and an uneven sex-specific size class distribution. Finally, I explored GA as a tool
to reconstruct plausible harvesting histories by assuming that a harvested population in Peru
started with the same population structure as the Ecuador population. Harvest regime variables
included harvest intensity (fraction removed), harvest frequency (return time) and the time span
with harvesting. No parameter combinations for regular uniform harvest regimes were found
that closely matched the observed Peru size class distribution.
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CHAPTER 1 INTRODUCTION
In general terms, population ecology entails analyzing the demography of a population
through estimating its vital rates (survival, growth, fecundity, mortality), and assessing change in
numbers over time. In particular, understanding population dynamics is important for evaluating
how a population density changes in response to external and/or internal influences. Modeling
population dynamics is useful for developing and evaluating hypotheses in population ecology.
This research employed simulation modeling to develop matrix population models for evaluating
the population behavior of a tropical palm, Mauritia flexuosa. Constructing matrix population
models, including density dependence, simulating sustainable harvesting scenarios, and
developing methods to calibrate poorly sampled model parameters was the main goals of this
research. This research is not recommended to be used directly for management purposes. The
simulated sustainable harvest regimes identified in this study represent testable hypotheses; and
rigorous testing should be done before any implementation.
The tropical palm Mauritia flexuosa is found in the Amazon Basin and often forms
monodominant stands. Destructive harvesting is occurring in parts of the Amazon to retrieve the
palm fruits, which are then sold in local markets. Demographic population modeling was used to
estimate the population’s current behavior, as well as estimate the population’s response to
assumed harvesting scenarios. This thesis is organized as two separate journal papers (chapter 2
and chapter 3). Chapter 2 describes the model structure, data and methods used for model
development, and results of harvest scenario analysis. One of the principal uncertainties of this
work is associated with the relatively short period of data collection (2 years). Chapter 3
describes the use of genetic algorithms for simultaneous estimation of up to 13 model
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parameters. This technique provides a test of the consistency of parameter estimates and the
observed size class distribution.
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CHAPTER 2 POPULATION DYNAMICS OF THE DIOECIOUS AMAZONIAN PALM MAURITIA
FLEXUOSA: SIMULATION ANALYSIS OF SUSTAINABLE HARVESTING
2.1 Introduction
There is growing concern for conserving and sustaining tropical forests (Houghton et al.
1991, Sioli 1991, Olmsted & Alvarez-Buylla 1995). Many tropical tree species provide
ecological as well as economic benefits. These benefits include valuable resource production or
important functions associated with tropical biodiversity and conservation. Managing these
critical species requires an understanding of their population dynamics by practitioners and
communities (Olmsted & Alvarez-Buylla 1995). Palms make up a large portion of the
economically useful tropical trees and are utilized for a wide range of products (Balick & Beck
1990, Anderson et al. 1991, Kahn 1991, Kahn & de Granville 1992, Henderson et al. 1995). The
palm Mauritia flexuosa L.f., also called canangucho or morete in the Ecuadorian Amazon, was
the focus species of this study, used in the development of matrix population models.
Mauritia flexuosa is found in tropical, flooded, swamps (Kahn & Mejia 1990, Kalliola et
al. 1991, Cardoso et al. 2002) throughout the Amazonia Basin and northern South America
(Henderson 1995, Ponce et al. 2000). Mauritia flexuosa has significant, but underdeveloped
potential as a multifunctional, non-timber forest resource of great economic value (Denevan &
Treacy 1987, Carrera 2000, Peters et al. 1989a, 1989b, Ponce et al. 2000). The fruit of the palm
is currently its most economically useful product (Padoch 1988). Oil fractions extracted from M.
flexuosa fruit have high concentrations of vitamins, carotene, and lipids (de Franca et al. 1999).
Mauritia flexuosa is one of the most commonly found palms in the Amazon, and forest
dwellers currently invest substantial effort in gathering fruits from these palms to generate
income (Kahn 1988, Peters 1992, Coomes et al. 2004). These products are not processed on an
industrial scale, but they do provide income and employment for many people in Iquitos and
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other Amazonian communities, with the fruit being sold in many forms (Padoch 1988). There
has been an increasing shift to growing M. flexuosa in small homegardens, also known as
chacras. Until recently, however most M. flexuosa fruit has been harvested from wild stands. In
dense, monodominant, flooded natural stands, the mature palm trees are typically greater than
20m in height making the fruit difficult to harvest. As a result, in many Amazonia locations the
fruit-bearing female palms are cut down leading to nonviable populations (Peters et al. 1989a,
Vasquez & Gentry 1989), which makes M. flexuosa a good candidate for non-timber forest
product (NTFP) management.
A goal of my research was to identify potential sustainable harvest regimes for M.
flexuosa. Because fruit harvest for this particular species results in tree mortality, matrix
population models are appropriate tools to simulate monodominant stands of M. flexuosa. If
markets continue to flourish with M. flexuosa products then in time formerly low levels of
harvesting will likely intensify in Ecuadorian forests as it has in other Amazon Basin locations
(Peters et al. 1989a, Vasquez & Gentry 1989). Many studies have looked at the 1) implications
of harvesting palm parts (NTFPs) as well as 2) identifying useful palms needing conservation
(Johnson 1988, Fonseca 1999, Mendoza and Oyama 1999, Endress et al. 2004a, Ticktin 2004).
Ticktin et al. (2002) used matrix models to assess the effects of harvesting on a NTFP bromeliad
in Mexico. Endress et al. (2004b) as well as Olmsted and Alvarez-Buylla (1995) used matrix
models to evaluate harvesting techniques for tropical palms (Chamaedorea radicalis, Thrinax
radiata, and Coccothrinax readii). Likewise, matrix models have been used on the tropical palm
Iriartea deltoidea to evaluate stem harvesting, population stability, and conservation (Pinard
1993, Anderson & Putz 2002). Matrix models have also been coupled with habitat
fragmentation analysis to assess changes in plant population dynamics in tropical environments
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(Bruna 2003). Improper harvesting of palm products has been demonstrated to have a negative
effect at the population level (O’Brien & Kinnaird 1996, Clay 1997).
Lefkovitch matrix models (1965), a generalization of matrix population models proposed
by Leslie (1945), typically simulate the population in sized-based stages as opposed to the age
classification of a Leslie model. In many tree populations, the demographic parameters (survival
probability, growth rate, and fecundity) are a function of tree size and not of tree age (Caswell
2001, Vandermeer & Goldberg 2003). The standard matrix population model will project
exponential growth if the dominant eigenvalue (λ) of matrix is greater than 1 (implying no
resource limitations or competition) or decline exponentially if λ is less than 1. Matrix
population models have been used to aid management and conservation of many species (Crouse
et al. 1987, Wootton & Bell 1992, Silvertown et al. 1996).
The role of density dependence is important in some tropical palm populations (Cropper &
Anderson 2004), but data are limited. A study of the tropical palm Euterpe edulis showed that
there was a clear effect of density on the population structure and demography (Matos et al.
1999). A second study of the same palm showed that density dependence, as well as timing of
harvest, must be considered for accurate assessment of population responses to harvesting
(Freckleton et al. 2003). Little is known about density dependence in tropical tree systems that
are harvested, but previous work suggests that density often has its strongest effect on seedlings
of tropical palms and other tree species (Augspurger & Kelly 1984, Sarukhan et al. 1985,
Martinez-Ramos et al. 1988, Matos et al. 1999). I hypothesize similar demographic patterns in
monodominant stands of M. flexuosa.
An important characteristic of M. flexuosa for harvest management is that the palm is
dioecious; only females bear the economically useful fruit. One study has looked at
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demographic consequences of harvesting of an understory dioecious palm, finding that leaf
harvest can reduce female fecundity (Berry & Gorchov 2007). I know of no studies using matrix
models to simulate sustainable harvest regimes in a tropical species with only female removals.
Specifically, my objectives were: (1) to determine how density dependence affects the
population dynamics and harvesting; (2) to estimate sustainable harvests with an assortment of
different harvesting intensities and frequencies of M. flexuosa, specifically looking at how
harvesting a dioecious species affects the population; and (3) to estimate a sustainable harvest
while maintaining a stable population (λ equal to 1.00).
2.2 Methods
2.2.1 Study Site
Data were collected in the Ecuadorian Amazon from the Cuyabeno Faunal Reserve, a
655,781 ha reserve located between the San Miguel and Aguarico river basins and managed by
Siona and Secoya indigenous groups. All field components were conducted near the Cuyabeno
Field Station (0º7’N, 76º11’W), located in a tropical rainforest with an elevation of 200m.
Cuyabeno is characterized by a series of oligotrophic lakes, connected to M. flexuosa swamps
(morichales) that ultimately drain into the Cuyabeno River. Water levels in M. flexuosa swamps
fluctuate depending on the season and rainfall level, which averages 3400 mm/yr. Three distinct
seasons are evident: dry (mid-December to March), wet (April to July), and transitional (August
to December) (Asanza 1985).
2.2.2 Study Species
Mauritia flexuosa is a long-lived, dioecious, canopy dominant palm, found throughout the
Amazon basin at elevations below 500m, but sometimes reaching 900m (Henderson et al. 1995).
Juveniles initially have only leaves above-ground, and then begin to form a trunk covered by
persistent petiole bases. As a palm matures, the petioles fall off exposing a permanent trunk.
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Mature palms have 8 – 20 leaves with leaf blades 2.5m long and 4.5m wide, and split into
approximately 200 stiff or pendulous leaflets (Kahn & de Granville 1992, Henderson et al.
1995). The inflorescences are 2m or more in length with 25 - 40 flowering branches. Fruits are
oblong drupes, 5 x 7cm on average, and are covered with a brick-red epicarp of scale texture.
The only edible part of the fruit for humans is its yellow mesocarp, but the seed is useful to
artisans who produce small carvings. Padoch (1988) describes a number of M. flexuosa products
found in the Iquitos market, including the ripe fruit and a pulp mash, a drink, popsicles, and ice
cream. Previously studied permanently flooded forests, inhabited by M. flexuosa, are seen to
have soil composed of decomposed organic matter for several meters saturated with acidic water
(Kahn 1991).
In the Ecuadorian Amazon these flooded forests that are mostly dominated by M. flexuosa
(called morichales) are found along river edges. In others parts of the Amazon, this palm is
intensely harvested from these wild stands. Wild harvesting of M. flexuosa has historically
occurred in Ecuador, but at low levels. M. flexuosa can be considered a keystone species
because of large number of other species that feed on the fruit and seed. These include agouties
(Dasyprocta leporina aguti), spider monkeys (Ateles geoffroyi), red and green macaws (Ara
chloroptera), lowland tapirs (Tapirus terrestris), red and gray brocket deer (Mazama americana
and Mazama gouazoubira respectively), white-lipped and collared peccaries (Tayassu pecari and
Tayassu tajacu respectively), and fish (Goulding 1989, Bodmer 1990, Bodmer 1991, Henderson
et al. 1995, Fragoso 1999, Zona 1999).
2.2.3 Data Collection
I used a demographic data set that was collected previously by a research collaborator (C.
Miller) from five plots (20m x 100m) in old growth natural stands in Ecuador (morichales).
Demographic data were collected from 1994-1996. I do not know the exact criteria for selecting
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the five plots. All five plots were within a half a day’s travel or less from each other. I assumed
that minimal female harvesting had occurred on the five plots (based on evidence from the size
distribution ratio of adult males to females and remnant trunks of harvested female individuals).
Harvest intensity prior to the study, however is unknown. In the first year demographic data was
collected for each palm individual over all five 20m x 100m plots. Palms were tagged with
numbered, metal tags. Data collection consisted of:
1) Palm height for all size classes (actual for palms that could be reached, and estimated with a clinometer for taller palms).
2) Leaf counts on seedlings and most juveniles. 3) Recording of sex for adults. 4) Leaf scars on palms that had developed trunks. 5) Raceme counts on females.
In the second year, the number of seedlings was based on ten 5m x 5m subplots (randomly
selected) within the 20m x 100m plots. Otherwise, the same data collection was repeated in the
second year. In the third year only seedling data was recorded in the previously marked ten
subplots.
2.2.4 Matrix Model Development and Parameter Estimation
Distribution of palms in each of the five plots was variable. For population analysis and
stage-based matrix modeling, I aggregated the population into a 1-ha pooled data group (Table 2-
1). The population was classified into seven size classes based on height. Only a limited
number of adult growth transitions (size class 5) were observed, leading to potentially poor
estimates of the vital rates. Growth rates were estimated for each size class in the pooled data
set. To estimate survival and growth transitions, I assumed that the observed size class
distribution was stable and that the average growth rates per size class applied to all individuals
within that class. Mean size class specific growth rates were estimated (0.4159 m/yr, 0.3902
m/yr, 0.8107 m/yr, 1.08 m/yr, and 0.4333 m/yr) for size class 1 through 5 respectively. The
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matrix parameters (survival, sij and growth, gij) that did not have a limited number of
observations were estimated by following the state vs. fate of the palms over time. Fecundity
(fij) parameter estimates were based on equation 2-1:
i
tnf
ij Nf
x2
))1()(( 0 +
= (2-1)
where f(x) is the seedling survival probability, n0(t+1) is the average number of established
seedlings at the next time interval, and Ni is the number of reproductive individuals. The term in
the numerator is divided by two, assuming a 1:1 sex ratio. The matrix model was simulated with
the equation 2-2:
)()1( tnAn t ∗=+ (2-2)
where n(t) represents the population vector at time t, and A represents the 7 x 7 transition matrix
containing the probabilities for individual palms to remain in the same stage or move to another
stage and their fecundity probabilities (Table 2-2). Elasticity analysis is often used to
demonstrate the sensitivity of the dominant eigenvalue to variations in matrix elements (survival,
growth, fecundity). Unlike absolute sensitivity, elasticity analysis shows the relative
contribution of each vital rate to the population growth rate, λ (Caswell 2001, Morris & Doak
2002).
Density dependence was simulated using the monotonic decreasing Ricker function:
)(max)( Nijij eaNa β−∗= (2-3)
Density dependence was applied to the two seedling parameters (survival and growth) in
the transition matrix, because density has been observed to influence seedlings of tropical palms
(Matos et al. 1999). The first seedling parameter is seedling survival, the probability that a
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seedling will survive and remain in the same size class. The second seedling parameter is
seedling growth, the probability that a seedling will survive and grow into the next size class. In
the Ricker function, aij(N) is the probability that a seedling will survive or grow as a function of
the total M. flexuosa population (N, the sum of n population vector). Seedling survival and
growth decreases as density of the entire palm population increases. aijmax represents the matrix
probabilities for the seedling parameters a00 and a10 in the original transition matrix with no
density limitation. β was found by using the bisection method (Cropper and DiResta 1999) to
estimate the seedling parameter values for a stable (λ = 1) population and equation 2-4:
Ka
a
ij
ij
maxln
′
=− β (2-4)
where K is the carrying capacity including all seedling and non-seedling individuals and
aij′ represents the matrix probability when λ, the dominant eigenvalue of the A matrix, equals
1.00 (the population is stable with a density equal to the carrying capacity). A 39.77 percent
reduction in seedling vital rates was consistent with an equilibrium population at K. Separate
density dependent models were simulated for males and females with identical parameters,
except that male fecundity values were set to zero. Male seedling recruits were assumed to equal
the number of female seedling recruits and were added directly to the male population vector.
I developed scenarios to estimate a sustainable harvest regime based on two options. The
first (1) setting a minimum female threshold (MFT) (20 individuals) to maintain a sustainable
population; and (2) finding the adult survival and growth probabilities that produce a stable, thus
sustainable, intrinsic population growth rate (λ = 1.00), using the bisection method. With the
first option I then: (1a) varied the intensity of harvests scenarios; (2a) varied the frequency of
harvest, from annual to periodic harvests to find a continuum of harvest scenarios that produced
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a sustainable population. In both harvesting scenarios separate population vectors were
simulated for males and females, since M. flexuosa is dioecious and only female palms are felled
during harvest. Harvesting scenarios are initiated after a 600 year density dependent simulation
to avoid transient dynamics associated with a possible non-equilibrium size class distribution.
There are short-lived transients associated with simulations started at the observed stage class
distribution, but they typically damp out rapidly. I assumed that the population has not been
recently harvested, and that the equilibrium size class distribution provides a good estimate of
the expected distribution used as a uniform basis for comparison. Evaluations of harvest
simulations for sustainability are not sensitive to this assumption.
2.3 Results
Elasticity analysis of the density independent M. flexuosa matrix showed that the stasis
probabilities (the elements in the main diagonal) contribute the most to λ sensitivity (Figure 2-1,
A). Specifically, the survival and stasis parameter in the second juvenile stage (size 3.0m –
6.0m), and the survival and stasis of the first adult stage (size 20.0m – 28.0m) were sensitive
parameters (Figure 2-1, B). The M. flexuosa transition matrix (Table 2-2) produced an
asymptotic population growth rate of λ = 1.046, which shows that the population has the
potential for rapid increase.
2.3.1 Density Dependence
With density dependence, the population growth rate slows as N approaches the carrying
capacity. I assume that for seedlings, transition rates depend on the number of individuals in
their own size class and all other size classes. The simulated density dependent model shows
that the M. flexuosa population at equilibrium (K) is large (Figure 2-2), but most of the
individuals are in the seedling class (Table 2-3). There was a large difference in the size class
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distribution between the density independent model and the density dependent model at 100 yr
simulation (Table 2-3). At approximately 100 to 150 years, the simulated palm population began
to reach equilibrium. The full density dependent simulation was run for 500 years (Figure 2-2).
At equilibrium (after 500 yr) the model predicted an adult size class distribution of
approximately 120 individuals per ha for each sex. The number of adults that were measured in
the study site was approximately 45 per ha for each sex. After equilibrium was reached in the
density dependent simulation, the following harvesting scenarios were initiated.
2.3.2 Sustainable Harvest Scenarios
Multiple harvesting options (Figure 2-3) are consistent with sustainable management of M.
flexuosa. Harvesting at intensities of 15 percent, 20 percent, 30 percent, 50 percent, and 75
percent removal of adult females are seen in Figure 2-3 (A-C). Harvest frequency, or return
time, is directly coupled with the total number of palms that can be harvested. Periodic
harvesting frequencies were simulated for return times of 5 yr, 10 yr, and 15 yr. I also simulated
an annual harvest regime (Figure 2-3, D), although harvesting is rarely that frequent from natural
M. flexuosa stands because local people understand the threat to these palms survival if
harvesting is done each year. Simulations at a range of intensities (Figure 2-3, D) support the
conventional wisdom that annual harvests are not sustainable in the long-term. With adequate
recovery time, the M. flexuosa population can be dynamically stable following periodic
harvesting (Figure 2-3, A-C). After each periodic harvest, there was a sharp decrease in adult
palm density, followed by an increase in population density (recovery), which is faster in the
years immediately after harvest then slows with increasing density. Recovery is defined as the
number of females that grow into the adult size class 5 from the juvenile size class 4. For all
harvesting intensities (15%-75%), female recovery was greatest with 15 yr harvest intervals
(Figure 2-3, C). Average number of female palms at simulated time of harvest ranged from 37 -
24
115 depending on harvest intensity and frequency (Figure 2-4). Larger female numbers available
for harvest are associated with longer harvest intervals and lower harvest intensities. Although a
less intense harvesting regime would increase biological sustainability, this may not be adequate
for supplying household income needs.
I have set a sustainable harvest rate for this palm through two different methods. The first
is by assuming 20 adult females per hectare as the MFT needed to sustain population viability.
With 20 adult females set as the threshold, Figure 2-3 shows that the following can be
sustainable; a 30 percent harvest every 5 yr, a 50 percent harvest every 10 yr, and a 50 percent –
75 percent harvest every 15 yr. Only these harvesting intensities are consistent with a viable
population for 100 years, because they maintain the number of female palms above the MFT.
These harvest options can only be done for a hundred year time span. After 100 years if the
harvest intensity remains constant, the population will fall below a minimum sustainable
threshold level. The second method I used to find a sustainable harvest rate allows for
harvesting over an indefinite time period, assuming that population parameters do not change.
By using the bisection method, I found that the adult survival and growth probabilities necessary
for λ = 1.00 are less than the observed probabilities (Table 2-4). I found that harvesting 22.45
percent of the females every 20 yr creates a sustainable harvest (Figure 2-5).
The biologically plausible assumption of density dependence leads to very different
harvest projections than that of the standard density independent matrix population model
(Figure 2-6). The simulated harvest scenario without a density dependence function shows a
large increasing female population. The same scenario modeled with density dependence drops
below MFT and does not provide a sustainable harvest.
25
2.4 Discussion
This study effectively examines impacts of harvesting a dioecious palm and, is among the
first to provide multiple sustainable, simulated harvesting scenarios for one species. While
population modeling may be a useful tool to project management scenarios, uncertainties in
demographic parameters and difficulties in social and economic planning are likely to preclude
precise harvest planning. A typical assumption in matrix population models is that the
populations are not limited by density. Using the standard density independent model, with
parameters estimated in the field, the M. flexuosa population examined increases by a factor of
1.046 each year (at the stable stage distribution). Given limitations on space and other resources,
it is clearly unrealistic that this population will increase indefinitely (Lack 1947, Milne 1957,
Weiner 1986). A population that is growing (λ = 1.046) would produce many more harvestable
palms than one limited by competition. At the limit, an exponentially growing population could
produce any desired harvest, given adequate time. I suggest that simulation of density
dependence in monodominant harvested populations is necessary to properly constrain the rate of
population recovery following harvest.
2.4.1 Sustainable Harvest Scenarios
The challenge for NTFPs is finding the harvest level that will supply enough income to
forest dwellers while at the same time maintaining population viability of harvested species. I
have shown that harvesting the specific M. flexuosa population examined at 22.45 percent every
20 yr could be a sustainable harvesting regime (Figure 2-5), but higher intensities or frequencies
of harvest could send the population into a decline.
Frequency/intensity of harvesting is hard to control and is a response to multiple issues,
such as market demand, fluctuating subsistence needs, accessibility, and morichal fruit
production rate. For these reasons, different harvesting scenarios can be chosen, all maintaining
26
a sustainable harvest rate for the span of 100 years (Figure 2-3). I have shown a tradeoff
between harvest frequency and intensity. Higher rates of removal will require longer recovery
times between harvests (Figure 2-3). This population’s MFT is assumed to be 20 individuals per
hectare. It is reasonable to select a conservative value for MFT, based on the Precautionary
Principle, but other M. flexuosa populations could have a different λ and a different minimum
female threshold. It can be misleading to evaluate harvesting regimes based on the number of
females to recover in only one year instead of the entire harvest period recovery. In the first
years following a harvest, initially a higher number of palms recover than in remaining years
after a harvest. A harvesting regime with a longer time interval between harvests will allow
more palms to recover into the adult size classes.
Understanding the implications of harvesting a dioecious species is one goal of this paper.
The current practice, selecting and removing female palms, results in recruitment limitation over
time. Females are directly affected by harvesting, and the male population is affected by
changing adult density and by reduced seedling recruitment. Initially, the male population
remains high, but after a lag time the male population begins to decline along with the females.
Over time, if heavy harvesting is maintained, it is predicted recruitment and regeneration of M.
flexuosa palms will decline.
2.4.2 Implications for Management
While population modeling may be a useful tool to project management scenarios,
uncertainties in demographic parameters and difficulties in social and economic planning are
likely to preclude precise harvest planning. With the market demand increasing for the M.
flexuosa fruit, many forest dwellers are beginning to cultivate the palm in small homegardens.
Research organizations and non-governmental organizations (NGOs), such as the Rainforest
27
Conservation Fund, are helping Amazonian mestizos to convert old swidden fields into M.
flexuosa gardens. These gardens can take 10 – 12 yr to become productive, but after trees grow
to maturity fruit can be harvested repeatedly from managed, easily accessible gardens. Wild
individuals may take an estimated 30 or more years to mature and become productive, based on
leaf and infructescence scars counts (pers. observation). Palms grow faster and mature more
quickly under high light conditions, such as those found in agroforestry gardens (Penn 1999).
Palms that mature more quickly will produce fruit at a shorter height, making harvesting easier.
While harvesting in natural, flooded swamp stands can be done at a sustainable level, if market
demand increases then M. flexuosa production gardens, as opposed to extracted natural stands,
may become a better option.
Many forest dwelling Amazonians understand the important economic role of M. flexuosa.
They also understand that natural palm densities are decreasing, but few written management
plans have been implemented to protect this resource. Our simulations demonstrate that
sustainable harvesting scenarios for a species can be found, but the precise nature of a
sustainable harvesting regime depends on accurate representation of the population demography.
Long-term palm survival, growth, and fecundity monitoring should be used to provide a sound
basis for developing harvest strategies for wild populations. Better understanding of density
dependence in monodominant M. flexuosa stands is also needed. In summary, the sustainable
harvest scenarios found in this study consist of a range of harvesting regimes for 100 years of
harvest, and an option for a continuous sustainable harvest over time. Management planning
should include community input and participation to generate community specific harvesting
management plans. Analyzing the population dynamics of Mauritia flexuosa can be used as one
28
component in management of its role as a NTFP, while conserving the natural Amazonian palm
stands it inhabits.
29
Table 2-1. Observed size class distribution (based on height) of M. flexuosa in five plots (plot 1-5 100x20m), and pooled plot 1-ha.
Size Class Stage Height (m) Plot 1 Plot 2 Plot 3 Plot 4 Plot 5 Pooled Plot
0 Seedling <1.0 45 62 59 42 52 260 1 Juvenile 1.0-3.0 2 14 32 29 10 87 2 Juvenile 3.0-6.0 13 18 25 23 22 101 3 Juvenile 6.0-10.0 6 8 6 7 0 27 4 Juvenile 10.0-20.0 12 7 2 9 2 32 5 Adult 20.0-28.0 9 11 8 10 9 47
6 Adult >28.0 13 5 8 13 3 42
30
Table 2-2. Transition matrix for M. flexuosa for pooled plot, from five flooded swamp sites in Ecuador. The dominant eigenvalue, lambda (λ) shows the growth rate. λ = 1 indicates a stable population, λ < 1 a decreasing population, and λ > 1 an increasing population.
Size Classes <1.0 m 1.0-3.0 m 3.0-6.0 m 6.0-10.0 m 10.0-20.0 m 20.0-28.0 m > 28.0 m
0.4923 0.0 0.0 0.0 0.0 16.8 16.8 Pooled Plot 0.0115 0.7471 0.0 0.0 0.0 0.0 0.0 λ = 1.046
0.0 0.2184 0.8911 0.0 0.0 0.0 0.0 0.0 0.0115 0.0990 0.7778 0.0 0.0 0.0 0.0 0.0 0.0099 0.2222 0.7813 0.0 0.0 0.0 0.0 0.0 0.0 0.1875 0.8723 0.0 0.0 0.0 0.0 0.0 0.0 0.0851 0.8810
31
Table 2-3. Size class distribution for density independent (DI) and density dependent (DD) models after 100 yr.
Size Class Number of palms: DI Model Number of palms: DD Model 0 45729.6 4224.32 1 2888.3 189.26 2 3388.1 271.36 3 832.5 70.60 4 1028.4 104.84 5 964.7 113.14 6 526.9 77.80
32
Table 2-4. Adult (stage 5 & 6) transition probabilities. Matrix element a55 and a66 are adult survival and element a65 is adult growth transition. Average of the death due to harvest produces the adult harvest percent for the second harvesting scenario.
Matrix element
Original survival/growth probability
Death due to natural causes
Survival/growth for λ =1.0
Average death due to
harvest a55 0.8723 0.128 0.6489 0.2234a65 0.0851 NA 0.0633 0.0218a66 0.8810 0.119 0.6554 0.2256Average 0.2245
33
0 1 2 3 4 5 6
0
0.05
0.1
0.15
0.2El
astic
ity %
Size Classes
A
0
0.05
0.1
0.15
0.2
0.25
0 1 2 3 4 5 6
Size Classes
FecundityStasisGrowth
B
Figure 2-1. Elasticity for the M. flexuosa matrix population model. (A) the 7 x 7 transition matrix, and (B) the three main vital rates (growth, stasis, fecundity).
34
Figure 2-2. Density dependent model for M. flexuosa simulated over 500 yr. The population
illustrates an asymptotic growth rate as it reaches the carrying capacity (K).
35
A
Figure 2-3. Four harvesting scenarios with various harvest frequencies and intensities. (A) five different harvesting intensities at a frequency of every 5 yr, (B) five different harvesting intensities at a frequency of every 10 yr, and (C) five different harvesting intensities at a frequency of every 15 yr. (D) six different harvest intensities (only females shown) with annual harvest.
Harvest Intensity
Years
N
0
20
40
60
80
100
120
140
1 10 19 28 37 46 55 64 73 82 91 100
F-15%F-20%F-30%F-50%F-75%M-15%M-20%M-30%M-50%M-75%
36
B
C
Figure 2-3. Continued
Harvest Intensity
Years
N
Harvest Intensity
Years
N
0
20
40
60
80
100
120
140
1 10 19 28 37 46 55 64 73 82 91 10
F-15% F-20% F-30% F-50% F-75% M-15% M-20% M-30% M-50% M-75%
0
20
40
60
80
100
120
140
1 11 21 31 41 51 61 71 81 91
F-15%F-20%F-30%F-50%F-75%M -15%M -20%M -30%M -50%M -75%
37
D
Figure 2-3. Continued
Harvest Intensity
N
Years
0
20
40
60
80
100
120
1401 9 17 25 33 41 49 57 65 73 81 89 97
15%20%25%30%40%50%
38
0
20
40
60
80
100
120
140
15 20 30 50 75
Harvest Percents (Intensities)
N
15 yr freq.10 yr freq.5 yr freq.
Figure 2-4. The average number of female palms the year before harvesting over a 100 yr harvest regime.
39
80
85
90
95
100
105
110
115
120
125
1 501 1001 1501
Years
N (a
dults
per
ha)
Male PalmsFemale Palms
Figure 2-5. Harvesting 22.45 percent at a frequency of every 20 yr.
40
Figure 2-6. Two harvest scenarios (both 75 percent at a frequency of every 10 yr) with density
independence (DI) and density dependence (DD).
41
CHAPTER 3 GENETIC ALGORIHTM OPTIMIZATION FOR DEMOGRAPHIC PARAMETER CALIBRATION AND POPULATION TRAITS OF A HARVESTED TROPICAL
PALM
3.1 Introduction
3.1.1 South American Palms and Consequences of Wild Harvesting
Tropical palms are important for many values such as, maintaining ecological
diversity, providing economic gains and subsistence products, and for aesthetic value
(Bates 1988, Mejia 1988, Boom 1988, Anderson et al. 1991, Henderson 1994, Henderson
et al. 1995, Johnson 1999). South American tropical palms in particular are widely used
in local environments and exported to outside markets (Balick 1988, Parodi 1988, Kahn
& de Granville 1992, Campos and Ehringhaus 2003). The South American palm,
Mauritia flexuosa, one of the most important palm species, has been widely studied
(Denevan & Treacy 1987, Kahn 1988, Padoch 1988, Bodmer et al. 1997, Carrera 2000,
Ponce et al. 2002, Coomes et al. 2004). This paper adds to the knowledge on the M.
flexuosa species. Simulation models are often used for managing harvested populations,
but calibration data are often quite limited. It is also difficult to fully understand the
dynamics of harvested palm populations based on short-term studies. I believe that
Genetic Algorithms can be used to improve the quality of calibration for harvested
populations such as those of Mauritia flexuosa.
Some wild palm populations in the tropics are being destroyed and/or degraded due
to overly high economic utilization (Balick 1988, Johnson 1988, Peters et al. 1989a).
There has been a switch to domestication and cultivation, but for certain palm species,
including M. flexuosa, this switch is slow, poorly understood, or involves species-specific
difficulties. It is important to first understand the population dynamics of palm
42
populations that are being over-harvested in wild settings. Wild palm extraction is one of
the main process threatening local populations. Extraction is occurring throughout
Amazonia, but is observed to be high around the Iquitos and surrounding regions of Peru
specifically for the palm M. flexuosa (Padoch 1988, Vasquez & Gentry 1989). It is
important to understand the impact of harvesting fruit of M. flexuosa, a dioecious species,
in the Peruvian lowlands, which is destructively harvested by felling adult female trees.
A high level of wild leaf extraction is seen to unfavorably affect a dioecious understory
palm (Berry and Gorchov 2007). Commercial palms (Chamaedorea and Astrocaryum)
are exploited for products like seeds and leaves (biologically important components),
leading to unsustainable harvesting of local populations (Fonseca 1999, Mendoza and
Oyama 1999, Endress et al. 2004, Seibert 2004). Current simulation models of non-
timber forest product harvesting do not adequately represent population dynamics in the
context of multiple use forest management (Valle et al. 2007).
3.1.2 Matrix Modeling and Population Dynamics
Matrix population models have often been used for studying single species
populations (e.g., Crouse et al. 1987, Wootton & Bell 1992, Vantienderen 1995,
Silvertown 1996, Kaye and Pyke 2003). These models typically follow a stage-based
size class model (Lefkovitch 1965) or Leslie’s age class model (1945), and have been
further developed in many studies (Caswell 1989, Morris & Doak 2002, Vandermeer &
Goldberg 2003). Many properties of tropical tree populations are difficult to accurately
measure (growth rates, response to density, regeneration rates) but important to
understand, especially in threatened or harvested species (i.e., M. flexuosa). Effective
management and conservation plans for a harvested palm depends on understanding
population dynamics and response to disturbances. Therefore, demographic parameters,
43
which make up population matrix models, must be understood in detail and accurately
represented. In chapter two of this thesis a study was performed using density dependent
matrix population models to simulate population dynamics of M. flexuosa from a site in
Ecuador. Several sustainable harvesting scenarios were identified, which may be used as
a component in management plans for the exploited palm. Using simulation models as a
management tool clearly requires the best possible parameter estimates. This study is a
continuum of the previous population modeling chapter on M. flexuosa.
3.1.3 Parameter Calibration
It is difficult to estimate demographic parameters of many tropical species (Wood
1994, Hunter et al. 2000); particularly long lived tropical trees (Alvarez-Buylla et al.
1996). Past studies have focused on demographic stochasticity (Shaffer 1987, Durant and
Hardwood 1992) and environmental stochasticity (Lacy 1993, Kendall 1998, Caswell
2001). Sampling error can also affect the accuracy of projections and the simulated
changes in demographic process over time (Parysow and Tazik 2002, Picard et al. 2007).
Accurate estimation of parameters could even be a matter of concern in a population with
no significant demographic or environmental stochasticity. Examples of likely data
problems include short data collection time frames, poor identification methods, and
measurement error, some of which are found in this study. Although model parameters
typically have varying degrees of influence on model results (Hamby 1994, Janssen
1994), the entire set of demographic parameters interact to produce population dynamics.
Carefully calibrating only the most sensitive parameters may miss other parameters that
were very badly sampled, as well as higher dimension parameter interactions. Genetic
Algorithms are well suited to problems of high dimension optimization.
44
3.1.4 Introduction to Genetic Algorithms
Evolutionary programming has been used since the 1950’s and 1960’s, but John
Holland of University of Michigan popularized the genetic algorithm in 1975. Genetic
algorithms (GA) are now used in many disciplines, such as engineering, computer
science, biology and ecology. GAs are modeled after the biological paradigm of natural
selection and survival of the fitness in generations over time. GA’s can be used as an
optimization algorithm that seeks to find solutions to multi-dimensional problems where
“fitness” is defined as a measure of closeness to the desired solution (Holland 1975, Koza
1992, Wang 1997, Mitchell and Taylor 1999). GA’s are also considered global
algorithms because they search within a population, and then use biological frameworks
of gene passing, mutation, selection, and crossover. The use and development of
evolutionary programming is practical in solving a wide range of problems, including
ecosystem and biological applications (Cropper and Comerford 2005, Yao et al. 2006,
Liu et al. 2006, Termansen et al. 2006, Dreyfus-Leon and Chen 2007).
Using genetic algorithms to understand tropical forest dynamics is an emerging
technique. For example, parameterization with genetic algorithms has been used in a
simplified, aggregated forest model to understand logging cycles across a range of
tropical forest types and forest dynamics (Tietjen and Huth, 2006), and a genetic
algorithm has been used to estimate fecundity, carrying capacity, and seedling
demographic parameters for the palm Iriartea deltoidea (Cropper and Anderson 2004).
The key assumptions of our approach to parameter estimation with genetic algorithms are
that, 1) the observed size class distribution of the Ecuador population represents an
equilibrium population at carrying capacity with no history of harvest, 2) measurements
of palm height (the basis of size classification) are more accurate than estimates of
45
transition rates (which depend on height measurements), and 3) the local population is
mono-dominant with no significant competition from other plant species.
3.1.5 Objectives
In this study, I proposed;
1 To use genetic algorithms for parameter calibration of a population model of the M. flexuosa palm. Calibrated parameters for the Ecuador palm population included; A) seedling survival and growth parameters, B) the carrying capacity on a 1 hectare plot of land, and C) the non-seedling demographic parameters (survival and growth).
2 To compare the population distributions and demographic characteristics between a harvested population (Peru) and a location where harvesting is minimal to none (Ecuador).
3 To test the hypothesis that a plausible harvest history of the Peruvian palm population can be found through the use of genetic algorithms. Optimization parameters include harvest intensity, harvest frequency, length that harvest has occurred, and carrying capacity for the Peru population.
3.2 Methods
3.2.1 Study Site: Ecuador
Data were collected in Ecuadorian Amazon from the Cuyabeno Faunal Reserve
(Figure 3-1). The reserve is managed by indigenous groups (mostly Siona and Secoya)..
This 655,781-ha reserve is located between the San Miguel and Aguarico river basins.
Palm demographic data were collected over the span of two years from five plots (each
20m x 100m) located in seasonally flooded forests. In the first year of sampling all palms
in the five plots (seedlings and non-seedlings) were recorded for demographic data. In
the second year of sampling the same procedure was used, except seedling data were
recorded within ten subplots (5m x 5m) within each of the larger plots. The data
collection in Peru follows the same methods of data collection from the Ecuador study
site, and will be discussed in further detail.
46
3.2.2 Study Site: Peru
Mauritia flexuosa demographic data were collected from sites in the lowland
forests of the Peruvian Amazon, in the department of Loreto, Peru during the summer of
2006. The field sites are approximately a 2-hour boat ride south of Iquitos, Peru on the
Amazon River and Tahuayo River (app. 90 miles). Specifically, field locations are
adjacent to the Tamshiyacu-Tahuayo Community Reserve (Figure 3-2). The
Tamshiyacu-Tahuayo Reserve is a 322,500ha protect area created by the Peruvian
government in 1991.
Palm data were collected from five plots in tropical forest swamps dominated by
M. flexuosa palms. Mauritia flexuosa is the monodominant species in these oligarchic
forests called Aguajales. Three out of the five plots were in close proximity to rivers and
seasonally flooded, while the remaining two plots were in low lying locations that
remained partially flooded through out the year and surrounded by terra firme.
Demographic data were collected for each non-seedling palm in all five plots (20m x
100m). In plot 1 seedling counts were low, allowing for data to be recorded for each
seedling. In plots 2-5 seedling counts were high and subplots were created to estimate
seedling data. Seedling data were recorded within eight subplots (5m x 5m) within the
larger 20m x 100m plots. In each of the plots the demographic data collected consisted
of height measurements (actual for palms that could be reached, and estimated with a
clinometer for taller palms), leaf counts on seedlings and most juveniles, sex, leaf scars,
diameter breast height (DBH), and raceme counts on females. Spatial distance was also
measured between each palm to help construct a layout of the plots and location of palms
from each other.
47
3.2.3 Study Species Role in Peru
Mauritia flexuosa is an economically and ecological important non-timber species
in the Peruvian Amazon (Padoch 1988, Peters et al. 1989b). The fruit of M. flexuosa has
been an important product in the Iquitos market as far back as the mid-1980s, selling
approximately 300 sacks per day and experiencing “extreme rise” in the cost per sack
during times of fruit scarcity (Padoch 1988). The largest numbers of fruit are harvested
from the large oligarchic palm swamps along the Maranon, Ucayali, and Chambira rivers
(Peters et al. 1989a), making M. flexuosa one of the highest exploited fruit tree species in
Peru. While income from harvesting these palms can average to high amounts, the
female trees are cut down to retrieve the fruit from the tall palm, ending the production of
fruit from harvested palms. Since, over half the total fruit sold in Iquitos is from wild
harvested species (Vasquez and Gentry 1989), destructive harvesting methods are a
matter of concern.
The rise in “Aguajale” palm swamps dominated by males following harvest, leads
to a need for better management and conservation, possibly through increased knowledge
of population dynamics in palm swamps. It has been suggested that a switch to growing
M. flexuosa in agroforestry or homegardens plots is beneficial for wild stand management
(Vasquez and Gentry 1989, Bodmer et al. 1997). It is hypothesized, growing M. flexuosa
in agricultural settings will reduce use of destructive harvesting techniques, maintain
palm populations, and allow wildlife to continue foraging on palm fruits. The following
wildlife all consume M. flexuosa from most frequent consumption to least, lowland tapir
(Tapirus terrestris), white-lipped peccary (Tayassu pecari), collared peccary (Tayassu
tajacu), gray brocket deer (Mazama gouazoubira), and red brocket deer (Mazama
americana) (Bodmer et al. 1989).
48
3.2.4 Palm Distribution and Matrix Model Development:
Stage-based matrix population models were used in the study. The development of
the matrix models for the Ecuador palm population was described in chapter two of this
research. The matrix models from Ecuador will be used as a basis for further analysis in
this chapter. The matrix model for palms populations in Ecuador consisted of 7
biological stages, based on size classes. Palms from Peru study sites were classified into
the same seven size classes based on height (Table 3-1) to be consistent with Ecuador
methods. Stages consist of 1 seedling, 4 juveniles, and 2 adult stages. The fecundity (fij)
for the Peru population was estimated with the same fecundity values used in Ecuador
(i.e. seedling survival value) due to lack of data. The established number of seedlings in
Peru at t+1 is also unknown; therefore the number of seedlings at t0 was used as an
assumption to provide estimated values of fecundity.
3.2.5 GA Method Description
A genetic algorithm is a method that finds optimal solutions by mimicking the
process of evolution. A population of individuals evolves over time in order to reach a
desired goal or fitness function by the following procedure. 1) An initial population is
created by randomly assigning “genes” from a defined range. 2) A reproductive
generation cycle is run from the initial population with selective reproduction (offspring
being chosen), mutation, and crossover occurring in the generation cycle. 3) The
population of individuals is evaluated for “fitness”. Individual solutions are represented
in the next generation proportionally to their fitness. 4) Iteration of generation cycle until
maximum fitness is met or until maximum iteration number is reached. During each
generation the genetic algorithm contains components for a fixed population size,
crossover and mutation rates, an acceptance or rejection criteria for optimal solution, and
49
time of iteration cutoff. This study defined fitness as the absolute deviation of the target
size-class distribution from the simulated size class distribution. The perfect solution
would have a fitness value of zero, indicating that each simulated size class was exactly
equal to the target number.
In this study problem-specific genetic algorithms were generated to find optimal
sets of M. flexuosa demographic parameters and plausible harvesting scenarios.
Following Cropper and Anderson (2004), the first GA optimization was designed to
calibrate seedling parameters and estimate carrying capacity. The initial population was
created by randomly selecting seedling survival (stasis) probability from range 0.1 – 0.8
and carrying capacity from range 100.0 – 2000.0 palms ha-1. The seedling growth
parameter was set using equation 3-1:
seedling growth = (1- stasis probability) * x (3-1)
where x is a random value from 0.0-1.0. This equation was used because the sum
of the seedling growth and stasis probabilities cannot be greater than one. These two
seedling parameters along with a carry capacity parameter are assigned to
“chromosomes” in each individual in the population. The size of the population in this
GA was 500. The program was run for 25 generations with selection occurring in each
generation. This program’s fitness goal was to match the observed Ecuador M. flexuosa
female distribution. The calibrated parameters were put into the new transition matrix
and produced a new simulated population distribution. Equation 3-2 evaluated the fitness
score for all GA optimizations in this study:
Fitness = Σ(abs(Ntargeti – Nsimulatedi)) (3-2)
50
where Ntargeti are the size-specific palm numbers that are the goal for calibration
and Nsimulatedi are the size-specific palm numbers produced by the individual’s
parameter set. A smaller difference is desired and indicates stronger population fitness.
The remaining GA optimizations used in the study were similar to the seedling and
carrying capacity optimization. The following GA was used to calibrate the observed
non-seedling demographic parameters (growth and survival) that make up the transition
matrix found in chapter one. There are thirteen non-seedling demographic parameters in
the palm population transition matrix. This optimization program created an initial
population by assigning random uniform parameters needed for calibration between zero
and one, for all thirteen demographic parameters. The demographic parameters for each
size class were normalized, if necessary, to prevent transition probabilities summing to
greater than one. Another set of calibrations used only eleven out of the thirteen values
(all six stasis values and all five 1-size class growth values) assuming that the rare 2-size
class transitions (only 2 observed) don’t occur. If the sum of these three values is greater
than one then the parameters were normalized by dividing each parameter by the sum of
all parameters. Mortality is implicit and does not need to be normalized. For each size
class (1-6) only the stasis and growth parameters (or genes) were assigned to
“chromosomes”. The size of the GA population is 1750 and ran for 75 generations. This
program’s fitness goal was also to reach the observed Ecuador M. flexuosa female
distribution.
The last GA optimization focused on the Peru M. flexuosa population. The goal of
this GA was to find a plausible past harvest history on the Peru M. flexuosa palm
population, a location of intense female harvesting. I assumed that the unharvested
51
Ecuador population is the starting point for a harvesting regime that leads to the size class
distribution observed in Peru (the GA target distribution). The optimization initiated by
using the values in the observed Ecuador transition matrix as initial parameters. The GA
population was created with the following parameters to be optimized: harvest intensity
percent, harvest frequency in years, length of harvesting (years), and carrying capacity.
The value for the harvest intensity was randomly picked from 0.0-100.0%. The harvest
frequency was randomly selected from two separate ranges 1-40 yrs and 1-80 yrs. The
length of harvesting was randomly selected from two ranges 50-300 yrs, 100-500 yrs
respectively correlating with the two harvest frequencies. The carrying capacity for the
Peru population was randomly selected from multiple ranges 200-900, 300-1000, and
400-1000 non-seedling individuals per ha. The size of the GA population in this program
was 500 and ran for 25 generations A second round of GA optimizations to find the past
harvesting history of the Peru palm forests was ran using the optimal Ecuador
demographic parameters found in this study, in place of the observed demographic
parameters.
3.3 Results
3.3.1 Genetic Algorithms
The genetic algorithm (GA) used to calibrate the seedling survival and growth
parameters had an average fitness (difference between observed and simulated size class
distributions) of 46.67 (Figure 3-3). GAs cannot be guaranteed to find the global
optimum. The stochastic elements of initial parameter selection, mutation, and crossover
are needed to reduce the computer time needed to exhaustively evaluate the parameter
space. Multiple GA runs were used to evaluate the robustness of the solution; each run
scored approximately 46. The probabilities for seedling survival (matrix position A00)
52
and seedling growth (matrix position A10) varied over a wide range (Table 3-2). The
values for carrying capacity in a 1ha area were found to range between 346 and 374 non-
seedling palms (Table 3-2).
I found that the observed demographic parameters do not closely match the
observed size class distribution. The matrix population model using the observed
demographic data from the study sites in Ecuador simulated a size class distribution
equivalent to a fitness score of 67.03 (Figure 3-4). The transition probabilities (also
called demographic parameters) of the Ecuador and seedling GA results were not
consistent with the observed size class distribution. I next explored calibration of all
stasis and growth parameters (mortality is implicit) for each non-seedling size class.
These GA optimizations are unconstrained, except for the requirement that the sum of
size class probabilities cannot exceed one. The result for the unconstrained GA that
found a set of 13 optimal demographic parameters has a fitness score of 14.14, producing
a lambda of 1.007 (Figure 3-5). The unconstrained GA with 11 demographic parameters
(excluding the 2-size class growth parameters) has a fitness score of 5.07, producing a
lambda of 1.039 (Figure 3-6). Some of the optimal parameter values fell outside the
range of plot variation (Figure 3-7). The danger of optimizing a large set of unknowns is
finding values that match the target, but do not have biologically plausibility.
Optimization with values constrained to the observed range (Table 3-3) was used to
address this issue.
Six separate GA runs used the constrained parameter ranges. Three GA runs
optimized all 13 parameters, and three others did not include 2-size class growth
transition parameters. The three runs for optimizing all 13 demographic parameters have
53
fitness scores of 6.29, 9.07, and 7.19 (Figure 3-8). The three runs for optimizing
demographic parameters without the 2-size class growth transitions have scores of 7.69,
12.03, and 13.96 (Figure 3-9). In figure 3-7, 3-8 and 3-9 the “combined data” is the
values for the observed Ecuador stasis and growth parameters of the transition matrix
created in chapter one of this thesis. These data were based on pooling all of the
individual plot data. The best scoring run (Figure 3-10) optimizing all 13 demographic
parameters has a score of 6.29 and a lambda of 1.040. The best scoring run (Figure 3-11)
with no 2-size class growth parameters is 7.69, which has a lambda of 1.038. In figure 3-
10 and 3-11, I found that size class three and four have the largest differences between
the observed and simulated size class distributions. Figure 3-8 and 3-9 shows that size
class three and four also have the largest difference observed and simulated demographic
parameters.
The new transition parameters from the two best constrained GA optimizations
were compared to the empirical transition parameters (Table 3-4). The CAV6.29
(constrained, all values) GA parameter set produced stasis parameters (except size class
1) that are lower then the empirical stasis parameters. The same GA optimization also
shows that the growth parameters are generally greater than the empirical growth
parameters (except size class 1 and both size class 2 growth transitions). Similar results
are seen for the optimal parameters in the matrix with CNT 7.69 (constrained, no two-
size class transitions). In the CNT 7.69, the optimal demographic parameters have a
larger difference from the empirical demographic parameters, then the optimal
parameters in the CAV6.29 run.
54
Optimization of seedling parameters and carrying capacity was conducted a second
time using the new optimal demographic parameters from both unconstrained and
constrained GA versions. Four separate replicates were run in each of the four GA
versions to assist in accessing variation. Table 3-5 shows the new results of the optimal
seedling survival, seedling growth, and carrying capacity for the Ecuador population. All
of the replicates in the two unconstrained GA versions (score 14.14 and 5.07) as well as
in the two constrained GA versions (score 6.29 and 7.69) show seedling parameter values
which vary over a wide range. In each of the four GA versions, the four separate
replicates all produce a very similar fitness score to each other, showing that the seedling
parameters are insensitive to contributing to the number of individuals in the non-
seedling size classes. While all the new fitness scores are preferable, seedling
demographic values vary and show inconsistency in each of the four replicates in all four
GA versions, and seedling parameters are insensitive during GA optimization. There
should be little confidence that the GA is a useful tool for seedling parameter
optimization based when each run finds a greatly different local optimum.
3.3.2 Peru Size Class Distribution and Demographic Characteristics
At the Peruvian study site 198 non-seedling individuals were present in the 1ha
area (seedling size class = 2342). The distribution of individuals shows the largest
amount of palms in size class 1, followed by size class 5, with the lowest amount of
palms in size class 2, 3, 4, and 6 (Table 3-1 and Figure 3-12). The total number of non-
seedling individuals in the Ecuador study site is 336 (seedling number were 260 and 1460
respectively during two years of sampling). The number of adult male and adult female
palms per ha area sampled in Peru is 54 and 23 respectively (Figure 3-13). The number
of adult male and adult female palms in Ecuador, where harvesting palms in minimal, is
55
54 and 35 respectively. The estimated average fecundity for females in the Peruvian
palm population is 18.2, with 5.2 for size class five and 31.2 for size class six. Size class
six has fewer reproductive females compared to size class five (3 to 18 respectively,
Table 3-1). The taller female palms in size class six are more likely to be felled for
retrieval of the M. flexuosa fruit. Further results of the Ecuador palm population
dynamics can be found in chapter 2.
Peru palm demographic data on number of leaf scars, DBH, and trunk height for
palm individuals in size class 3, 4, 5, and 6 can be found in table 6. Demographic data
were recorded for palms in all size classes, and in the juvenile and adult size classes
(three through six); data related to palm trunks is available. At size class three some
palms transitioned from multiple petioles to beginning to form a trunk. Palms in the
increasing size classes (4-6) have trunks formed. The number of leaf scars was highest
for palms in size class 5 (20-28m), with an average of 61.5 scars present on the trunk.
The tree diameter at breast height was largest for palms in size class 6 (>28m), with an
average of 99.2 cm. Palms are originally assigned into size classes based on their total
height (trunk height and leaf height). The average height of only trunks (not total height)
for pre-reproductive palms in size class three was 2.6m and in size class four was 9.0m
(Table 3-6). Between each size class there was approximately 6.5 – 7.5m difference in
average trunk height.
3.3.3 Genetic Algorithm: Harvest History for Peru M. flexuosa Palm Population
GA optimizations have been run to find plausible harvesting histories that could
lead from a population distribution observed in Ecuador to the distribution that is
currently seen in Peru. Although this technique cannot reconstruct actual harvest
histories, it may illustrate harvest regimes of realistic magnitude. The transition matrix
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from the study site in Ecuador produced a lambda of 1.046 (a growing population
projection) and 336 non-seedling individuals per ha. It is assumed that Ecuador’s
population demographic parameters and distribution of individuals are at a somewhat
stable, healthy state. The lambda for the population in Peru in unknown at this point, but
as reported there are 198 non-seedling individuals per ha. Six GA runs using the
observed Ecuador demographic parameters had fitness scores ranging from 62.8 to 135.4
(Table 3-7) and varying parameter results (harvesting percent, harvesting frequency,
harvest length, and fitness scores). In all six runs the carrying capacity value showed a
trend of reaching the lowest value allowed in the range. Harvest lengths were highly
variable and tended to be extreme values within the range. These optima represented
poor fits to the target and do not represent plausible harvesting regimes for transition
from the Ecuador to Peru size class distribution.
The GA-based optimal demographic parameters were used in a second round of
GA optimizations to find plausible harvest histories in Peru, using the same parameter
inputs. Each of the four optimal demographic parameter results (two unconstrained
trails: score 14.14 and 5.07, and two constrained trails: score 6.29 and 7.69) had six
separate GA runs for a total of 24 harvesting optimizations, which produced fitness
scores varying from 41.4 to 74.7 (Table 3-8). Harvest percent and harvest frequency
were the most variable; changing in each of the 24 runs. Typically the optimal carrying
capacity was found at the lowest end of the range possible, except for the six versions in
the GA with all 13 unconstrained demographic parameters. Another trend was that the
length of harvest is typically found at the highest end of the range, except for the six
versions in the GA with all 13 unconstrained demographic parameters.
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3.4 Discussion
3.4.1 Genetic Algorithms
The first GA approach was to calibrate seedling survival and growth in the
transition matrix and carrying capacity for a palm population from Ecuador. As noted
earlier in this study, Cropper and Anderson (2004) successfully found the seedling
survival and growth parameters for the palm Iriartea deltoidea. Our study did not find
seedling survival and growth parameters that closely matched the observed Ecuador
population distribution. The seedling parameters found by the GA created a simulated
size class distribution that had a difference of 46.62 individuals from the observed
population. Furthermore, an assortment of seedling survival and growth transition values
repeatedly produced a similar population distribution for each size class. Seedling
parameters found by the GA were insensitive to matching non-seedling size classes with
the observed size classes. This led us to believe that other demographic parameters might
be poorly estimated. The carrying capacity found by the GA is similar to the observed
Ecuador carrying capacity.
Assuming that the Ecuador size class distribution was measured with less error than
the transition rates, GA optimization should lead to improved parameter estimates.
Separate runs of GAs were able to generate optimal non-seedling demographic
parameters that did match the observed population distribution. It was first found that the
empirical demographic parameters from the pooled data in the Ecuador study plots did a
relatively poor job of matching the observed Ecuador population distribution (a
difference of 67.03 individuals). Poorly estimated demographic parameters are most
likely a result of sampling error in this study. All four GAs that estimated optimal
demographic parameters produced a good fit to the fitness goal, the observed population
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distribution. Interestingly, the unconstrained GA (with a difference of 14.14 individuals)
had an optimum matrix, which was not similar to the observed transition matrix, even
though the simulated and observed size class distributions were similar. The consistent
deviations of GA estimates of size classes three and four parameters from the observed
data may implicate these data as poorly sampled. In the observed data there were rare 2-
size class growth transition probabilities in size class 1 and 2. Only one palm in each size
class makes this rare 2-size class growth transition. The next GA assumes that there are
never these rare 2-size class growths. This GA produced demographic parameters that
had the best fitness (a summed difference of 5.07 individuals).
Optimal demographic parameters from the two previous GAs were a good fit to the
observed size class distribution, but optimal stasis and growth parameters fell outside the
observed range of demographic parameters. By constraining the optimal parameters to
within the range of observed parameters, more realistic parameters can be found which
still have a strong fitness score. Usually it is not beneficial to constrain initial parameters
in a GA, but results from the unconstrained GAs produced stasis and growth parameters
in size class 1, 3, and 4 that were unlikely. Both constrained GAs create good fits to the
observed distribution, with similar fitness scores (6.29 and 7.69). Abandoning the 2-size
class growth transition does not notably affect the GA optimizations. Multiple runs of
the same GA are recommended because GA optimizations can get “stuck” in a local
parameters space minimum.
Since the GA technique was able to calibrate the non-seedling demographic
parameters, it was beneficial to use these new parameters to re-estimate the seedling
survival and growth parameters. Using the optimal demographic parameters did find
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seedling parameters that produced a size class distribution that matched the observed
population distribution, but as seen before the seedling parameters varied over a wide
range in each separate trial. It would be premature to conclude that seedling survival is
of little demographic importance in these populations, but variation in seedling survival
and growth may not contribute significantly to the size class distribution of larger palms.
3.4.2 Peru Size Class Distribution and Demographic Characteristics
The ratio of adult males to female palms in Peru implies that removal of female
palms has been occurring. The main target of female palm removal is size class six,
which contains the tallest palms and is assumed to be the most difficult to climb. This
removal of adult female palms can alter the seedling regeneration, density dependence,
and interactions with other species. Comparing the distribution of M. flexuosa palms in
Ecuador and Peru displays the impact of harvesting in Peru and consequently the
eradicate number of individuals in each size class. This study has shown there is
difficulty in estimating demographic transition values in Ecuador, leading to the use of a
GA to calibrate parameters, it is also predicted that the difficulty will be just as
challenging if not more for the Peru population.
Leaf scars on palms are one method to estimate the rate at which palms are
growing, as well as the length in time palms have been growing. It is predicted that the
palms in the larger size class six are growing at a fast rate, presumably to reach the
canopy and become emergent. Size class six M. flexuosa have on average fewer leaf
scars than size class five M. flexuosa palms, and may indicate growing at a faster rate
than shorter M. flexuosa palms. It is also interesting to look into the difference in trunk
height between size classes. The large increase in trunk height from size class three to
size class four, (as well as into size class five), might suggest that palm growth is rapid in
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late juvenile and possibly early reproductive stages. This coincides with data collected
on palms in Ecuador (see second chapter). The Ecuador transition matrix shows a high
growth probability in size class three (although GA parameter estimates indicate that the
observed rate could be an overestimate). The relatively low numbers in size classes three
and four may also indicate a rapid growth to the adult sizes.
3.4.3 Genetic Algorithm: Peru M. flexuosa Palm Population
Estimating the harvesting history and carrying capacity of the Peruvian palm
population was challenging. Our study did not find harvesting values that closely
matched the observed Peru size class distribution. There are many combinations of
harvesting parameters that could have occurred in the past to produce the observed
population distribution. Consequently, the GA technique was not able to provide
plausible levels of prior palm removal in Peru. Reasons might include: 1) the Peru
population has different demography (survival, growth, fecundity) than Ecuador’s
population and 2) the actual history of harvest was not regular and uniform. Estimating
the optimal carrying capacity was also a challenge, but it is possible that the carrying
capacity in Peru is lower than observed in other M. flexuosa populations, because the GA
generally converges on lowest carrying capacity possible. Through communication with
local Peruvians and knowledge of past area history, we know that female palm harvesting
has occurred in our area of data collection.
3.5 Conclusions
Genetic algorithms may be useful for calibrating demographic parameters in a
matrix model. Constraining the demographic parameters to be chosen within a realistic
range resulted in the best procedure. Usually GA initial search parameters are limited
when they are constrained, providing lower fitness results than unconstrained GAs, but
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that was not the case in this study. The demographic data showed that this particular
palm population has rare transitions (two individuals grew two size classes in one time
step). I found that excluding the rare, two size class growth transitions did not strongly
affect the GA optimizations. These large, rare transitions and other vital rates might have
been incorrectly recorded due to sampling error. Sampling error is a common problem in
population data collection. This study found that sampling error (specifically in
estimating stasis parameters) could affect the accuracy of transition matrix models, while
rare growth transitions do not have an effect.
While a previous GA has estimated seedling survival and growth parameters for a
tropical palm, this study was unable to estimate consistent seedling parameters that
matched the non-seedling population distribution. In this study, the value of seedling
survival and growth parameters for the Ecuador palm population is insensitive to
optimization. The recorded palm data from Peru does show that the population is
experiencing loss of females due to harvesting. This study was also unable to accurately
estimate the harvesting trends that have occurred in the past to produce the observed Peru
study site distribution. Palm removals in wild locations in Peru are likely to continue in
the future, until there is a full switch to agricultural gardens of M. flexuosa. Accurately
understanding demographic parameters through the use of parameter calibration is greatly
needed for management of harvesting or species recovery and restoration efforts.
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Table 3-1. M. flexuosa population distribution, for palms in a 1ha area, from Peru and
Ecuador, as well as the number of male and female palms in each size class from both locations. (Palms generally become reproductive at size class 5, but in Peru some palms were seen to become reproductive in size class 4).
Peru Peru Peru Ecuador Ecuador Ecuador Size Classes N(t) 2006 Males Females N Males Females
0 <1.0 2342.0 1171.0 1171.0 260.0 130.0 130.01 1.01-3.0 72.0 36.0 36.0 87.0 43.5 43.52 3.01-6.0 22.0 11.0 11.0 101.0 50.5 50.53 6.01-10.0 10.0 5.0 5.0 27.0 13.5 13.54 10.01-20.0 20.0 10.0 10.0 32.0 16.0 16.05 20.01-28.0 60.0 41.0 18.0 47.0 29.0 18.06 >28.01 14.0 11.0 3.0 42.0 25.0 17.0
Total 198.0 54.0a 23.0a 336.0 54.0a 35.0a
a Total number of only reproductive individuals.
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Table 3-2. Optimal values for two seedling parameters (seedling stasis probability (matrix position A00), seedling growth probability (matrix position A10)), and for Ecuador’s carrying capacity (K) in a 1ha area, using observed demographic data.
Seedling and K runs with observed data K A00 A10 Opt Score
348 0.5899 0.0050 46.766346 0.1734 0.7178 46.624374 0.0257 0.0056 46.617
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Table 3-3. Observed range of the 13 non-seedling demographic transition probabilities, found from data collected at 5 separate study plots in Ecuador.
Ecuador Plot Observations
Matrix
position Low range High range 1 A11 0.50 0.92902 A21 0.07 0.50003 A22 0.62 0.96004 A31 0.00 0.01155 A32 0.04 0.38006 A33 0.66 0.85007 A42 0.00 0.00998 A43 0.14 0.33009 A44 0.50 0.8800
10 A54 0.00 0.500011 A55 0.67 1.000012 A65 0.00 0.330013 A66 0.67 0.9230
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Table 3-4. Transition matrices for 1) the observed pooled data in Ecuador, 2) GA optimization for all 13 demographic parameters, with constraints on parameters, and 3) GA optimization for all demographic parameters expect 2 size class growth transitions, with constraints on parameters.
Observed transition values Seedlings Young Juveniles Old Juveniles Adult
<1.0 m 1.0-3.0 m 3.0-6.0 m 6.0-10.0 m 10.0-20.0 m 20.0-28.0 m > 28.0 m 0.4923 0.0 0.0 0.0 0.0 16.8 16.80.0115 0.7471 0.0 0.0 0.0 0.0 0.0
0.0 0.2184 0.8911 0.0 0.0 0.0 0.00.0 0.0115 0.0990 0.7778 0.0 0.0 0.00.0 0.0 0.0099 0.2222 0.7813 0.0 0.00.0 0.0 0.0 0.0 0.1875 0.8723 0.00.0 0.0 0.0 0.0 0.0 0.0851 0.8810
Score 6.29 Optimal GA values - all demographic parameters Seedlings Young Juveniles Old Juveniles Adult
<1.0 m 1.0-3.0 m 3.0-6.0 m 6.0-10.0 m 10.0-20.0 m 20.0-28.0 m > 28.0 m 0.4923 0.0 0.0 0.0 0.0 16.8 16.80.0115 0.8204 0.0 0.0 0.0 0.0 0.0
0.0 0.1700 0.8536 0.0 0.0 0.0 0.00.0 0.0077 0.1276 0.6440 0.0 0.0 0.00.0 0.0 0.0059 0.3171 0.6040 0.000 0.00.0 0.0 0.0 0.0 0.3450 0.8150 0.00.0 0.0 0.0 0.0 0.0 0.1310 0.8460
Score 7.69 Optimal GA values - no 2 size class transition parameters Seedlings Young Juveniles Old Juveniles Adult
<1.0 m 1.0-3.0 m 3.0-6.0 m 6.0-10.0 m 10.0-20.0 m 20.0-28.0 m > 28.0 m 0.4923 0.0 0.0 0.0 0.0 16.8 16.80.0115 0.8210 0.0 0.0 0.0 0.0 0.0
0.0 0.1590 0.8602 0.0 0.0 0.0 0.00.0 0.0 0.1389 0.6234 0.0 0.0 0.00.0 0.0 0.0 0.3098 0.6457 0.000 0.00.0 0.0 0.0 0.0 0.3295 0.8250 0.00.0 0.0 0.0 0.0 0.0 0.1698 0.7800
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Table 3-5. Optimal values for two seedling parameters, seedling stasis probability (matrix position A00), seedling growth probability (matrix position A10), and for Ecuador’s carrying capacity (K) in a 1ha area.
Results from using unconstrained parameters All Transitions (14.14) No 2-size Class Transitions (5.07)
K A00 A10 Opt Score K A00 A10 Opt Score 380 0.03061 0.77135 14.193 350 0.4341 0.00507 5.008380 0.13129 0.82250 14.193 350 0.4931 0.00463 5.008
1660 0.53000 0.00971 13.870 348 0.1786 0.00814 5.214379 0.11627 0.51079 14.252 430 0.7700 0.00173 4.958
Results from using constrained parameters All Transitions (6.29) No 2-size Class Transitions (7.69)
K A00 A10 Opt Score K A00 A10 Opt Score 368 0.16995 0.19438 6.225 361 0.64787 0.13415 7.674475 0.76935 0.00201 6.362 362 0.63258 0.00407 7.683369 0.23126 0.00898 6.212 361 0.10501 0.89291 7.674370 0.31195 0.00676 6.210 361 0.17342 0.80883 7.674
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Table 3-6. Demographic traits for the Peru population in size classes 3-6 (palms that have
developed trunks). Pre-reproductive Juveniles Reproductive Adults Size Class 3 Size Class 4 Size Class 5 Size Class 6 Avg. # of Leaf Scars na 29.4 61.5 60.4 Avg. DBH (cm) na 84.2 86.6 99.2 Avg. Trk. Height (m) 2.6 9.0 16.5 24.2
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Table 3-7. GA estimates of harvest regimes consistent with the observed size class distribution. RESULTS USING OBSERVED DEMOGRAPHIC PARAMETERS
Parameter Inputs Parameter Outputs
harvest percent
harvest frequency
(yr) harvest
length (yr) carrying capacity
harvest percent
harvest frequency
(yr) harvest
length (yr) carrying capacity
opt score
0.0-100.0 1.0-41.0 50-301 400-1000 0.74 31.0 50.0 400.0 130.80.0-100.0 1.0-81.0 100-501 400-1000 0.42 21.0 101.0 400.0 135.4
0.0-100.0 1.0-41.0 50-301 300-1000 0.49 6.0 300.0 300.0 99.70.0-100.0 1.0-81.0 100-501 300-1000 0.01 13.0 500.0 300.0 99.7
0.0-100.0 1.0-41.0 50-301 200-900 0.70 6.0 300.0 200.0 62.80.0-100.0 1.0-81.0 100-501 200-900 0.27 79.0 482.0 200.0 62.8
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Table 3-8. Peru’s harvesting history found using separate GAs which uses the four sets of Ecuador optimal demographic parameters to reach Peru’s observed population distribution. Optimization found harvest percent, harvest frequency, length harvesting has occurred, and carrying capacity.
RESULTS USING CAV 6.29 (CONSTRAINED, ALL VALUES) OPTIMAL DEMOGRAPHIC PARAMETERS Parameter Inputs Parameter Outputs
harvest percent
harvest frequency
(yr) harvest
length (yr) carrying capacity
harvest percent
harvest frequency
(yr) harvest
length (yr) carrying capacity
opt score
0.0-100.0 1.0-41.0 50-301 400-1000 0.71 27.0 300.0 400.0 59.90.0-100.0 1.0-81.0 100-501 400-1000 0.61 1.0 414.0 400.0 59.9
0.0-100.0 1.0-41.0 50-301 300-1000 0.56 23.0 300.0 300.0 48.10.0-100.0 1.0-81.0 100-501 300-1000 0.14 54.0 429.0 300.0 48.1
0.0-100.0 1.0-41.0 50-301 200-900 0.42 37.0 300.0 200.0 47.00.0-100.0 1.0-81.0 100-501 200-900 0.46 45.0 451.0 200.0 47.0
RESULTS USING CNT 7.69 (CONSTRAINED, NO TWO SIZE-CLASS TRANSITIONS) OPTIMAL DEMOGRAPHIC PARAMETERS Parameter Inputs Parameter Outputs
harvest percent
harvest frequency
(yr) harvest
length (yr) carrying capacity
harvest percent
harvest frequency
(yr) harvest
length (yr) carrying capacity
opt score
0.0-100.0 1.0-41.0 50-301 400-1000 0.39 18.0 300.0 400.0 55.80.0-100.0 1.0-81.0 100-501 400-1000 0.29 36.0 462.0 400.0 55.8
0.0-100.0 1.0-41.0 50-301 300-1000 0.77 19.0 300.0 300.0 45.80.0-100.0 1.0-81.0 100-501 300-1000 0.61 56.0 444.0 300.0 45.8
0.0-100.0 1.0-41.0 50-301 200-900 0.65 36.0 297.0 200.0 45.50.0-100.0 1.0-81.0 100-501 200-900 0.14 72.0 459.0 200.0 45.5
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Table 3-8. Continued
RESULTS USING UCNT 5.07 (UNCONSTRAINED, NO TWO SIZE-CLASS TRANSITIONS) OPTIMAL DEMOGRAPHIC PARAMETERS Parameter Inputs Parameter Outputs
harvest percent
harvest frequency
(yr) harvest
length (yr) carrying capacity
harvest percent
harvest frequency
(yr) harvest
length (yr) carrying capacity
opt score
0.0-100.0 1.0-41.0 50-301 400-1000 0.86 34.0 300.0 400.0 74.70.0-100.0 1.0-81.0 100-501 400-1000 0.63 1.0 469.0 400.0 74.7
0.0-100.0 1.0-41.0 50-301 300-1000 0.59 17.0 300.0 300.0 48.50.0-100.0 1.0-81.0 100-501 300-1000 0.44 80.0 491.0 300.0 48.5
0.0-100.0 1.0-41.0 50-301 200-900 0.51 11.0 300.0 200.0 46.40.0-100.0 1.0-81.0 100-501 200-900 0.51 10.0 499.0 200.0 46.4
RESULTS USING UCAV 14.14 (UNCONSTRAINED, ALL VALUES) OPTIMAL DEMOGRAPHIC PARAMETERS Parameter Inputs Parameter Outputs
harvest percent
harvest frequency
(yr) harvest
length (yr) carrying capacity
harvest percent
harvest frequency
(yr) harvest
length (yr) carrying capacity
opt score
0.0-100.0 1.0-41.0 50-301 400-1000 0.36 23.0 50.0 999.0 41.40.0-100.0 1.0-81.0 100-501 400-1000 0.8 56.0 100.0 999.0 45.0
0.0-100.0 1.0-41.0 50-301 300-1000 0.38 35.0 50.0 999.0 41.40.0-100.0 1.0-81.0 100-501 300-1000 0.29 69.0 101.0 998.0 45.1
0.0-100.0 1.0-41.0 50-301 200-900 0.72 34.0 50.0 896.0 42.30.0-100.0 1.0-81.0 100-501 200-900 0.25 57.0 102.0 897.0 45.9
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Figure 3-1. Map of study site in Ecuador. Cuyabeno Faunal Reserve is located in the
north-eastern section of Ecuador in the highlighted area. (Source: http://www.ecuaworld.com/map_of_ecuador.htm, last accessed July 25, 2007).
N
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Figure 3-2. Map of study site in Peru. (Source:
http://www.micktravels.com/peru/images/peru_map.jpg, last accessed July 22, 2007).
Study site along Tahuayo River, adjacent to Tamshiyacu-Tahuayo Communal Reserve.
N
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Figure 3-3. Genetic algorithm simulated (red bars) and observed distribution (blue bars) for the
Ecuador palm population after running a GA to find optimal seedling survival and growth parameters using the observed transition parameters. Fitness score for this GA is 46.67, found by ((Σ(abs(observed distribution – simulated distribution)).
74
Figure 3-4. Genetic algorithm simulated and observed distribution for the Ecuador palm
population after running a GA using the observed transition parameters and evaluating how well it matches the observed population distribution. Fitness score for this GA is 67.03, found by ((Σ(abs(observed distribution – simulated distribution)).
75
Figure 3-5. Genetic algorithm simulated and observed distribution for the Ecuador palm
population after running an unconstrained GA to optimize all non-seedling demographic parameters in the transition matrix. Fitness score for this GA is 14.14, found by ((Σ(abs(observed distribution – simulated distribution)).
76
Figure 3-6. Genetic algorithm simulated and observed distribution for the Ecuador palm
population after running an unconstrained GA to optimize non-seedling stasis and growth parameters in the transition matrix (two size class growth transitions not included). Fitness score for this GA is 5.07, found by ((Σ(abs(observed distribution – simulated distribution)).
77
0
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GA optimum14.14GA optimum5.07
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0.6
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CombineddataGA optimum14.14GA optimum5.07
B
Figure 3-7. Stasis and growth demographic points generated from an unconstrained GA. The red lines in both figures A and B, are the low and high ranges of possible demographic points measured from the five plots in Ecuador. (A) Demographic data of stasis transition parameters for three separate trials, 1) the combined data from the observed study plots, 2) the unconstrained GA run with all 13 demographic parameters, and 3) the unconstrained GA run without the 2 size class growth parameters. (B) Demographic data of growth transition parameters for the same three separate trials.
78
0
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CombineddataGA optimum6.29GA optimum9.07GA optimum7.19
A
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0 1 2 3 4 5 6
Size Class
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High range
CombinedDataGA optimum6.29GA optimum9.07GA optimum7.19
B
Figure 3-8. Stasis and growth demographic points generated from a constrained GA. The red lines in both figures A and B, are the low and high ranges of possible demographic points measured from the five plots in Ecuador. (A) Demographic data of stasis transition parameters for the combined data from the observed study plots, and three separate constrained GA trials that calibrate estimates of all 13 demographic parameters. (B) Demographic data of growth transition parameters for the combined data from the observed study plots, and the same three separate trials
79
0
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GA optimum7.69GA optimum12.03GA optimum13.96
A
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0.3
0.4
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0 1 2 3 4 5 6
Size Class
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High range
CombinedDataGA optimum7.69GA optimum12.03GA optimum13.96
B
Figure 3-9. Stasis and growth demographic points generated from a constrained GA. The red lines in both figures A and B, are the low and high ranges of possible demographic points measured from the five plots in Ecuador. (A) Demographic data of stasis transition parameters for the combined data from the observed study plots, and three separate constrained GA trials that calibrate estimates of demographic parameters without the 2 size class growths. (B) Demographic data of growth transition parameters for the combined data from the observed study plots, and the same three separate trials.
80
Figure 3-10. Simulated output of the best constrained GA run with all 13 demographic parameters. Simulated and observed distribution for the Ecuador palm population after running a GA to optimize all non-seedling demographic parameters in the transition matrix. Fitness score for this GA is 6.29 found by ((Σ(abs(observed distribution – simulated distribution)).
81
Figure 3-11. Simulated output of the best constrained GA run with demographic parameters that
do not include 2 size class growths. Simulated and observed distribution for the Ecuador palm population after running a GA to optimize all stasis and 1 size class growth non-seedling demographic parameters in the transition matrix. Fitness score for this GA is 7.69 found by ((Σ(abs(observed distribution – simulated distribution)).
82
0
20
40
60
80
100
120
1 2 3 4 5 6
Size Class
N
PeruEcuador
Figure 3-12. M. flexuosa population distribution for palm populations in a 1ha area in Peru and
Ecuador (seedling, size class zero, not included).
83
0
10
20
30
40
50
60
Male Female Avg. Fecundity
N
PeruEcuador
Figure 3-13. Distribution of male vs. female palms and estimated, averaged fecundity values from Peru and Ecuador.
84
CHAPTER 4 SUMMARY
4.1 Applicability
This research has potential use for creation of Mauritia flexuosa management plans that
can be applied to the studied Ecuadorian palm population. Forest-dwelling people who utilize
M. flexuosa can use the results from the harvesting simulations for specifically the examined
Ecuador population. Multiple communities who harvest wild M. flexuosa from the same
populations will need to create collaborative harvesting plans that meet all stakeholders’ needs as
well as abide by sustainable harvesting limits proposed in this research. It is the hopes of this
author that these methods can also be applied to M. flexuosa palm populations in all parts of the
Amazon. To do so, specific population dynamics such as transition probabilities and growth rate
will have to be estimated for populations in separate locations. Then similar methods of
development for modeling sustainable harvesting scenarios can be applied. This study is also
applicable to other harvested palm species through the tropics.
The results found from the genetic algorithm (GA) optimization conclude that matrix
model parameters can be calibrated to find optimal demographic parameters. The GA
optimizations in this study have applicability to aid in parameterization of current and future
matrix population models that are developed with sampling error. Accurate matrix population
models can be applied to improvement of population management plans.
4.2 Future for M. flexuosa
It is difficult to predict the exact future for a species, but it is estimated that fruit from M.
flexuosa will continue to be a marketable resource. In Peru there is a switch from harvesting
palms in the wild, to growing M. flexuosa in gardens and small agricultural plots. It is predicted
that this palm could become a domesticated crop in other Amazon locations and countries. Data
85
collected on palms grown in homegardens in Peru show that palms mature at a shorter height and
in a faster time span (Figure A-1). Data collected on juvenile M. flexuosa in homegardens also
show that the number of petioles is on average higher than palms located in wild populations
(Figure A-2). Palms that are maintained in gardens with initial weeding, spacing, and some
maintenance can develop into each size class at a faster rate then seen in the wild (Figure A-3).
This data shows that M. flexuosa has the potential to successfully be domesticated.
4.3 Future Research
To fully understand the switch to growing M. flexuosa as a cultivated palm, crop evolution
and genetics should be studied for the species. There is a potential that a genetic selection is
already occurring for choosing dwarf palms. Agricultural research, such as planting season,
intercropping management, plant nutrition, and disease and pest management, should be
considered for this species before it goes into large-scale tropical crop production. Future
research on understanding the population dynamics of this species is still needed. For example,
each size class’s role in density dependence should be further understood. Fecundity rates for
female palms during different stages of population equilibrium and non-equilibrium should be
understood in more detail. A prompt future study should use the optimal transition matrices
containing optimal demographic parameters to immediately re-estimate sustainable harvesting
scenarios for Ecuador populations. It is proposed that the demographic parameters found by
GA’s in this study should estimate more accurate harvesting regimes.
86
APPENDIX A PERU GARDEN DATA FOR MAURITIA FLEXUOSA
Data collected from three separate homegardens in the Peruvian Amazon show the
difference between palms grown in gardens and palms in wild locations. This difference is seen
in palm height, number of petioles, and the size of petiole sheaths. A main difference is that
cultivated palms become mature and reproductive at a shorter height. This is an important
process for harvesting fruit in a non-destructive manner. I believe more data on cultivated M.
flexuosa is needed to understand the difference between palms growing in the wild and palms in
gardens. In Figure A-1 the following is the number measured (N) for each category of palms.
Wild population: 76, 12, and 36 for young juveniles, old juveniles, and adults respectively.
Garden population: 104, 26, and 11 for young juveniles, old juveniles, and adults respectively.
Seedlings were not measured in garden locations. In Figure A-2 the following is the number
measured (N) for each category of palms. Smaller juveniles: 34 and 32, respectively for garden
palms and wild palms. Larger juveniles: 70 and 50, respectively for garden palms and wild
palms.
87
0
5
10
15
20
25
30
Seedling Young Juv. Old Juv. Adult
Palm Stages
Hei
ght (
m) Wild population
Garden population
Figure A-1. Average height (m) for M. flexuosa palms in the seedling stage, young juvenile
stage, old juvenile stage, and adult (reproductive) stage; from palms sampled in wild population and gardens in Peru.
p j g
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
Garden height(m)
Wild pop.height (m)
Gardenpetiole count
Wild pop.petiole count
Heig
ht a
nd p
etio
le c
ount
s Smaller Juveniles
Larger Juveniles
Figure A-2. Comparison of average palm height and average number of petioles, for juvenile M.
flexuosa located in gardens and wild populations (in Peru).
88
A
B
Figure A-3. M. flexuosa palms in Peru homegardens. (A) Picture of juvenile (pre-reproductive) M. flexuosa palms in a homegarden. (B) Picture of dwarf, reproductive female palm. Both pictures were taken by Dr. Jim Penn in 2006.
89
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96
BIOGRAPHICAL SKETCH
Jennifer grew up in the wooded area of Douglasville, Georgia, a suburb of Atlanta. Her
parents always encouraged her to play and explore outside, and it was through this
encouragement that she developed a love for the interactions in the forested environment around
her. In her early education she was always excited to read many books and learn about anything
related to science. From a young age she knew that she wanted to get a higher education in the
biological sciences and hopefully become a scientist at some point. Jennifer’s father, being a
physicist had a large influence on her. Jennifer graduated high school with a 4.0 GPA and was
valedictorian. Her next stop on her educational path was Emory University in Atlanta, GA in
2000.
At Emory University Jennifer majored in environmental studies and minored in
anthropology. Her classes ranged between many sub-disciplines in environmental education,
including classes in geology, earth systems dynamics, behavioral ecology, and tropical ecology.
The summer before her junior year made the largest impact on her decision for future path of
studies. Jennifer was accepted into the School for Field Studies and traveled to Queensland,
Australia where she took a field course in tropical restoration. During this trip she partially
worked on a 5-year project that focused on tropical corridor construction in the rainforests of
northern Australia. Upon her return to Emory University and Atlanta, she began an internship at
the Atlanta Botanical Gardens working with neo-tropical plants, Nepenthes. She wanted to learn
anything she could about tropical plants and tropical ecology. During Jennifer’s time at Emory
University she also took a field course that offered a trip to Costa Rica to learn about its
environment. After her four years at Emory University, she next enrolled at University of
Florida in the Interdisciplinary Ecology program in the School of Natural Resources and
Environment.
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At University of Florida Jennifer worked under the guidance and leadership of Dr. Wendell
P. Cropper Jr. in the School of Forest Resources and Conservation. She considered her graduate
studies to have two different concentrations, 1) forest ecology and 2) tropical conservation and
development. During her 2 ½ years as a masters student at University of Florida, one of her
biggest moments was conducting field research in the Peruvian Amazon. This was a big step for
Jennifer as a researcher and helped her develop field data collection experience. Another large
moment for her was presenting at the 2006 Ecological Society of American annual meeting, and
at various other conferences and meetings. Jennifer’s classes and work at University of Florida
have been worthwhile and a good learning experience. After finishing her research and
graduating with a master’s degree, she considers herself a tropical forest ecologist who focuses
on population and simulation modeling. It is with the help and guidance of her advisor,
committee, fellow graduate students, and especially her family that she has gotten to where she is
today.
