Size Ratios

Size Ratios

• The analysis of size ratios has been of interest to ecologists and evolutionary biologists

• Dyar (1890) described a constant increment of hard part length for insects at each molt was ≈ 1.28

• Others have shown good examples of character displacement (sympatric populations differing more than allopatric)

Size Ratios

• First suggested by Hutchinson (1959; Homage to Santa Rosalia)

• An approximate value of 1.3 was the tentative amount of separation necessary to permit coexistence of species at the same tropic level

3 Patterns

• 1) minimum size ratios, below which species cannot coexist

• 2) constant size ratios, in which the species in a community display an orderly spacing

• 3) unusually large ratios in island assemblages, which are though to be experiencing more sever competition than comparable mainland assemblages

Assumptions

• 1) Morphology is linked to resource consumption and the appropriate morphological features of the organisms have been measured

• For example, Carothers (1982) found that resource partitioning in a guild of Hawaiian honeycreepers depended on the morphology of the tongue rather than the size or shape of the bill

• Because size and shape are related, multivariate analyses of morphological displacement may be more appropriate than analyses of a single character

Assumptions

• 2) the underlying resource spectrum is symmetric

• This has rarely been tested and may not be true

• It is important in that it affects the amount of divergence and hence the observed pattern

Example

• Evenly distributed resource

• Unevenly spaced resource (a cluster)

Assumptions

• 3) the environment is stable and the system has reached an ecological and evolutionary equilibrium

• If the environment is variable, divergence of competitors may not be pronounced because specialization on a particular part of the resource spectrum will no longer be favored by selection

Assumptions

• 4) competition occurs only among adult organisms

• Size ratios analyses of adult animals ignore ontogenetic shifts in body size and resource use and do not consider the possibility that different age classes are acting as ‘ecological’ species

Assumptions

• 5) sexual dimorphism in body size is not important

• When species are sexually dimorphic in body size, differences have either been ignored, averaged, or analyzing a single sex

• Sexual dimorphism is related to dimorphism in trophic appendages and feeding ecology and should be considered in analysis; although little theoretical work has been done

Assumptions

• 6) abundances of species are approximately equal

• The intensity of competition depends not only on the amount of overlap in resource use, but also on the densities of the two competing species

• Some have considered ‘common players’ only in analyses (Hanski 1982; bumblebee proboscis length of local vs. regional)

Models of Divergence

• Three mechanisms, two evolutionary and one ecological, could cause divergence of species occurring in sympatry

Models of divergence

• 1) Divergence would be favored if it prevented hybridization

• Has received little attention from animal biologists, although some from plant biologists

Models of divergence

• 2) Divergence might occur in sympatry through selection against intermediate phenotypes

• This evolutionary mechanism has been invoked for cases in which a species shows intraspecific variation in body size that is related to the presence or absence of competitors

Models of divergence

• 3) Divergence may result through species limiting similarity of resources. The resource spectrum is fixed and if species overlap too much in resource use, one will be driven to extinction.

• Through repeated extinctions and colonizations, a community with a constant spacing of body sizes may be achieved

Models of divergence:alternatives and artifacts

• Competition has almost always been invoked as the mechanism

• However, selective responses to predators may drive size selection

• Certainly groups are phylogenetically constrained

• Finally, the ratios themselves may be mathematical artifacts that merely reflect the underlying distribution of body sizes

Statistical Properties• The expected ratio in a large assemblage

depends on the underlying distribution of body sizes and on the end points of possible body sizes

• In the ecological model (limiting similarity) this distribution represents the body sizes of existing phenotypes that could colonize

• In evolutionary models, the distribution represent the probability that a particular body size will evolve

Statistical Properties

• Tonkyn and Cole (1986) assumed that the distribution of available body sizes was either uniform or unimodel (as fit by the Weibull distribution; which is skewed towards small or intermediate-sized species and is defined by a shape parameter and a scale parameter (in Ecosim we have 5 options, including ‘data defined’)

Statistical Properties

Statistical Properties

• Regardless of the shape of the body size distribution, there are two general properties of size ratios

• 1) the most common size ratio for a pair of adjacent species was the min. ratio of 1.0

• 2) the more species in the assemblage, the smaller the expected body size ratio (e.g. larger ratios on islands)

Null Model

• Because these predictions hold for any set of species that are drawn randomly, they constitute a simple null model for the distribution of body size ratios in a large assemblage

Null Model

• Fig 6.3 and 6.4

Null Model: an example

• Fig 6.4 from Gotelli and Graves

• Expected distribution based upon null model of smallest to second-smallest pairs

• Note few very small ratios in observed data

Null Model(s)

• We have our three patterns (previous slide), which dictate three different null models

Review of Patterns

• 1) minimum size ratios, below which species cannot coexist

• 2) constant size ratios, in which the species in a community display an orderly spacing

• 3) unusually large ratios in island assemblages, which are though to be experiencing more sever competition than comparable mainland assemblages

Null Model 1

• 1) minimum size ratios, below which species cannot coexist

• Simberloff and Boecklen (1981) adapts conventional statistical tests to examine pattern of regularity or unusual minima in size ratios

• Use this test for a single assemblage of co-occurring species

Null Model 2

• 2) considers intraspecific variation in body size data among a set of communities, usually on islands (Strong et al. 1979)

• Use a Monte Carlo simulation in which different species populations are sampled to generate null communities and size ratios that would be expected in the absence of competition

Null Model 3

• 3) examining size spacing patterns in multiple communities containing the same guilds and usually some of the same species (Schoener 1984, Hopf and Brown 1986)

• Although replication yields more power in these analyses, they are complicated by variation in species number and variation