Evaluating and Improving Current Metapopulation Theory for Community and Species-Level Models

Evaluating and Improving Current Metapopulation Theory for Community and Species-level Models

A dissertation submitted to the

Graduate School

of the University of Cincinnati in partial fulfillment of the

requirements for the degree of

Doctor of Philosophy

in the Department of Biological

Sciences of the College of Arts and

Sciences by

Natasha A. Urban

University of Cincinnati

July 2018

Committee Chair: S.F. Matter, Ph.D.

Abstract Ecological models that attempt to unite biodiversity and biogeography concepts have been used to describe and predict the distribution and abundance of species. Mechanistic ecological models theorize that demographic and distributional dynamics affect the success and persistence of the species making up the community. The community-level metapopulation model is one such model and assumes that the species at a particular island are determined by species-specific extinction and colonization rates which vary with island area and isolation from the mainland. In this dissertation, I tested the extent of the model’s ability to capture the underlying mechanisms shaping the community and compare that to another mechanistic model and a null model. I used simulated island-mainland systems with varying number of islands, island sizes, and distances to mainland along with mainland communities with varying numbers of species and densities. I found that there was a limited range of system and community variables where the community- level metapopulation model could accurately describe the species richness on islands created using metapopulation dynamics better than the alternative models. Using these guidelines for system and community structure, I empirically tested evidence for metapopulation dynamics structuring small mammal, tree, and moth communities within an island-mainland system that fit the requirements. The community-level metapopulation model was not found to be better than a null model for describing the species richness patterns of all three functional taxa. The moth taxon was best described by the diversity of host plant species. Lastly, the descriptive ability of the community-level metapopulation model is dependent upon the accuracy of the underlying

single-species model. An assumption of the metapopulation model that is often violated is the

assumption of a constant density-area relationship. I incorporate a method to correct for variable

density-area relationships within the single-species metapopulation model estimate of extinction

risk. I then compared estimates of extinction risk with and without accounting for variable

i density-area relationships on empirical data: the density of mammals, trees, and moths in an island-mainland system. I found 63% of species across the three taxa violated the assumption of a constant density-area relationship. I found variability in the relationship between density and area. Estimates of extinction risk were inflated for most species before accounting for a variable density-area relationship on smaller islands.

iii

Acknowledgements

For my two loving families; especially my mom and Corey.

Table of Contents

Abstract ...... i Acknowledgements ...... iv Table of Contents ...... v Table of Tables ...... vii Table of Figures ...... x 1. Introduction ...... 1 2. Metapopulation Mirages: Problems Parsing Process from Pattern (Urban and Matter 2018) ...... 7 ABSTRACT ...... 7 INTRODUCTION ...... 9 Neutral model ...... 10 Metapopulation model ...... 12 Null model ...... 14 MATERIALS AND METHODS ...... 15 Simulation structure ...... 17 Analyses ...... 21 Simulation evaluation ...... 22 RESULTS ...... 23 Null generated data ...... 23 Neutral Generated Data ...... 26 Metapopulation Generated Data ...... 29 Effects of Uniform distributions ...... 32 DISCUSSION ...... 33 Appropriate systems to test for metapopulation dynamics ...... 34 Conclusions ...... 35 3. Community Structure Is Not Determined by Metapopulation Dynamics ...... 37 ABSTRACT ...... 37 INTRODUCTION ...... 38 METHODS ...... 42 System ...... 42 Data Collection ...... 44 Data Analysis ...... 46 EVF glm ...... 46

System Optimization ...... 47 RESULTS ...... 48 DISCUSSION ...... 52 4. Incorporating Density-Area Relationships in Estimates of Extinction Risk: An Empirical Example 56 ABSTRACT ...... 56 INTRODUCTION ...... 57 METHODS ...... 59 System ...... 59 Data Collection ...... 59 Data Analysis ...... 61 RESULTS ...... 63 DISCUSSION ...... 80 5. Conclusions ...... 84 Bibliography ...... 87

Table of Tables

Table 2-1. The base variables used to simulate abiotic and biotic structure. Numbers of islands (Island) and species (Species) did not vary among replicates. Island area (Area), distance to mainland (Distance), and mainland species’ density (Density) were generated for each replicate following a log normal distribution with mean = 1 and the listed range of standard deviations (SD) for log-scaled variates. Thus, individual values for Area, Distance, and Density vary among replicates but maintained a mean of 1; the specified SD incorporated variation into each replicate. Each combination of variables was replicated 100 times...... 17 Table 2-2. Range of values used to simulate the abiotic and biotic structure of each simulation varied if the simulation followed a log-normal or uniform distribution. Island number and species number did not vary between replications or distribution. Values for the standard deviation in log-transformed island area (Area), mainland species’ densities (Density), and distance to mainland (Distance) varied between replicates. To keep the same range of values for different distributions, the average maximum values ( ) for the uniformly distributed variables were based on the lognormal values. The log-normal variables had a mean =1 and the uniform variables had a minimum =0...... 18 Table𝑀𝑀𝑀𝑀𝑀𝑀 2-3. Conditions where the null model excelled at explaining data generated under null conditions. Shaded areas were conditions where the null model did not consistently have good explanatory power. Variables included in analysis were ranges of standard deviation (SD) for log-transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands (Island) and species (Species) were also included in the analysis. Distance did not influence explanatory ability of the null model. The null model had a large range of possible conditions where it could successfully describe null-derived data including almost the full range of Area and Species...... 24 Table 2-4. Multinomial log-linear regression AIC “best” model results indicating where the neutral and metapopulation (Met) models’ best descriptive ability differentiated from the baseline null model. Top of table gives parameter estimates and standard errors for the best models. Bottom of table provides test results comparing to the baseline null model. Unshaded bold values indicate a significant difference in descriptive ability compared to the null model at alpha=0.05. The dependent variable was proportion of total runs where model was the best qAICc model. Independent variables included in analysis were ranges of standard deviation (SD) for log-transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands (Island) and species (Species) were also included in the analysis. Area, Density and Species were important predictors for when the null model had a higher proportion of success at describing null data in comparison to the neutral and metapopulation models. .. 25 Table 2-5. Conditions where the neutral model excelled at explaining data generated following conditions assumed by the neutral hypothesis (unshaded). Shaded areas were conditions where the neutral model did not have consistent explanatory ability of replications. Variables included in analysis were ranges of standard deviation (SD) for log-transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands (Island) and species (Species) were also included in the analysis. Distance did not influence explanatory ability of the neutral model and the remaining variables had limited ranges where the neutral model successfully described neutrally derived data...... 27 Table 2-6. Multinomial log-linear regression AIC “best” model results indicating what variables influenced model descriptive ability from the baseline neutral model when describing neutrally-generated data. Top of table gives parameter estimates and standard errors for the best models. Bottom of table provides test results comparing to the baseline neutral model. Unshaded bold values indicate a significant difference in descriptive ability compared to the neutral model at alpha=0.05. Dependent variable was proportion of total runs where model was the best qAICc model. Independent variables included in

vii analysis were ranges of standard deviation (SD) for log-transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands (Island) and species (Species) were also included in the analysis. The interaction between Area and Density was a significant predictor for when the neutral model had higher success describing neutral data in comparison to the null and metapopulation models...... 28 Table 2-7. Conditions where the metapopulation model excelled at explaining data generated following conditions assumed by the metapopulation hypothesis. Variables included in analysis were ranges of standard deviation (SD) for log-transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands (Island) and species (Species) were also included in the analysis. Shaded areas were conditions where the metapopulation model did not explain the data well. Distance was an influential explanatory variable for the metapopulation-generated data as compared to the null and neutral generated data. The metapopulation model successfully described metapopulation derived data no matter the values for Island and Species but had limited success for certain ranges of area and distance...... 30 Table 2-8. Multinomial log-linear regression AIC “best” model results indicating where model descriptive ability was different from the baseline metapopulation model when describing metapopulation-based generated data. Top of table gives parameter estimates and standard errors for the best models. Bottom of table provides test results comparing to the baseline metapopulation model. Unshaded bold values indicate a significant difference in descriptive ability compared to the metapopulation model at alpha=0.05. Dependent variable was proportion of total runs where model was the best qAICc model. Independent variables included in analysis were ranges of standard deviation (SD) for log-transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands (Island) and species (Species) were also included in the analysis. The interaction between Density and Distance was an important predictor when comparing the descriptive abilities of all three models...... 31 Table 2-9. Conditions where the metapopulation models has the most favorable potential to describe data following metapopulation dynamics. Greyed out portions indicate the model did not describe data well. Variables considered were ranges of standard deviation (SD) for log-transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands (Island) and species (Species) were also included in the analysis...... 35 Table 3-1. Optimal system conditions for testing the differences between the community-level metapopulation model and the EVF null model (Urban and Matter 2018). The log-transformed variables for island area (Area), island distance to mainland (Distance), and mainland species’ densities (Density) had varying standard deviations (SD) around a mean of 1. The number of islands (Island) and total number of species found on the mainland (Species) are the total number possible used in the simulation. When comparing the metapopulation to the null model under a system and community which are outside these conditions, an investigator should not conclude whether or not metapopulation dynamics are occurring. When a system does fit these conditions, there is a higher chance that the model comparisons will indicate whether or not metapopulation dynamics are occurring...... 40 Table 3-2. A summary of the functional taxa of interest in this study. These different taxa were chosen for investigation because of differing life history traits and therefore we make different predictions on which models will best describe them. The models tested were the community-level metapopulation model and the extreme value function (EVF) null model...... 42 Table 3-3. The island-mainland system at Pymatuning reservoir did not meet the optimum testing conditions when comparing the metapopulation versus a null EVF model. To test under optimum conditions, a subset of Pymatuning data was selected to fit the ranges of the following variables: standard deviation (SD) for the log transformed variables of island area (Area) and island distance to mainland

viii

(Distance), number of islands, number of species, and standard deviation of species’ densities on the mainland (Density)...... 48 Table 3-4. The EVF null was the best model (bold) for describing species richness patterns for the mammal and tree full datasets. The metapopulation model did not significantly improve the amount of deviance explained compared to the EVF null evaluated using a likelihood ratio test with alpha=0.05. There was a significant difference between the EVF and metapopulation model for the moth taxon with the metapopulation model having better fit to the data...... 49 Table 3-5. Island area (Area) was a significant (bold) predictor of species richness for both tree and moth taxa compared to α=0.05 for the full datasets. Island distance to mainland (Distance) was only significant for the moth taxa...... 49 Table 3-6. The EVF null was the best model (bold) for describing species richness patterns for all taxa under optimized datasets. The metapopulation model did not significantly improve the amount of deviance explained compared to the EVF null evaluated using a likelihood ratio test with alpha=0.05. ... 50 Table 3-7. Neither island area (Area) nor distance to mainland (Distance) were significant (bold) predictors of the optimized species richness data for taxa compared to α=0.05...... 51 Table 3-8. To test the hypothesis that moth diversity may be tied to host plant diversity, a subset of moth species was chosen who had known tree species as host plants. Moth species who also had herbaceous host plants were not included. The best metapopulation model included tree species richness (TreeS) and island distance to mainland (Distance), not the classic combination of metapopulation variables of island area and Distance. Both Distance and Tree S were significant (bold) predictors of species richness compared to α=0.05...... 52 Table 4-1. Results of log-likelihood test between GLM with log(area) as a dependent variable and as an offset in order to compare the slope of the density-area relationship (DAR) to a value of 1. Slope of the density-area relationship (B) was extracted from the results of the GLM and used to adjust estimates of extinction risk. The DAR was significantly different (bold) for all mammal and the majority of tree and moth species, indicating that the DAR slope may affect the calculation of metapopulation extinction risk and should be incorporated into the scaling parameter...... 64 Table 4-2. Change in the estimate of the metapopulation scaling parameter (X) for those species when accounting for density-area slopes. The extinction risk per area scaling parameter (x) is also the uncorrected metapopulation scaling parameter. The majority of species had density-area relationships less than the assumed constant density-area relationship indicating lower densities than expected on larger islands. This resulted in lower than estimated values for X...... 67 Table 4-3. As expected, island area is a significant driver for the abundance distribution for most species in the mammal and tree taxa studied located in the Pymatuning system. This is indicated by the results of individual species GLM where log(area) (Area) was a significant (bold) predictor of abundance for the majority of species at an alpha of 0.05. Area was less important for the members of the moth taxon; Area was not a significant predictor of abundance for 45 moth species...... 72 Table 4-4. The results of individual moth species GLMs when tree species richness on each island (Tree S) was added as a predictor. Moth species with known tree host plants and adequate captures on islands were analyzed using log(area) (Area) and tree species richness. Host tree plant richness was not a significant (bold) predictor of moth abundance for most species...... 78

Table of Figures

Figure 2-1. A flowchart of methods in this paper illustrating how all simulation datasets shared the same set of five base variables. Hypothesis-specific mechanisms were then incorporated in generating occupancy and abundance data. These datasets for the null, neutral, and metapopulation hypotheses were described using generalized linear models (GLM) and GLM performance was compared using qAICc and multinomial log-linear regression (MLR). The basic simulation structure was created using lognormal distribution for island area, distance to mainland, and species’ mainland densities. It was then repeated using a uniform distribution for those three variables...... 16 Figure 2-2. Difference in simulation structure when island area, species mainland density, and island distance are based on log-normal (A.) versus uniform distributions (B.). The number of species and islands for the system remained the same but the island-specific species richness values varied in response to the differences in structure of the system. The figure was generated following metapopulation dynamics with 100 possible species and 50 islands. Size of circles is representative of island area with white circles representing full possible species richness and black circles represent no occupying species. The x-axis is distance from the mainland (Distance) and the y-axis is a random value to allow visualization...... 19 Figure 2-3. The neutral model had limited descriptive ability of neutrally-generated data. Panel A shows the narrow range of instances where the neutral model was able to explain 100% of all 100 replications. The combination of low standard deviation in mainland density (Density) and moderate standard deviation in island area (Area) was when the neutral model had the greatest ability to describe neutrally derived data. In contrast, panel B demonstrates when the neutral model was ranked “best” 0% of all replications. This occurred for the majority of all combinations of Density and number of islands (Islands)...... 27 Figure 2-4. As expected, the null (A.) and neutral (B.) models had poorer descriptive ability compared to the metapopulation (C.) model for metapopulation generated data due to the distance to mainland (Distance) variable. This interaction of mainland species’ densities (Density) and island distance to mainland were significantly different in the MLR (Table 2-8). There was a narrow range of the Density and Distance interaction where the null model had high descriptive ability when describing metapopulation generated data. This occurred with high standard deviation in Density but very low standard deviation in Distance...... 32 Figure 3-1. The island-mainland system of Pymatuning Reservoir consists of 32 islands and is immediately surrounded by a forested mainland. The reservoir is bound by state park lands on both the Ohio and Pennsylvania sides of the state line. The northeastern section of the reservoir is bisected by a spillway and road, separating the reservoir into two bodies of water. Surveys were conducted only southwest of the spillway in the main portion of the reservoir. State park and reservoir shapefiles were freely available (http://geospatial.ohiodnr.gov/, http://www.pasda.psu.edu/, accessed 4/1/2018)...... 43 Figure 3-2. The individual and confounded effects of island area (Area), distance to mainland (Distance) and tree species richness (TreeS) on moth species richness. Deviance of tree-dependent moth species richness was best explained by TreeS in the Pymatuning system. Area was highly correlated with TreeS and shared 57.07% variance and was not included in best model for predicting moth richness on islands...... 52 Figure 4-1. Comparisons of the metapopulation extinction risk estimate (µ) when corrected for variable density-area relationship (red) compared to the uncorrected extinction risk estimate (black) that assumes a constant density-area relationship. Corrected estimates produce reduced estimates of extinction risk on

x large islands and increased on small islands for the majority of species. Lines were smoothed using locally weighted scatterplot smoothing...... 71

1. Introduction Ecologists have had difficulty attempting to answer a seemingly simple question: What

determines species richness? Mechanistic hypotheses have been developed to attempt to answer

this question and explain patterns in the distribution and abundance of organisms (Schoener

1986). As opposed to descriptive approaches, where distributional patterns are simply identified and used to predict species richness, mechanistic approaches theorize the drivers behind why these patterns exist. A discrete set of measurable mechanisms that can be universally applied

across taxa and systems would be a powerful tool in the pursuit of understanding species

distributions.

One set of mechanisms theorized to affect community composition are demographic and

distributional dynamics (e.g. extinction and migration rates) thought to affect the success and

persistence of the species making up the community in suitable habitat patches. Initial attempts

to apply dynamics to the study of species distributions include the landmark theory of island biogeography by MacArthur and Wilson (1967). Their theory postulated that the physical characteristics of a mainland-island system influenced the dynamics of species and therefore impacted species richness on islands. Small and/or isolated islands would result in fewer species due to low rates of immigration and high rates of extinction. Large islands could support more species and those islands closer to a source of immigrants (i.e. the mainland) would have a higher number of species.

A benefit of the mechanistic approach using population dynamics to describe species richness is that the proposed mechanisms do not apply to only one hierarchical study level, communities, but can be studied for metapopulations, populations, and individuals. The effects of habitat size and isolation were similarly but separately derived for the single-species

metapopulation hypotheses postulated by Levins (1969) and developed by others (Hanski and

Gilpin 1991, Hanski 2009). A metapopulation exists in a spatially differentiated environment,

not limited to island-mainland systems, and is comprised of geographically discrete populations

of a single species. The incidence of a species in a suitable habitat patch is determined by the

balance of local extinction and (re)colonization (Hanski and Gilpin 1991, Hanski 1994b). The

metapopulation model and its derivations have been evaluated for species from different taxa and

systems (Cappuccino and Price 1995, Husband and Spencer 1996, Harrison and Taylor 1997,

Krohne 1997, Nieminen and Hanski 1998, Gotelli and Taylor 1999, Rieman and Dunham 2000,

Lamy et al. 2012, Eaton et al. 2014). The metapopulation model is also used for conservation

purposes due to its application to fragmentation issues and the ability to estimate extinction risk

(Wilcox and Murphy 1985, Hanski and Simberloff 1997, Esler 2000, Hanski and Ovaskainen

2000, Thrall et al. 2000, Akçakaya et al. 2007).

The single-species metapopulation approach was further developed by bridging concepts

from island biogeography theory (Hanski 2001) thereby gaining the ability to describe species

richness on islands (Hanski and Gyllenberg 1997). This community-level hypothesis attempts to

describe species richness patterns using mechanisms occurring at the species level. The

hypothesis assumes species-specific extinction and colonization rates which vary with island

area and isolation from the mainland. These species-specific responses are used to estimate the

richness on islands and have been evaluated using empirical data for birds and mammals (Matter

et al. 2002). While the community-level metapopulation model was found to described the

species richness on islands well, Matter et al. (2002) found its performance to be similar to a null model, William’s (1995) extreme value function.

There are additional mechanistic models for describing species richness that are also

potentially similar in descriptive ability to the community-level metapopulation model. One such

model that is similarly derived from island biogeography concepts is the unified neutral theory of

biodiversity and biogeography (Hubbell 2001). The neutral concept refers to the assumption that

all individuals of a community have identical population dynamic rates and the mechanisms

determining species richness are also assumed to be equal. Mechanisms can include rates of birth, death, migration, even speciation and ecological drift on evolutionary timescales (Hubbell

2001). The neutral theory also postulates that interactions among individuals are equal.

Despite the utility of the community-level metapopulation dynamic model to describe species richness, the extent of the model’s ability to capture the actual mechanisms shaping the community remains untested. Due to the possible similarities in descriptive ability between the community-level metapopulation model to the extreme value null and possibly other mechanistic models, the “fit” of the community-level metapopulation model to empirical data may not reflect the underlying dynamics structuring the community. The system conditions where the community-level metapopulation model has the potential to capture underlying metapopulation dynamics is still unknown. The goal of this dissertation was to evaluate the community-level metapopulation model, identify conditions where it has the ability to capture the structuring dynamics, and attempt to account for violations of underlying assumptions in the single-species metapopulation model that is the basis for the community-level model.

The aim of Chapter 2 was to identify the island-mainland system conditions where the abilities of the community-level metapopulation, extreme value null, and unified neutral theory models are able to detect underlying process. I run a series of simulations where species richness is generated either following metapopulation dynamics, random placement, or neutral dynamics

for a variety of island-mainland and taxon structures. Using the cumulative results of model

descriptive ability, I set a series of guidelines where these three models have the potential to

capture the underlying processes structuring the community. Additionally, I illustrate the

limitations of these models, identifying where dynamics would be inferred but are not occurring or where the models fail to identify when dynamics are actually occurring. Model shortcomings

may lead to incorrect conclusions regarding the mechanisms producing observed patterns.

The aim of Chapter 3 was to use empirical data taken from an island-mainland system

that conforms to the guidelines developed in Chapter 2. I tested model fit for the community- level metapopulation and extreme value null models to see if the underlying processes could be detected from pattern. I gathered data from three taxa, mammals, mature trees, and moths to see if there was one model that universally described the system data or if there were taxon-specific differences.

The underlying basis of the community-level metapopulation model is the single-species metapopulation model, where individual species incidences are used to determine species richness (Hanski and Gyllenberg 1997). Therefore, the descriptive ability of the community-level metapopulation model is dependent upon the accuracy of the underlying single-species model.

One assumption these metapopulation models make is the assumption of a constant density-area relationship. Previous studies have shown that this assumption is commonly violated both for island-mainland situations and fragmented habitat patches (Bowers and Matter 1997, Bender et al. 1998, Connor et al. 2000, Gaston and Matter 2002). The density-area relationship has been shown to vary from having a negative, neutral, or positive relationship in many species including birds, terrestrial and aquatic insects, mammals, and spider species (Bowers and Matter 1997,

Bender et al. 1998, Connor et al. 2000, Gaston and Matter 2002, Lancaster and Downes 2014).

There are also differences in the density-area relationship at the species versus functional-taxon level (Connor et al. 2000), at local versus landscape scales (Bowers and Matter 1997, Schnell et al. 2013), for generalist versus specialist species (Bender et al. 1998, Lancaster and Downes

2014), and habitat patches versus true island-mainland systems (Wilder and Meikle 2005, Zhao et al. 2012).

A variety of hypotheses have been proposed to explain why the density-area relationship can be variable: (1) The density-area relationship is variable because of incorrect estimation of area that corresponds to the species (Bender et al. 1998). (2) As survey area increases, the amount of unsuitable habitat also increases (Smallwood and Schonewald 1996, Gaston et al.

1999, Gaston and Matter 2002). (3) Resources are not equal in availability which may influence

where individuals congregate and migrate (Root 1973, Matter 1997, Bowers and Dooley 1999).

(4) Herbivores and predators are more effective in small habitat patches (Root 1973, Raupp and

Denno 1979, Denno and Dingle 1981, Risch 1981, Risch et al. 1982, Kareiva 1985). (5) A

combination of the previous factors influence density of species and can have long-term

influence on patch carrying capacity (Matter 1999).

The estimation of extinction probability and risk for the single-species metapopulation

model explicitly incorporate the constant density-area assumption. Simulations by Matter (2000)

demonstrated that metapopulation persistence can be vastly different when constant density-area

assumption is violated. This results in part because the risk of extinction for a local population is

linked to abundance of that species and area. Specifically, extinction risk increases when a

species has low abundance (MacArthur and Wilson 1967, Fenchel and Christiansen 1977, Brown

1995, McKinney 1997). When density increases with area, the persistence of the metapopulation

is dependent upon the largest habitat patches both in terms of containing the largest number of

individuals but also as a source of colonizers to aid in dispersal (Matter 2000). Therefore, a lower

than expected density-area relationship (slope <1) can result in higher extinction rates than

expected in large patches and lower than expected extinction rates in small patches, the inverse is

true with an increased density-area relationship (slope >1).

The connection between abundance and habitat area and extinction risk has been shown

in both ecological and geological time scales (Jablonski 1991, Pimm 1991, Gaston 1994,

Jablonski and Raup 1995, Rosenzweig 1995, McKinney 1997). Generally, increased extinction

risk has been shown for rare species and those with small ranges and low densities (Stanley et al.

1990, Gaston 1994, Mace and Kershaw 1997, McKinney 1997). In terms of metapopulation

dynamics, these locally rare species are hypothesized to have poor dispersal ability and fewer

source populations (Hanski 1985, Hanski and Gilpin 1991, Hanski 1999). Besides range size, the

inverse relationship between area and extinction risk has been shown when habitat patches

become smaller and more fragmented (Laurance 1995, Turner 1996, Turner and Corlett 1996).

Therefore, the aim of Chapter 4 was to account for variability in the density-area

relationship when estimating extinction risk for the single-species metapopulation model. I utilized empirical data collected in an island-mainland system to demonstrate the variability in the density-area relationship and how accounting for the assumption violation can change extinction risk estimates for members of three taxa.

2. Metapopulation Mirages: Problems Parsing Process from Pattern (Urban and Matter 2018)

ABSTRACT Ecological models attempting to unite the concepts of biodiversity and biogeography have been

used to describe and predict the distribution and abundance of species. Two mechanistic

hypotheses, the neutral model and the community-level metapopulation model, have the

potential for direct comparison. However, there is potential for incorrectly inferring the

underlying mechanisms of observed data if the hypotheses have similar descriptive ability. In

this paper, we simulated a range of abiotic island-mainland system and biotic community

structure variables following the mechanisms underlying these two hypotheses in order to

compare model descriptive ability relative to each other and to a null model. We found that the

null and metapopulation models could accurately describe data created under their respective

assumptions for many of the simulated system structures. The neutral model generally failed to

describe data created under neutral conditions relative to the null model. Modelling also revealed limitations of these mechanistic models identifying conditions where metapopulation dynamics

would be inferred but were not occurring, and failing to detect metapopulation dynamics where it

was actually occurring. To help alleviate this problem, we also identified sets of conditions

where metapopulation dynamics, if it is actually occurring, could be distinguished from null or

neutral models. Such systems have moderate variability in distance to mainland, density of

mainland species and island area, as well as low to moderate numbers of islands and species (10-

50). Simulations demonstrated the potential to distinguish unified models under certain conditions, but there are also conditions where models are equivalent and where the model that best described the data was not consistent with the underlying mechanism. These shortcomings

7 may lead to incorrect conclusions regarding mechanisms presumed to be producing observed patterns in species abundance and distribution.

INTRODUCTION Understanding and predicting the distribution and abundance of species lies at the heart

of Ecology (Andrewartha and Birch 1954). Thus, it is not surprising that ecologists have

developed a variety of hypotheses to explain patterns in species richness and abundance. Several

of these hypotheses are referred to as “unified hypotheses” in their attempt to unify the fields of

biodiversity and biogeography. McGill (2010) identified six unified hypotheses: Hubbell (2001)

Unified Neutral Theory of Biodiversity and Biogeography, the metapopulation-derived

hypothesis developed by Hanski and Gyllenberg (1997), Gauch and Whittaker (1972) continuum

hypothesis, Storch et al. (2008) fractal hypothesis, the cluster Poisson hypothesis (Stoyan and

Stoyan 1994, Plotkin and Muller-Landau 2002, Morlon et al. 2008), and the maximum entropy

hypothesis (McGill 2006, Harte 2008). Subsequent to the McGill (2010) review there have been

additional attempts at unifying the concepts of biodiversity and biogeography and extensions of

these hypotheses (e.g., (Whittaker et al. 2010, May et al. 2013, Rosindell and Harmon 2013,

Borregaard et al. 2016, May et al. 2016, Connolly et al. 2017)). These competing hypotheses all

describe patterns of biodiversity and hold promise for predicting the distribution and abundance

of species and potentially for understanding the biological mechanisms thought to produce these

patterns (Jones et al. 2011, Cabral et al. 2017, Leidinger and Cabral 2017).

A limitation of current unified hypotheses is that there have been few quantitative comparisons among them (Jones et al. 2011). Evaluation often has been limited to qualitative analysis of a single hypothesis (e.g.,(McGill 2006)) and less commonly between or among hypotheses (e.g., (McGill 2010)). Where quantitative comparisons exist, the studies generally have tested a single hypothesis within a taxon versus a null model, in contrast to testing competing hypotheses (e.g., (Matter et al. 2002, McGill 2006)). Quantitative comparison among all unified hypotheses is difficult due to the inherit dissimilarities among them, including the

9 spatial and temporal scale of investigation, mechanisms influencing distribution and abundance assumed, and underlying theories used to develop the hypotheses. However, comparisons can be made among unified hypotheses derived from similar theory.

Two of the unified hypotheses can be used to investigate the same community scale structure and were similarly derived. Both the unified neutral and metapopulation hypotheses incorporate similar mechanisms and are derived from the theory of island biogeography

(MacArthur and Wilson 1967) to produce patterns of species incidence and abundance.

Assuming these mechanisms, small and/or isolated areas of habitat would have lower colonization and higher extinction rates compared to larger, less isolated areas, producing a positive relationship between species richness and area and a decreasing relationship between species richness and isolation (Hanski and Gyllenberg 1997, Matter et al. 2002). These two hypotheses have the potential to be useful for ecological studies because of the limited set of mechanisms, but their performances have not been directly compared.

The general background of the two unified hypotheses used in this paper, neutral and metapopulation, are briefly described here, but are described in detail elsewhere including their derivations (Hanski and Gyllenberg 1997, Hubbell 2001, Matter et al. 2002, McGill 2010,

Rosindell et al. 2011, May et al. 2013, Rosindell and Harmon 2013, May et al. 2016). The two unified models can only be compared within an island-mainland system for a variety of reasons detailed in the model descriptions. Island-mainland systems historically have served as important models to study ecological theories and continue to be important for elucidating mechanisms driving biodiversity (Warren et al. 2015).

Neutral model The neutral hypothesis is considered neutral because all individuals in the community are assumed to have identical migration, birth, and death rates. The interactions among species at the

level of individual organisms is also considered equal. The hypothesis’ mechanisms, such as

colonization, extinction, and speciation, determine species richness and are assumed to be equal

for all individuals and in the community (Hubbell 2001). Specifically, the neutral hypothesis

describes both local and regional (metacommunity) patterns of relative abundance and can

include the mechanisms of random migration, speciation, as well as ecological drift. While the neutral hypothesis has application over evolutionary time, it also can be applied to biodiversity

patterns in island-mainland systems over ecological time, which is the focus of this study. The

neutral hypothesis also follows a zero-sum dynamics assumption; there is a constant number of

individuals in a system with equal birth and death rates (Hubbell 1979; 2001). Under these

assumptions, the distribution and abundance of species can be predicted from the relative

abundance of each species in the community.

The neutral hypothesis has been used to predict the distribution and abundance of

different taxa, such as tropical trees, marine invertebrates, temperate herbaceous plants, birds,

fish, and insects (Pandolfi 1996, Terborgh et al. 1996, Hubbell 2001, McGill 2003, Fuller et al.

2004, He 2005, McGill et al. 2006, McGill et al. 2007), but generally has not been applied to

island-mainland systems despite its flexibility to be used in these systems (Rosindell and

Phillimore 2011, Leidinger and Cabral 2017). Previous studies generally only evaluated this

hypothesis for a single island and for fragmented habitat patches (Pandolfi 1996, Terborgh et al.

1996, Hubbell 2001, McGill 2003, Fuller et al. 2004, He 2005, McGill et al. 2006, McGill et al.

2007). A unified hypothesis should not be taxon-specific, but rather have the ability to be

universally applied to any ecological communities. Few studies have tested the neutral

hypothesis in an island-mainland system and tests generally have only considered a single taxon

(Rosindell and Phillimore 2011, Leidinger and Cabral 2017).

McGill et al. (2006) reviewed multiple sets of empirical tests and found that all failed to

support the neutral model. Despite that the development of the neutral model was done with

single island data (Hubbell 2001), none of these empirical tests were done in an island-mainland setting using multiple islands. The distribution patterns of such a system may vary from patterns seen for a single sample or habitat patch. One example is a study done by Leigh et al. (1993) on islands of Gatun reservoir in Central Panama which was the same system where Hubbell (2001) collected the data that the neutral hypothesis was based on. The authors indirectly tested neutrality for the same taxa as well, mature tropical tree species, and found that some species were lost more rapidly than expected by random extinction on the six smallest islands. Hubbell

(2001) found neutrality for data collected on one of the largest islands of Gatun reservoir, Barro

Colorado Island. Therefore, evaluating the assumption of neutrality for all islands in a multiple island-mainland setting may yield different results than if it was studied in a single island setting, or a subset of island sizes (Bowers and Matter 1997, Connor et al. 2000). Differences in

community structure may also occur depending on the sampling scale. Gaston and Matter (2002)

found the relationship between the number of individuals of a species and area can change

depending on whether sampling was at a habitat-specific patch level versus a general sampling area. Similarly, neutrality may also be scale dependent since it operates on the level of the individual. Since the neutral hypothesis was originally derived using islands as patches, it may be more appropriate to test it in island systems.

Metapopulation model The second unified hypothesis is the metapopulation hypothesis which scales up

predictions made for single species to the community-level. Thus, this model can be used to

describe species incidence as well as species richness. The metapopulation hypothesis was

developed assuming island-mainland conditions, i.e., there is a mainland that is a source of

species that (re)colonize islands (Hanski and Gyllenberg 1997). Therefore, comparative tests are

only valid under island-mainland conditions. The metapopulation hypothesis assumes that

species richness (S) for a given island is determined by a balance of local extinction occurring on

islands and (re)colonization from a mainland species pool (R):

Equation 2-1 = + , 𝑆𝑆𝑗𝑗 � 𝑅𝑅 𝑆𝑆𝑗𝑗 𝑗𝑗 𝑗𝑗 𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑎𝑎 𝑥𝑥̅𝑙𝑙𝑙𝑙𝑙𝑙𝐴𝐴 − 𝛼𝛼�𝑑𝑑 where A is the area and d1 the− distance𝑅𝑅 from the mainland of island j, and and describe the

mean extinction risk and the mean migration ability of species in the community,𝑥𝑥̅ 𝛼𝛼� respectively

(Hanski and Gyllenberg 1997, Matter et al. 2002). The parameter is an amalgam of mean

population density, the scaling of extinction risk with area, and a constant𝑎𝑎 parameter.

This “bottom-up” approach, scaling a population-level hypothesis to the community-

level, is potentially beneficial because extinction and recolonization are viewed from the species

level. Species richness is then determined by summing incidence for individual species on an

island. As opposed to the neutral hypothesis, species in the metapopulation model are not treated

equally but instead have individual estimates using the following the incidence ( ) function for

species i on island j: 𝑃𝑃

Equation 2-2 = 𝐾𝐾𝑖𝑖𝑖𝑖 𝑒𝑒 𝑖𝑖𝑖𝑖 𝐾𝐾𝑖𝑖𝑖𝑖 where is the logit-transformed𝑃𝑃 species𝑒𝑒 +1 -specific incidence:

𝐾𝐾𝑖𝑖𝑖𝑖 Equation 2-3 = + (1 + ) + 𝑝𝑝𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖 𝑖𝑖 𝑖𝑖 𝑖𝑖 𝑗𝑗 𝑖𝑖 𝑗𝑗 where describes𝐾𝐾 𝑙𝑙𝑙𝑙𝑙𝑙 the1− 𝑝𝑝migration𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 ability of𝑥𝑥 species𝑙𝑙𝑙𝑙𝑙𝑙𝑤𝑤 i in𝑥𝑥 the𝑙𝑙𝑙𝑙𝑙𝑙 community𝐴𝐴 − 𝛼𝛼 𝑑𝑑 and is the constant

𝛼𝛼𝑖𝑖 13 𝑤𝑤𝑖𝑖

density of species i (Hanski and Gyllenberg 1997, Matter et al. 2002). c is a constant parameter.

Null model An important consideration when testing mechanistic models is its performance relative

to a null hypothesis – a model that does not include the postulated mechanisms (Gotelli and

Graves 1996). By comparing the unified hypotheses to a null, we can test if the mechanistic

processes are important as well as if one unified hypothesis explains significantly more variance

in the data than the other. In the current case, the null hypothesis is random placement of

individuals into habitat patches which can be described by Williams (1995) extreme value

function. This null hypothesis does not contain mechanisms found in the neutral and

metapopulation hypotheses and also has the benefit of being able to accommodate sites with no

species.

Since unified hypotheses have the potential to be important tools for investigating

biodiversity from a mechanistic biogeographic perspective, their limitations and use should be

clearly defined for empirical comparison (Rosindell et al. 2012). One problem when applying

mechanistic models to describe biological patterns is the tendency to assume that the presumed

mechanisms produced the observed patterns. Observable patterns have the potential to be caused

by alternative mechanisms. Thus, the ability of a mechanistic model to describe data does not

necessitate that the mechanism actually caused the pattern (Levin 1992, Jeltsch et al. 1999,

Kendall et al. 1999). Null models help in these situations (Gotelli and Graves 1996), but different

mechanistic models and null models can be similar in their descriptive and predictive abilities.

Hence, the ability to distinguish among them and identify when particular mechanisms are occurring may be limited. In such cases an investigator looking to empirically compare mechanistic hypotheses may not find a difference between models due to their inherent similarities and not because the hypotheses have an equivalent ability to discriminate among

mechanisms (Pontarp et al. 2017).

The purpose of this study was to determine the conditions that a real-world system would

require in order to detect a difference between the performance of the metapopulation and the

unified neutral biodiversity hypotheses. We simulated a range of conditions based on the

underlying theory and assumptions made by both unified hypotheses (i.e., species-area

relationships) as well as different possible island-mainland and taxon structures where neutral and metapopulation models could be directly compared. Our aim was to further define the potential application of these models under ecological timescales and allow for meaningful comparison under appropriate, real-world conditions.

MATERIALS AND METHODS We ran a series of simulations to compare the abilities of the neutral and metapopulation

hypotheses as well as a null model to describe species richness on islands under different conditions. We created three different sets of occupancy and abundance values where we knew the mechanisms responsible for the “observed” species distribution, i.e., we generated them following either null, neutral, or metapopulation rules (Figure 2-1). Each of these datasets used the same abiotic and biotic conditions. We then fit statistical models based on the null, neutral, and metapopulation hypotheses to each of the datasets and compared their ability to describe the data.

2.1 Shared Island-Mainland Simulation Structure

100 Replications Basic Simulation Structure Island area Distance to mainland Number of islands Number of species Mainland density of species

2.1 Hypothesis-Specific Generation of Island Abundance

Null Dataset Metapopulation Dataset Neutral Dataset Island abundance Island abundance based on based on mainland Island abundance mainland density & island area based on mainland density & island Incorporated one “round” of proportions & island area extinction and colonization to area island abundance

2.2 Use Generalized Linear Models to describe dataset

Null Dataset Metapopulation Dataset Neutral Dataset Null GLM Null GLM Null GLM Neutral GLM Neutral GLM Neutral GLM Metapopulation GLM Metapopulation GLM Metapopulation GLM

2.3 Model Comparison

Null Dataset Neutral Dataset Metapopulation Dataset Rank GLM Performances Rank GLM Performances Rank GLM Performances MLR MLR MLR

Simulation structure For the abiotic island-mainland system we established a range of values to represent the number of islands and variation in island area and distance to mainland (Table 2-1). Island area

and distance to mainland were simulated following a log-normal distribution with a mean =1 and a varying range of standard deviations (log-scaled). The resulting values were multiplied by 10 to arrive at a realistic final area. Simulated mainland area was calculated as the sum of all island

areas multiplied by 100. We chose a log-normal distribution for our simulation since it is

common to a variety of island systems, for example the Aleutian archipelago, Japanese

archipelago, Hawaiian Islands, and Svalbard archipelago (Kolmogorov Smirnov test, α = 0.05,

Wolfram Mathematica v.10).

Abiotic Variables Biotic Variables Area Distance Island Density Species SD SD Number SD Number 0.01 0.01 10 0.01 10 0.50 0.50 50 0.50 50 1.00 1.00 100 1.00 100 2.50 2.50 200 2.50 200 5.00 5.00 500 5.00 500

For taxon structure, we set species richness of the system using a range of values from 10

to 500 species. For each species on the mainland, we generated densities in a similar manner to

island size and distance to mainland by following a log-normal distribution with mean = 1 and

range of standard deviations of log-scaled variates (Table 2-1). We calculated mainland

abundance by multiplying the species-specific density values by area of the mainland. We used a factorial design to create a total of 3,125 different system and taxon structures; each of these combinations of parameters were replicated 100 times.

As previously stated, the 3,125 systems were generated following log-normal distributions for area, distance to mainland, and species mainland densities. To explore the robustness of our results to this assumption, we also generated systems following uniform distributions. Island size, distance to mainland, and species mainland density were generated with a minimum = 0 and a maximum value equal to the maximum values of the log-normal generated values averaged across replicates (Table 2-2). We wanted both sets of data to have the same range of values with the only difference between sets being the distribution pattern, which can produce vastly different systems (Figure 2-2).

Table 2-2. Range of values used to simulate the abiotic and biotic structure of each simulation varied if the simulation followed a log-normal or uniform distribution. Island number and species number did not vary between replications or distribution. Values for the standard deviation in log-transformed island area (Area), mainland species’ densities (Density), and distance to mainland (Distance) varied between replicates. To keep the same range of values for different distributions, the average maximum values ( ) for the uniformly distributed variables were based on the lognormal values. The log-normal variables had a mean =1 and the uniform variables had a minimum =0. 𝑀𝑀𝑀𝑀𝑀𝑀��

Lognormal Uniform Variable Area Density Distance

0.01 𝑀𝑀��1.03�𝑎𝑎��𝑥𝑥� 𝑀𝑀𝑀𝑀𝑀𝑀��1.02� 𝑀𝑀𝑀𝑀𝑀𝑀�� 1.02 0.50 3.60 3.51 3.54 1.00 1.37E+01 1.38E+01 1.38E+01 2.50 1.49E+03 1.37E+03 1.26E+03 5.00 6.45E+06 1.29E+07 1.25E+07

Random ValueRandom

A. B.

Distance Distance

Figure 2-2. Difference in simulation structure when island area, species mainland density, and island distance are based on log-normal (A.) versus uniform distributions (B.). The number of species and islands for the system remained the same but the island-specific species richness values varied in response to the differences in structure of the system. The figure was generated following metapopulation dynamics with 100 possible species and 50 islands. Size of circles is representative of island area with white circles representing full possible species richness and black circles represent no occupying species. The x-axis is distance from the mainland (Distance) and the y-axis is a random value to allow visualization.

In order to generate occupancy and abundance data that conform to each hypothesis, we

incorporated their basic assumptions. The structure for island occupancy and abundance for the

null and starting structure for the metapopulation hypotheses were based on the species-specific

densities on the mainland. We generated these datasets by multiplying mainland densities by

island area and rounding down to the nearest whole individual. For the neutral hypothesis,

structure was based on the proportion of total individuals comprising each species on the

mainland. The total numbers of individuals on islands were derived from the null dataset by

summing all individuals of all species. The neutral dataset was then generated by multiplying the

proportion of individuals of species i on the mainland out of the total number of all individuals of

all species by the total number of individuals on an island, rounding down to the nearest

individual. The resulting null and neutral datasets were similar, but not always identical since

datasets had a similar number of individuals but varying abundances among species since species

identity was based on density versus proportion. These datasets tended to be most similar when

there were few individuals on islands.

To incorporate metapopulation dynamics into metapopulation datasets, we conducted one

“round” of extinction and recolonization on data generated by mainland density (see above).

Extinction and recolonization were based on island area and isolation, respectively as well as species-specific colonization and extinction rates.

To incorporate extinction, we followed Hanski (1992) metapopulation extinction probability (E) where islands with larger area have a lower extinction probability than smaller islands:

Equation 2-4 , = 𝜇𝜇𝑗𝑗 𝑗𝑗 𝑖𝑖 𝑥𝑥𝑖𝑖 𝐸𝐸 𝐴𝐴𝑗𝑗 is an extinction constant and xi is a parameter incorporating how extinction risk scales with

𝑗𝑗 area𝜇𝜇 for species i (Hanski 1994b, Hanski and Gyllenberg 1997, Matter et al. 2002). We created an extinction probability for island j by randomly generating and following a normal

𝑗𝑗 𝑖𝑖 distribution ( and =0.2, SD=0.5). Then, for each island, we𝜇𝜇 determined𝑥𝑥 a base island

𝑗𝑗 𝑖𝑖 extinction value𝜇𝜇̅ following𝑥𝑥̅ a uniform distribution (min = 0 and max = 1). If this uniform island

extinction value was smaller than the extinction probability then a local extinction occurred on

that island for that species. The process was repeated for each species on an island and across all

islands.

To incorporate (re)colonization, we determined colonization probability ( , ) for each

𝑖𝑖 𝑗𝑗 species (i) on each island (j): 𝐶𝐶

Equation 2-5

, = ,

𝐶𝐶𝑖𝑖 𝑗𝑗 𝑐𝑐𝑖𝑖𝑤𝑤𝑖𝑖 ∗ 𝐷𝐷𝑖𝑖 𝑗𝑗 Equation 2-6

, = −𝛼𝛼𝑖𝑖𝑑𝑑𝑗𝑗 𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝐷𝐷𝑖𝑖 𝑗𝑗 𝑒𝑒 −𝛼𝛼𝑖𝑖𝑑𝑑𝑗𝑗 �∑𝑗𝑗 𝑒𝑒 where is a constant we generated using a normal distribution ( =1, SD=0.05) and ,

𝑖𝑖 𝑖𝑖 𝑖𝑖 𝑗𝑗 represents a connectivity𝑐𝑐 value where was generated using a normal distribution𝑐𝑐̅ ( =2, 𝐷𝐷

𝑖𝑖 𝑖𝑖 SD=0.5) taken from previous metapopulation𝛼𝛼 estimates (Hanski 1998b, Matter et al. 𝛼𝛼2002)� .

Where extinction was absent and colonization rate was greater than zero, we assumed an island to be occupied by a species. We only applied one round of extinctions and recolonizations once to represent a static island-mainland community following metapopulation dynamics. We did this to follow ecological timescales (rather than evolutionary timescales) which would mimic the “snapshot” data collected by ecological field studies that often can only gather species richness and abundance data over a short period of time.

Analyses We took the datasets generated under null, neutral, and metapopulation assumptions and fit each dataset to the following null, neutral, and metapopulation generalized linear models

(GLM) to compare the ability of each to describe the data.

Null Model GLM:

Equation 2-7 ~ 𝑆𝑆𝑗𝑗 𝑗𝑗 𝑗𝑗 1−𝑆𝑆 𝐴𝐴

Equation 2-8

𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜𝑜𝑜 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑜𝑜𝑜𝑜 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑗𝑗 𝑗𝑗 Equation 𝑊𝑊ℎ𝑒𝑒𝑒𝑒𝑒𝑒 𝑆𝑆 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑟𝑟𝑟𝑟𝑟𝑟ℎ𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 2-9

𝑆𝑆𝑗𝑗 𝑗𝑗 is the expected fraction of species𝑎𝑎𝑎𝑎𝑎𝑎 present1−𝑆𝑆 on island j out of total species pool. We used a

conjugate log-log link function to fit the null model which is referred to as the extreme value

function (Williams 1995).

Neutral Model GLM:

Equation 2-10 ~1 + 1 + 𝑆𝑆𝑗𝑗 ��𝑤𝑤��𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤𝚤��∗𝐴𝐴𝐴𝐴𝐴𝐴𝑎𝑎𝑗𝑗�−1 1−𝑆𝑆𝑗𝑗 𝜃𝜃 ∗ 𝑙𝑙𝑙𝑙𝑙𝑙 � � 𝜃𝜃 �� Where is double the number of individuals of all species on the mainland (Hubbell 2001).

𝜃𝜃 Metapopulation Model GLM:

Equation 2-11 ~ + 𝑆𝑆𝑗𝑗 𝑗𝑗 𝑗𝑗 𝑗𝑗 We used a logit link1 function−𝑆𝑆 𝐴𝐴 to fit𝑑𝑑 the metapopulation and neutral models and compared

all three models using qAICc values for overdispersed data corrected for small sample sizes

since some combinations of parameters had only 10 islands and 10 species (Burnham and

Anderson 2003).

Simulation evaluation For each of the three datasets, we determined the “best” model using the lowest qAICc

value. When models had qAICc scores within two value points, we assigned the same ranking to

avoid overestimating a model’s descriptive power. We then determined the number of times the

model was ranked “best” out of the 100 replicates, with ties receiving half value, to summarize the results. This proportion was used as the dependent variable in a multinomial log-linear regression (MLR) analysis in order to determine how biotic and abiotic conditions affected the explanatory ability of the models. The MLR allowed the comparison of independent variables across the three models and indicated what variables are important for seeing a difference in the models’ descriptive abilities. The independent variables we considered were the five abiotic and biotic variables used to construct the simulated datasets: island area, distance to mainland, species mainland density, number of islands, and number of species. We considered all interactions between variables in our analysis. The MLR was run using the “multinom” function within the “nnet” package available for program R (Venables and Ripley 2002). We determined the “best” regression models based on AIC for each dataset and full interactions between all five variables using the “step” function in the stats package (R Core Team 2012). The MLR test compares models using one as the baseline for evaluation. The baseline for each MLR test was the model matching the generated dataset (e.g., null model as baseline when the dataset was generated under null conditions).

RESULTS Null generated data The null model generally was ranked as the “best” model (46.80%, model with lowest

qAICc) over the neutral (15.75%) and metapopulation (41.69%) models for null generated data.

Some runs resulted in models tied for the “best” model and not all replications had successful convergence due to insufficient variation; however, overall the null model had the highest descriptive ability under null conditions. Generally, the null had better descriptive ability when data was sparser such as when there were few species and islands (Table 2-3). Distance to

mainland had no influence on how the data was structured and the null model descriptive ability

reflected this. The MLR results supported these findings particularly how null descriptive ability

was dependent upon the interactions of variables (Table 2-4) such as area, density, and number of species which reflected the variables used in generating the underlying structure of the null data.

Although the null model correctly described the data for the majority of combinations of conditions, the metapopulation model was also ranked as the “best” model over 41% of the time, despite the fact the statistical metapopulation model contains an extra parameter for distance from the mainland. The metapopulation model generally exceeded the null when all islands had full species richness values. This scenario leads to the potential error of assuming metapopulation dynamics are occurring when no such dynamics are influencing the community structure.

Table 2-3. Conditions where the null model excelled at explaining data generated under null conditions. Shaded areas were conditions where the null model did not consistently have good explanatory power. Variables included in analysis were ranges of standard deviation (SD) for log-transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands (Island) and species (Species) were also included in the analysis. Distance did not influence explanatory ability of the null model. The null model had a large range of possible conditions where it could successfully describe null-derived data including almost the full range of Area and Species.

Null Model Under Null Conditions Abiotic Variables Biotic Variables Area Distance Island Density Species SD SD Number SD Number

0.01 0.01 10 0.01 10 0.50 0.50 50 0.50 50 1.00 1.00 100 1.00 100 2.50 2.50 200 2.50 200 5.00 5.00 500 5.00 500

1 Table 2-4. Multinomial log-linear regression AIC “best” model results indicating where the neutral and metapopulation (Met) 2 models’ best descriptive ability differentiated from the baseline null model. Top of table gives parameter estimates and standard 3 errors for the best models. Bottom of table provides test results comparing to the baseline null model. Unshaded bold values indicate 4 a significant difference in descriptive ability compared to the null model at alpha=0.05. The dependent variable was proportion of 5 total runs where model was the best qAICc model. Independent variables included in analysis were ranges of standard deviation (SD) 6 for log-transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands 7 (Island) and species (Species) were also included in the analysis. Area, Density and Species were important predictors for when the 8 null model had a higher proportion of success at describing null data in comparison to the neutral and metapopulation models.

9 (Intercept) Area Density Islands Species Area:Density Area:Islands Density:Islands Area:Species Density:Species Islands:Species Area:Density:Islands Area:Density:Species

Parameter estimates and standard error (SE) for best models

Neutral 0.509 -0.749 -0.971 -0.002 <0.001 0.416 0.001 0.001 0.001 0.002 <0.001 -0.001 -0.001 estimate

Met 0.586 -1.143 -0.920 -0.001 -0.001 0.501 0.001 0.001 0.001 0.002 <0.001 <0.001 -0.001 estimate

Neutral <0.001 <0.001 <0.001 0.001 0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 0.000 SE

Met SE <0.001 <0.001 <0.001 0.001 0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 0.000

Test results comparing descriptive ability compared to null model

Neutral <0.001 <0.001 <0.001 0.001 0.482 <0.001 0.002 0.001 0.061 <0.001 0.022 0.008 0.044 p-value

Met p- <0.001 <0.001 <0.001 0.064 0.053 <0.001 0.202 0.046 0.008 <0.001 0.121 0.379 0.024 value

10 11

Neutral Generated Data The neutral model generally had poor descriptive ability for all datasets, including the

neutrally generated dataset. The neutral model was ranked “best” only 14.20% out of all

neutrally simulated data sets. In contrast, the null model and metapopulation models ranked

“best” describing neutral data 44.00% and 42.10%, respectively. The neutral model had a limited

range of system conditions where it excelled at describing its own data (Table 2-5). Descriptive ability depended heavily on island area and variability in mainland density as expected due to how the data was generated (Figure 2-3, Table 2-6).

The majority of all replications for the neutrally-derived dataset were better described by

the null and metapopulation models. This lack of model descriptive ability was most apparent

when the system had few islands (10-50) and few species (10-50), indicating sparse

presence/absences of species usually in a dataset with few data points (i.e., islands).

Interestingly, for the MLR results, number of species alone was not a significant predictor but it

was included in three significant interaction terms comparing the neutral to the null (Table 2-6).

The three way interaction between density:islands:species was significantly different between the

null and neutral models.

Table 2-5. Conditions where the neutral model excelled at explaining data generated following conditions assumed by the neutral hypothesis (unshaded). Shaded areas were conditions where the neutral model did not have consistent explanatory ability of replications. Variables included in analysis were ranges of standard deviation (SD) for log-transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands (Island) and species (Species) were also included in the analysis. Distance did not influence explanatory ability of the neutral model and the remaining variables had limited ranges where the neutral model successfully described neutrally derived data.

Neutral Model Under Neutral Conditions Abiotic Variables Biotic Variables Area Distance Island Density Species SD SD Number SD Number 0.01 0.01 10 0.01 10 0.50 0.50 50 0.50 50 1.00 1.00 100 1.00 100 2.50 2.50 200 2.50 200 5.00 5.00 500 5.00 500

A. B.

Figure 2-3. The neutral model had limited descriptive ability of neutrally-generated data. Panel A shows the narrow range of instances where the neutral model was able to explain 100% of all 100 replications. The combination of low standard deviation in mainland density (Density) and moderate standard deviation in island area (Area) was when the neutral model had the greatest ability to describe neutrally derived data. In contrast, panel B demonstrates when the neutral model was ranked “best” 0% of all replications. This occurred for the majority of all combinations of Density and number of islands (Islands).

Table 2-6. Multinomial log-linear regression AIC “best” model results indicating what variables influenced model descriptive ability from the baseline neutral model when describing neutrally-generated data. Top of table gives parameter estimates and standard errors for the best models. Bottom of table provides test results comparing to the baseline neutral model. Unshaded bold values indicate a significant difference in descriptive ability compared to the neutral model at alpha=0.05. Dependent variable was proportion of total runs where model was the best qAICc model. Independent variables included in analysis were ranges of standard deviation (SD) for log-transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands (Island) and species (Species) were also included in the analysis. The interaction between Area and Density was a significant predictor for when the neutral model had higher success describing neutral data in comparison to the null and metapopulation models.

(Intercept) Area Density Islands Species Area:Density Density:Islands Density:Species Islands:Species Density:Islands:Species

Parameter estimates and standard error (SE) for best models

Null estimates -0.301 0.346 0.778 0.002 <0.001 -0.115 -0.001 -0.002 <0.001 <0.001

Metapopulation 0.056 -0.473 0.034 0.001 <0.001 0.155 <0.001 <0.001 <0.001 <0.001 estimates

Null standard errors <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001

Metapopulation <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 standard errors

Test results comparing descriptive ability compared to neutral model

Null p-values <0.001 <0.001 <0.001 <0.001 0.407 <0.001 <0.001 <0.001 <0.001 0.020

Metapopulation p- <0.001 <0.001 <0.001 0.204 0.895 <0.001 0.524 0.521 0.323 0.584 values

Metapopulation Generated Data The metapopulation model generally was ranked as the “best” model over the null and neutral models for metapopulation generated data but its descriptive ability was imperfect. The metapopulation model was the “best” model 58.60% out of all combinations of variables and replications compared to the null (27.37%) and neutral (14.01%) models. Those conditions where the metapopulation model could explain ≥75% of all replications included a limited range of SD values for distance to mainland and island area (Table 2-7). The MLR results further differentiated where the null and neutral models’ descriptive ability were different from the metapopulation model (Table 2-8). Area and density were significantly different from the metapopulation model for both the null and neutral models and the only significant interaction term for both comparisons was the density:distance interaction.

System conditions where the metapopulation model had poor descriptive ability included the extremes in variation for distance to mainland (0.01 and 2.50-5.00). There was an interaction between mainland species’ densities and distance where systems with high variation in densities and low variation in distance to mainland had the poorest descriptive ability for the metapopulation model (Figure 2-4). Most of the systems with low variability in island distance resulted in all islands having full species richness values due to recolonization. When there is high variability in species’ densities, almost all islands had some species missing. The null model was ranked “best” for most of these systems incorrectly indicating that metapopulation processes were not influencing species richness.

Table 2-7. Conditions where the metapopulation model excelled at explaining data generated following conditions assumed by the metapopulation hypothesis. Variables included in analysis were ranges of standard deviation (SD) for log-transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands (Island) and species (Species) were also included in the analysis. Shaded areas were conditions where the metapopulation model did not explain the data well. Distance was an influential explanatory variable for the metapopulation-generated data as compared to the null and neutral generated data. The metapopulation model successfully described metapopulation derived data no matter the values for Island and Species but had limited success for certain ranges of area and distance.

Metapopulation Model Under Metapopulation Conditions Abiotic Variables Biotic Variables Area Distance Island Density Species SD SD Number SD Number 0.01 0.01 10 0.01 10 0.50 0.50 50 0.50 50 1.00 1.00 100 1.00 100 2.50 2.50 200 2.50 200 5.00 5.00 500 5.00 500

Table 2-8. Multinomial log-linear regression AIC “best” model results indicating where model descriptive ability was different from the baseline metapopulation model when describing metapopulation-based generated data. Top of table gives parameter estimates and standard errors for the best models. Bottom of table provides test results comparing to the baseline metapopulation model. Unshaded bold values indicate a significant difference in descriptive ability compared to the metapopulation model at alpha=0.05. Dependent variable was proportion of total runs where model was the best qAICc model. Independent variables included in analysis were ranges of standard deviation (SD) for log-transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands (Island) and species (Species) were also included in the analysis. The interaction between Density and Distance was an important predictor when comparing the descriptive abilities of all three models.

Density:Distance:Speci (Intercept) Area Density Distance Species Area:Density Area:Distance Density:Distance Density:Species Distance:Species Area:Density:Distance es

Parameter estimates and standard error (SE) for best models

Null -1.058 0.989 0.827 0.428 <0.001 -0.405 -0.461 -0.621 -0.001 <0.001 0.298 0.001 estimate

Neutral -0.283 0.276 -0.458 -0.086 <0.001 0.110 0.040 0.230 0.001 <0.001 -0.049 <0.001 estimate

Null SE 0.151 0.122 0.124 0.126 0.001 0.100 0.101 0.108 0.001 0.001 0.084 <0.001

Neutral 0.149 0.126 0.144 0.128 0.001 0.111 0.102 0.114 0.001 0.001 0.087 <0.001 SE

Test results comparing descriptive ability compared to metapopulation model

Null p- <0.001 <0.001 <0.001 0.001 0.834 <0.001 <0.001 <0.001 0.126 0.610 <0.001 0.128 value

Neutral 0.058 0.028 0.001 0.501 0.880 0.321 0.693 0.043 0.327 0.600 0.577 0.576 p-value

Figure 2-4. As expected, the null (A.) and neutral (B.) models had poorer descriptive ability compared to the metapopulation (C.) model for metapopulation generated data due to the distance to mainland (Distance) variable. This interaction of mainland species’ densities (Density) and island distance to mainland were significantly different in the MLR (Table 2-8). There was a narrow range of the Density and Distance interaction where the null model had high descriptive ability when describing metapopulation generated data. This occurred with high standard deviation in Density but very low standard deviation in Distance. Effects of Uniform distributions Our results are somewhat sensitive to the underlying distributions of island area and

isolation and species density. When we replaced the log-normal with uniform distributions it

resulted in a large increase in the neutral model’s descriptive ability when describing neutrally

generated data. The neutral model went from 14.20% “best” rankings for log-normal data to

32.07% for uniform data. Conditions where the neutral model had highest descriptive ability

under uniform conditions include low variation in mainland species density (SD=0.01) when

variation in island area was moderate (SD=1.00) for systems with many species (200-500).

Despite the increase in neutral model descriptive ability, however, the null model still had better

(61.67%) and the metapopulation had comparable (25.44%) descriptive ability for neutrally

generated data than the neutral model.

The null and metapopulations models were also sensitive to the change in underlying

distribution. When using uniformly distributed data, the null model’s descriptive ability for the

null generated data increased with the null being ranked “best” 46.80% for log-normal data to

63.74%. In contrast, the metapopulation model had slightly poorer descriptive ability when data was generated under uniform (49.51%) compared to log-normal (58.60%) distributions.

DISCUSSION Inferring process from pattern continues to be fraught with difficulty. While unified

mechanistic models are a positive step, they are by no means perfect. In this paper, we have

demonstrated two possible errors when comparing unified models to a null: (I) not detecting

processes, such as metapopulation dynamics, when they are actually occurring or (II) model

selection choosing a unified model over a null when those processes are not occurring. Care must

be taken when ranking empirical data since it may not necessarily reflect the true mechanisms or

the mechanisms may not be the main driving force in determining species richness in all

circumstances. The same observable patterns in nature can be generated by multiple processes

(Cale et al. 1989).

Testing mechanistic models versus a null model is a common and recommended method

for trying to tease apart process from pattern in ecological studies (Gotelli and Graves 1996). We

agree that null models are a useful tool; however, we caution against their use to infer

mechanisms because there is potential to conclude they are occurring when they are not and to

miss them when they are. In some cases, this involves situations where the underlying mechanism would be occurring but either the landscape or biotic conditions do not allow the

mechanism, i.e., extinction may not occur in a particular landscape despite the potential for

extinction. Similarly, observable patterns can be caused by different mechanisms and model

selection may not even include a model with the mechanism that is actually occurring (Peters

1991, Gotelli and Graves 1996). In contrast, failing to reject a null model does not guarantee that

there is only random placement of species and mechanisms are not occurring for some species in

the community. Sometimes mechanisms are occurring but cannot be detected over the general

“noise” of a null pattern (May 1974, Hastings 1987, Gotelli and Graves 1996).

The neutral model did not exceed the descriptive ability of competing models, despite not varying greatly from the null. While the neutral model has been proposed as a null model in

which to compare individual versus species differences or test for niches or mechanisms that

may account for species distribution patterns (Rosindell et al. 2011, Rosindell et al. 2012), the

neutral model is not a traditional null model containing no assumed mechanisms (Gotelli and

Graves 1996, Gotelli and Ellison 2002, Gotelli and McGill 2006). The results of this simulation,

although there was a narrow set of conditions where the neutral model was ranked “best”,

suggest against using the neutral model as a baseline null model, at least in the context of

community structure over ecological timescales. While the basic neutral model used in this

simulation is able to be extended temporally with other variables such as ecological drift and

different types of speciation (Hubbell 2001, Rosindell et al. 2011, Rosindell and Phillimore

2011), the main mechanism of neutrality in a variety of simulated systems cannot always be

differentiated from the null model of random placement. Therefore, empirical studies trying to

distinguish among these models are limited when trying to determine if neutral mechanisms are

occurring in a community.

Appropriate systems to test for metapopulation dynamics There was a set of conditions where an investigator could be more confident that they are

detecting metapopulation dynamics in comparison to a null model (Table 2-9). These guidelines are based on when there was the largest discrepancy in model ranking averaged across replications and include island-mainland systems with moderate variation in island distance to mainland, mainland species densities and island area (0.50-1.00). The number of islands and species was less influential on model performance, but having a system with low to moderate

34 numbers of islands and species had better metapopulation performance. Therefore, real-world systems fitting these restrictions would be optimal for empirically distinguishing the metapopulation model from the null model. Having good model fit in a system without the correct ranges of system structure values could result in the incorrectly assuming the underlying mechanism, especially when the variability in island distance to mainland is low.

Table 2-9. Conditions where the metapopulation models has the most favorable potential to describe data following metapopulation dynamics. Greyed out portions indicate the model did not describe data well. Variables considered were ranges of standard deviation (SD) for log- transformed island area (Area), distance to mainland (Distance), and mainland densities (Density). The number of islands (Island) and species (Species) were also included in the analysis.

Suggested Empirical Testing Conditions for Metapopulation Dynamics Abiotic Variables Biotic Variables Area Distance Island Density Species SD SD Number SD Number 10 10 0.50 0.50 50 0.50 50 1.00 1.00 1.00

Conclusions When investigating whether certain mechanisms are influencing species richness, it is advisable to first check the structure of the system and taxa. Whenever possible it is recommended that preliminary surveys to estimate variables like species’ mainland density are employed. Alternatively, previously reported system components can aid in determining whether or not a system can be used to differentiate between a mechanistic model and a null. Setting guidelines where mechanistic models can be evaluated helps eliminate studies that have a low potential to distinguish underlying mechanisms. Based on the results of this simulation, even when these guidelines have been set and there is a higher possibility that the correct model is describing the mechanisms, an investigator cannot be completely sure of the mechanisms

structuring the community using these unified models.

Unified models attempt to simplify the complex study of species distribution patterns in order to identify important mechanisms influencing community structure. This simulation demonstrated that under certain conditions there is a potential to distinguish mechanisms of these unified models. However, there is also a range of conditions where models have equivalent descriptive abilities and where the model that best described the data was not consistent with the underlying mechanism. These shortcomings merit caution when applying unified models to identify mechanisms presumed to be acting in nature.

3. Community Structure Is Not Determined by Metapopulation Dynamics ABSTRACT Unified mechanistic hypotheses have the potential to explain patterns in the distribution and abundance of organisms. The community-level metapopulation hypothesis was developed to explain species richness in island-mainland systems using species-specific responses to habitat area and isolation which presumably affect colonization and extinction rates and thus species richness. Recent research has indicated that community and system structure can influence the ability to discriminate between random placement and metapopulation processes in setting community structure. We evaluated the metapopulation hypothesis versus a null model of random placement under conditions where these processes can be tested. We found that there was no significant difference between the random placement and metapopulation model for mammals, trees, and moths. The richness of moth species that are dependent upon trees as host plants was best described by the species richness of trees on islands, rather than island area.

While metapopulation dynamics may be acting on individual species, we did not find that the community as a whole was structured by metapopulation dynamics.

INTRODUCTION Current ecological studies attempting to describe species richness and distribution patterns have

utilized “unified” hypotheses that combine the fields of biodiversity and biogeography (McGill

2010). The appeal of a unified method is the ability to describe communities using a marriage of

once disparate theoretical approaches. Joining different concepts, such as biodiversity and

biogeography, has the potential to capture some of the complexity of ecological systems. Unified

hypotheses classified as mechanistic assume a discrete set of biological dynamics thought to

produce observed richness patterns. One problem with current mechanistic unified hypotheses is

that in attempting to use a simplified set of measurable variables to describe complex systems,

they can have equivalent descriptive ability to other mechanistic unified models and null models

(Matter et al. 2002, Urban and Matter 2018). The structure of the biological community and geography of the system can also affect the ability to accurately attribute the underlying mechanisms of some unified hypotheses (Urban and Matter 2018).

One such unified hypothesis is the metapopulation-based hypothesis developed by

Hanski and Gyllenberg (1997) which is derived from MacArthur and Wilson’s theory of island biogeography (1967). The hypothesis assumes that the mechanisms determining species richness in a system include species-specific extinction and colonization rates which vary with habitat area and isolation. Small habitat size and increased isolation are assumed to produce lower colonization and increased extinction rates of species resulting in lower species richness in comparison to large, less-isolated islands (Hanski and Gyllenberg 1997).

This community-level metapopulation hypothesis attempts to describe species richness patterns using mechanisms occurring at the species level. Species-specific responses to habitat area and isolation are used to estimate species richness in an island-mainland system (Hanski and

Gyllenberg 1997):

Equation 3-1 = + , 𝑆𝑆𝑗𝑗 � 𝑅𝑅 𝑆𝑆𝑗𝑗 𝑗𝑗 𝑗𝑗 𝑙𝑙𝑙𝑙𝑙𝑙 � 𝑎𝑎 𝑥𝑥̅𝑙𝑙𝑙𝑙𝑙𝑙𝐴𝐴 − 𝛼𝛼�𝑑𝑑 where the mainland species1− pool𝑅𝑅 (R) is the source for species (re)colonization on islands and

species richness (S) is determined by recolonization and island extinctions. Island area (A) and

distance from the mainland (d) of island j influence the incidence of species. The parameters

and describe mean extinction risk and mean migration ability of species (Hanski and 𝑥𝑥̅

Gyllenberg𝛼𝛼� 1997, Matter et al. 2002). The parameter describes a combination of mean

population density, the scaling of extinction risk with𝑎𝑎 area, and a constant.

The metapopulation model has been evaluated by Matter et al. (2002) using five

empirical island-mainland datasets for two taxa, birds and mammals. The metapopulation model

demonstrated good fit of species richness with island area. The fit of the metapopulation model

for describing system data was evaluated using the coefficient of determination (R2) which

ranged from 0.38 to 0.80. This study found that for four out of the five systems, a reduced

metapopulation model including only area was better than the full model which included

isolation. While this study illustrated that the metapopulation model can describe species

richness data, the authors also found that the fit of the metapopulation model was not different

from a null model, William’s (1995) extreme value function (EVF). The EVF describes the

relationship between species richness and area based on the random placement of individuals

into habitat patches. The EVF can be used as a null model since it makes no assumption about

the mechanisms producing the species-area relationship (Gotelli and Graves 1996). The EVF

null outperforms other descriptive functions for studying species-area relationships (Burbidge et

al. 1997, Veech 2000, Belant and Van Stappen 2002).

Since the descriptive capabilities of the metapopulation and EVF models are similar, it is unknown in the results of Matter et al. (2002) whether metapopulation dynamics were influencing observed species richness. Simulations by Urban and Matter (2018) also highlighted the descriptive similarities of the two models. Metapopulation dynamics can be distinguished from random placement only under a limited range of species and island system conditions

(Table 3-1). Such system conditions are restricted to standard deviations of log transformed island area and distance to mainland ranging from 0.50 to 1.00 and systems containing 50 or fewer islands. Additionally, there should be 50 or fewer species with the standard deviations of their densities on the mainland ranging from 0.50 to 1.00. If system and community conditions fall outside of these ranges, there is little ability to distinguish between metapopulation dynamics and random placement.

Table 3-1. Optimal system conditions for testing the differences between the community-level metapopulation model and the EVF null model (Urban and Matter 2018). The log-transformed variables for island area (Area), island distance to mainland (Distance), and mainland species’ densities (Density) had varying standard deviations (SD) around a mean of 1. The number of islands (Island) and total number of species found on the mainland (Species) are the total number possible used in the simulation. When comparing the metapopulation to the null model under a system and community which are outside these conditions, an investigator should not conclude whether or not metapopulation dynamics are occurring. When a system does fit these conditions, there is a higher chance that the model comparisons will indicate whether or not metapopulation dynamics are occurring.

We used a system that meets the requirements to be able to distinguish between random

placement and metapopulation dynamics to compare the performance of the metapopulation and

EVF models in a single island-mainland system. We assumed that, because of differing life

history characteristics for different functional taxa, the distribution of species had the potential to

be influenced by different mechanisms. We addressed this assumption by comparing the models

for three different taxa; mammals, trees, and moths (Table 3-2). We hypothesized that small and

meso-sized mammals, in part because of limited dispersal and susceptibility to local extinction because of stochastic events (Gaines and McClenaghan 1980, Verboom and Van Apeldoorn

1990, Krohne 1997, Moilanen et al. 1998, Elmhagen and Angerbjörn 2001, Bowman et al. 2002,

Olivier et al. 2009, Schloss et al. 2012), would be best described by the metapopulation model.

We also hypothesized that tree species would not follow metapopulation dynamics because of similarities in intra- and intraspecific competition and comparatively similar seed dispersal distances, i.e., individual trees, regardless of species, are similar enough to not affect species richness. Lastly, we hypothesized that the moth taxa would be best described by neither the metapopulation nor null models. Instead, species richness of moths is likely tied to habitat heterogeneity which would influence species richness distribution because of host specialization of herbivorous insects (Strong et al. 1984). We predicted that species richness estimates of moths would be best described by the diversity of vegetation (Janzen 1968, Strong et al. 1984,

Thompson and Pellmyr 1991).

Table 3-2. A summary of the functional taxa of interest in this study. These different taxa were chosen for investigation because of differing life history traits and therefore we make different predictions on which models will best describe them. The models tested were the community-level metapopulation model and the extreme value function (EVF) null model.

Species Predicted Best Taxa Description Richness Justification Model (S)

• limited dispersal Small and meso-sized Mammal 11 Metapopulation • susceptibility to local mammals < 15kg extinction

• similar growth and Tree species >5cm DBH and resource competition Tree 16 EVF >0.5 m height • similar seed dispersal distances

• species richness tied to Neither (Tree Moth species >1cm total habitat heterogeneity Moth 321 diversity may be length • influenced by host best descriptor) specialization

METHODS System

The island-mainland system we studied was Pymatuning Reservoir (41° 29′ 54″ N, 80° 27′ 41″

W) near Linesville, Pennsylvania, USA (Figure 3-1). The system currently consists of 32 islands

with areas ranging from 0.0001 to 68.0313 ha and distance to mainland varying from 9.2 to

670.8 m. The reservoir was created in 1932 to prevent local flooding and maintain water-levels in the Ohio River for shipping purposes (Harshman 1934). Before construction of the reservoir, the system was primarily swamp habitat, remnant pieces of which are adjacent to the reservoir

(i.e., Black Jack Swamp Natural Area). The majority of the habitat surrounding the reservoir and on islands is comprised of mesophytic mixed hardwood forest. Additionally, the Civilian

Conservation Corps established small acreage, coniferous plantations on cleared areas of shoreline and larger islands which are still maintained.

Figure 3-1. The island-mainland system of Pymatuning Reservoir consists of 32 islands and is immediately surrounded by a forested mainland. The reservoir is bound by state park lands on both the Ohio and Pennsylvania sides of the state line. The northeastern section of the reservoir is bisected by a spillway and road, separating the reservoir into two bodies of water. Surveys were conducted only southwest of the spillway in the main portion of the reservoir. State park and reservoir shapefiles were freely available (http://geospatial.ohiodnr.gov/, http://www.pasda.psu.edu/, accessed 4/1/2018).

Data Collection Species counts for mammals, trees, and moths were collected from May through August

2012-2014 on all 32 islands and mainland sites. Mainland data were collected to establish the

mainland species pool and estimate mainland densities to test for optimal conditions

recommended by Urban and Matter (2018). The number of mainland sites varied for each taxon based on species accumulation curves.

Small and meso-sized mammals (up to 12 kg) were live-trapped using standard mark-

recapture methodology for five consecutive nights on all islands and nine mainland sites (Conard

et al. 2008, Hoffmann et al. 2010). Larger islands and mainland sites had an effective trapping

grid size of 1 ha with traps spaced 20 m apart. Grids were comprised of 25 small live traps (H.B.

Sherman Trap, Inc., Tallahassee Fla.; 7.6 x 8.9 x 22.9 cm) and five large live traps (Havahart®

Woodstream Corp., Lititz, PA; 81.3 x 26.7 x 31.8 cm) baited with rolled oats and black oil

sunflower seeds. Additionally, large traps were also baited with canned cat food. The number of

grids per island was proportional to island area with 250 m minimum spacing between grids. For

islands with an area <1 ha, the number of traps per grid was proportional to island area with a

minimum of 5 small and 2 large traps. Monel fingerling ear tags were used to identify

individuals for species with large external pinnae and toe clipping was used for shrew species

(Blarina and Sorex sp.). Density was calculated as the number of unique individuals per ha

averaged over sites and years. Mammal work followed UC IACUC protocol 13-02-22-01 and

standards set by the American Society of Mammalogists (Sikes et al. 2011). A subset of five

islands and mainland sites were resampled every year to monitor for yearly variance.

Vegetation surveys for tree species consisted of 10 m radius circle plots to estimate

species richness and mean density on the 32 islands and 33 mainland sites. The number of plots

on each island was proportional to area. For islands and mainland, a minimum of 250 m spacing

was used between plots. Smaller islands required irregularly shaped plots but maintained a plot

area of 314.16 m2. Total island surveys were done when island area was less than plot area. Plots on larger islands and the mainland also had a minimum buffer of 100m from habitat edges including roadways and trails. Trees with diameters of breast height (DBH) ≥ 5 cm and taller than 0.5 m were counted and identified using Rhoads and Block (2007). To improve species

richness estimates, a timed meander method also was employed (Goff et al. 1982, Huebner

2007). Timed meanders were set at 10 minutes with a maximum distance of 100m from plot

center. All tree species not found within tree plots were identified and their distance to plot

center recorded.

Moth trapping on the 32 islands and 24 mainland sites took place across two consecutive

nights for each trap location. Sampling was repeated during the sampling season to capture a

range of species’ different emergence times. Moths were collected using ultra-violet light funnel

traps with automatic light sensors powered by 12-volt batteries (BioQuip Inc., Rancho

Dominguez, CA). Traps contained Dichlorvos strips for collection of specimens for later

identification. Spacing of traps followed vegetation plot locations and a proportional number of

light traps were placed on each island. Traps were hung 1.5-2.5 m off the ground from natural

vegetation or shepherd hooks when natural vegetation was unavailable. Trapping was suspended

on nights with heavy rains or high winds. Traps were at least 100 m from other artificial lights

sources and trapping did not take place during weeks with full and new moons. We assumed a

radius of attraction of 20 m or the total area of smaller islands when estimating density, using

counts of collected individuals for each species (Plaut 1971, Truxa and Fiedler 2012).

Data Analysis Generalized linear models (glm) were used to evaluate the fit of the EVF and

metapopulation models for the three taxa following the procedures in Urban and Matter (2018).

EVF glm

Equation 3-2 ~ 𝑆𝑆𝑗𝑗 � 𝑅𝑅 𝑆𝑆𝑗𝑗 𝑗𝑗 � 𝐴𝐴 where the proportion of species1− is𝑅𝑅 determined by the number of species on island j out of the

total mainland species pool (R). Only island area (A) influences the number of species on island

The EVF uses a conjugate log-log link function in the fitting of the binomial glm (Williams

1995).

Metapopulation glm

Equation 3-3 ~ + 𝑆𝑆𝑗𝑗 � 𝑅𝑅 𝑆𝑆𝑗𝑗 𝑗𝑗 𝑗𝑗 � 𝐴𝐴 𝑑𝑑 where island area (A) and distance1− 𝑅𝑅 to mainland (d) influence the number of species found on

island j. Here, a logit link function is used to fit the binomial glm. Goodness of fit between the

metapopulation and EVF null models was evaluated using likelihood ratio tests at an alpha=0.05.

To test the hypothesis that moth species richness may be influenced by host plant

diversity, we also tested a metapopulation model including tree species richness as a dependent

variable. Not all moths have trees as host plants, thus we chose the subset of species known only

to feed on trees based on the online HOSTS database (Robinson et al. 2010). Nested combinations of island area, distance to mainland, and tree diversity were evaluated for the metapopulation model using F-statistic likelihood ratio tests with alpha=0.05.

System Optimization The EVF and metapopulation glms were fit to the Pymatuning system for all three taxa.

We also fit the glms to subsets of our data to optimize the likelihood of “seeing” metapopulation dynamics, if it was acting (Table 3-1). The Pymatuning system matched the optimal system

requirements for number of islands but was not optimal for island area and distance to the

mainland (Table 3-3). To conform to optimum system requirements, we subset the island data by

randomly selecting a combination of island areas and distances to mainland that most closely

matched a target standard deviation of 0.75. Two of the taxa had the appropriate number of

species, mammals and trees, but none showed the ranges of mainland density that would be

optimal (Table 3-3). To subset the taxa datasets we selected the maximum number of species to

still achieve a standard deviation in the optimum range for mainland density. Random selections

of subsets were chosen after 100,000 iterations and subsets were chosen that fit within the range

of optimized criteria while retaining the maximum number of islands and species.

Table 3-3. The island-mainland system at Pymatuning reservoir did not meet the optimum testing conditions when comparing the metapopulation versus a null EVF model. To test under optimum conditions, a subset of Pymatuning data was selected to fit the ranges of the following variables: standard deviation (SD) for the log transformed variables of island area (Area) and island distance to mainland (Distance), number of islands, number of species, and standard deviation of species’ densities on the mainland (Density).

Optimum System Variables Full System Optimized Data Conditions Area SD 0.50-1.00 2.43 0.91 Distance SD 0.50-1.00 1.08 0.81 Island Number 10-50 32 15 Taxon-specific Optimum Mammal Tree Moth Mammal Tree Moth Variables Conditions Density SD 0.50-1.00 8.01 7.75 20.11 0.77 1.00 1.00 Species Richness 10-50 11 16 321 8 11 20

RESULTS The full datasets for mammals and trees in the Pymatuning reservoir system were best

described by random placement (Table 3-4). The EVF null had effectively the same descriptive

ability as the more complex metapopulation model and the models were not significantly

different in the amount of deviance explained in the data. The best model for both taxa included

only island area, but it was not a significant predictor of species richness for mammals (Table

3-5). The metapopulation model was significantly better at explaining species richness patterns

for the full moth dataset (Table 3-4). Both island area and island distance to mainland were

significant predictors for moths (Table 3-5).

Table 3-4. The EVF null was the best model (bold) for describing species richness patterns for the mammal and tree full datasets. The metapopulation model did not significantly improve the amount of deviance explained compared to the EVF null evaluated using a likelihood ratio test with alpha=0.05. There was a significant difference between the EVF and metapopulation model for the moth taxon with the metapopulation model having better fit to the data.

Residual Residual Taxon Model Df Deviance Df Deviance F p-value EVF 13 20.570 Mammals Metapopulation 12 20.171 1 0.399 0.239 0.634

EVF 13 149.260 Tree Metapopulation 12 145.950 1 3.306 0.796 0.380

EVF 13 421.960 Moths Metapopulation 12 302.200 1 119.750 11.988 0.002

Table 3-5. Island area (Area) was a significant (bold) predictor of species richness for both tree and moth taxa compared to α=0.05 for the full datasets. Island distance to mainland (Distance) was only significant for the moth taxa.

Taxon Model Covariates Estimate SE t value Pr(>|t|) Intercept -2.093 0.207 -10.137 3.329E-11 EVF Area 0.020 0.010 2.042 0.050 Mammal Intercept -1.667 0.279 -5.977 1.695E-06 Metapopulation Area 0.028 0.012 2.362 0.025 Distance -0.003 0.002 -1.674 0.105

Intercept -2.208 0.138 -15.960 3.336E-16 EVF Area 0.026 0.006 4.425 1.173E-04 Tree Intercept -2.238 0.201 -11.114 5.708E-12 Metapopulation Area 0.030 0.008 3.929 4.847E-04 Distance 4.882E-04 0.001 0.580 0.566

Intercept -3.264 0.178 -18.367 7.211E-18 EVF Area 0.030 0.006 4.748 4.742E-05 Moth Intercept -2.750 0.204 -13.476 5.150E-14 Metapopulation Area 0.039 0.007 5.889 2.159E-06 Distance -0.005 0.002 -2.752 0.010

However, when comparing models using the optimal subset of the Pymatuning data, the

EVF null model was the best model for all three taxa (Table 3-6). The optimized island-mainland

dataset included 15 islands with a standard deviation of log-transformed island area of 0.91 and

0.81 for distance to mainland (Table 3-3). Eight species of mammals were selected to achieve a

standard deviation of mainland density of 0.77. The subset of tree species included 11 species

with a standard deviation of mainland density of 1.00. The moth taxon had the greatest reduction

in numbers, decreasing from 321 to 20 to achieve a standard deviation of 1.00. The results of the

model selection for the optimized subset indicated that metapopulation dynamics may not be the

determining mechanisms for species richness in the Pymatuning system for the three taxa (Table

3-6). For all three taxa, the EVF model was the best model, but area was not a significant

predictor of species richness (Table 3-7).

Table 3-6. The EVF null was the best model (bold) for describing species richness patterns for all taxa under optimized datasets. The metapopulation model did not significantly improve the amount of deviance explained compared to the EVF null evaluated using a likelihood ratio test with alpha=0.05.

Residual Residual Taxa Model Df Deviance Df Deviance F p-value EVF 13 20.57 Mammals Metapopulation 12 20.17 1 0.40 0.24 0.63

EVF 13 25.54 Tree Metapopulation 12 24.99 1 0.55 0.32 0.58

EVF 13 19.48 Moths Metapopulation 12 19.09 1 0.39 0.25 0.63

Table 3-7. Neither island area (Area) nor distance to mainland (Distance) were significant (bold) predictors of the optimized species richness data for taxa compared to α=0.05.

Taxon Model Covariates Estimate SE t value Pr(>|t|) Intercept -3.807 1.056 -3.607 0.003 EVF Area 2.037 1.381 1.475 0.164 Mammal Intercept -3.475 1.574 -2.208 0.047 Metapopulation Area 1.860 1.734 1.073 0.304 Distance -0.002 0.008 -0.279 0.785

Intercept -2.993 0.535 -5.593 8.732E-05 EVF Area 1.254 0.786 1.595 0.135 Tree Intercept -3.165 0.833 -3.799 0.003 Metapopulation Area 1.494 1.019 1.467 0.168 Distance 0.001 0.003 0.325 0.751

Intercept -4.719 1.033 -4.568 0.001 EVF Area 1.981 1.349 1.468 0.166 Moth Intercept -4.384 1.508 -2.907 0.013 Metapopulation Area 1.744 1.637 1.066 0.308 Distance -0.002 0.008 -0.284 0.781

We found that moth species richness was not best described by island area (Table 3-8).

Instead, the richness of tree-dependent moth species was best described by distance to mainland

and tree species richness. Tree species richness described the greatest amount of deviation in

moth richness (Figure 3-2). The effect of island distance to mainland was masked and by itself

did not explain much deviation (5.8%). However, when paired with either tree species richness or island area, the deviation explained increased (26.8%) and became a significant predictor of

moth richness (Figure 3-2). The classic metapopulation variable, island area, had similar

descriptive ability to tree species richness and these variables were highly correlated (Pearson’s

correlation coefficient=0.755, t=6.315, df=30, p-value<0.01). Tree species richness explained more overall deviance than island area, however, which is supported by the previous results where the optimized dataset for moths did not have area as a significant predictor, leading to the

conclusion that host tree species richness is more influential than metapopulation dynamics in

structuring the moth community in Pymatuning reservoir.

Table 3-8. To test the hypothesis that moth diversity may be tied to host plant diversity, a subset of moth species was chosen who had known tree species as host plants. Moth species who also had herbaceous host plants were not included. The best metapopulation model included tree species richness (TreeS) and island distance to mainland (Distance), not the classic combination of metapopulation variables of island area and Distance. Both Distance and Tree S were significant (bold) predictors of species richness compared to α=0.05.

Covariates Estimate Std. Error t value Pr(>|t|) (Intercept) -1.630 0.760 -2.145 0.041

Distance -0.452 0.188 -2.396 0.023

TreeS 0.113 0.025 4.531 9.32E-05

Figure 3-2. The individual and confounded effects of island area (Area), distance to mainland (Distance) and tree species richness (TreeS) on moth species richness. Deviance of tree-dependent moth species richness was best explained by TreeS in the Pymatuning system. Area was highly correlated with TreeS and shared 57.07% variance and was not included in best model for predicting moth richness on islands. DISCUSSION We found a lack of evidence to support that metapopulation dynamics of individual

species is the predominant driver of community structure at Pymatuning reservoir for mammals,

trees, and moths. Our study compared the metapopulation model to a null model under natural

and used optimized testing conditions for three different taxa. We assumed that the richness of

mammals on islands was the most likely taxon to be influenced by metapopulation dynamics and

the tree taxon were the least likely. Our results indicate that metapopulation dynamics is not

determining species richness for any of the study taxa, including mammals. These results are

similar to the findings of Coleman et al. (1982) who concluded that the songbird community at

Pymatuning reservoir followed random placement. Random placement of species can explain the

species richness patterns of island species for a variety of situations (Connor and Simberloff

1979) so unless metapopulation dynamics were heavily influencing the community, it may be

unlikely to find evidence to the contrary.

Possible explanations for the lack of evidence of metapopulation dynamics in the

Pymatuning system include the strong past and current anthropogenic influences on the system,

including the fairly recent age of the man-made island-mainland system, only 86 years old.

Although the notion of equilibrium is questionable (Kricher 2009), “relaxation” of a system into a stable state has been estimated to take thousands of years (Diamond 1972, Simberloff 1974,

Terborgh 1975). While these relaxation times are theorized to be shorter for smaller islands like those in our study system, the wildlife and plant communities at Pymatuning may not be in an equilibrium state, an assumption of the metapopulation theory. Evidence supporting the idea that plant communities are still responding exists in the presence of remnant coniferous plantations and nonnative homestead vegetation on both the islands and mainland surrounding the reservoir.

The tree community has not had time to adjust to the creation of the reservoir and the human- mediated plantings that occurred around the time of dam construction.

Current anthropogenic influence may further affect whether the plant and animal communities are at equilibrium. Land use outside of the state park area includes non-forested habitat, such as agricultural fields, which may influence the species found at Pymatuning. For

example, moth community composition included nonnative crop pest species, such as western

bean cutworm (Striacosta albicosta) and European corn borer (Ostrinia nubilalis). Invasive

species have been found to change species richness estimates (Hejda et al. 2009) which can

potentially mask the underlying dynamics influencing species richness.

We hypothesized that species richness of the moth taxon on Pymatuning islands may best

be described by the diversity of vegetation reflecting the specialization of some moth species to

their host plants (Table 3-2). We found support for this hypothesis since the best model

describing moth species richness included the diversity of tree species on the islands and distance

to the mainland. Classic metapopulation theory predicts island area would be one of the main

mechanisms influencing the presence of moth species (Hanski 1998b). Island area may have an

indirect effect on moth species richness since habitat heterogeneity is hypothesized to increase

with area (Connor and McCoy 1979, Rosenzweig 1995). The correlation we found between island area and tree species richness corroborates the hypothesis that habitat diversity is driven by area. Species richness can have a direct relationship to habitat heterogeneity in island systems

(Hortal et al. 2009). Habitat diversity has been found to be a better predictor for species richness compared to study area for a variety of taxa including mammals on small islands (Fox and Fox

2000, Báldi and Sadler 2008). In contrast, other studies found no correlation between area and habitat diversity and area was the greatest predictor of species richness for woody plants, beetles, and land snails (Nilsson et al. 1988, Kohn and Walsh 1994).

Current theories attempting to describe the influential mechanisms of biodiversity and biogeography are beneficial in the process of understanding what impacts the distribution of organisms. Evaluating these theories in conjunction with standard empirical testing is a crucial step for investigations to avoid misspent effort and preventing inaccurate conclusions. This step

54 can aid in trying to identify the processes behind the patterns we observe. While evidence has been found that metapopulation dynamics structure individual species (Eriksson 1996, Harrison and Taylor 1997, Wright et al. 2006), the results of our study indicate that metapopulation dynamics is not a driving force behind community structure.

4. Incorporating Density-Area Relationships in Estimates of Extinction Risk: An Empirical Example ABSTRACT Metapopulation dynamics are an important tool in conservation biology because of it is often

applied to fragmentation issues and estimates for extinction risk. Current methods for estimating

the extinction risk of local populations within metapopulations assume that density is equal

across all patches, i.e., a constant density-area relationship. The assumption of a constant

density-area relationship has been shown to be violated for a number of species. We propose a

method to correct for variable density-area relationships within metapopulations. Our method

was tested on density of mammals, trees, and moths in an island-mainland system. We found the

majority of species for all three taxa violated the assumption of a constant density-area relationship and found taxonomic differences in how species abundance changed with habitat area both within and between taxa. Not accounting for the variable relationship between density and area over-estimated the extinction risk for most species, in this system particularly for smaller islands.

INTRODUCTION A critical step in conservation efforts is identifying imperiled populations of species. Estimating

the risk of extinction of local populations can aid management and prioritization decisions

(Moilanen and Cabeza 2002), but conservation priorities are often derived from life history traits

which may be difficult to quantify or require large effort to measure in rare or elusive species

(Margules and Usher 1981, Lande 1993, Sæther et al. 1996, Keith 1998, Brook et al. 2000,

Purvis et al. 2000, Loyola et al. 2008, Mace et al. 2008). Additionally, there is increased concern

about the impacts of anthropogenic disturbance and the effects of climate change on extinction

risk which calls for improved methods to accurately estimate risk (Thomas et al. 2004, Kujala et

al. 2013, Urban and Matter 2018).

Mechanistic models offer methods to calculate extinction rate based on a few sets of

hypothesized mechanisms that can be measured. One such model is the metapopulation

hypothesis derived from Levins (1969) original metapopulation theory and MacArthur and

Wilson (1967) equilibrium theory of island biogeography, developed by others to include

extinction rate calculations (Hanski and Gilpin 1991). Further development of the

metapopulation hypothesis assumes that the incidence of a species in a given island or habitat

patch is determined by a balance of local extinction and (re)colonization. The rate of local

extinction is given as:

Equation 4-1 1 = (w A ) µj xi Where µ is the extinction rate for island j; w is thei j constant density of species i; A is the area of

island j, and x is the scaling parameter of extinction risk with area for species i (Hanski 1994b,

Hanski and Gyllenberg 1997, Hanski 1999, Matter et al. 2002).

One key assumption of extinction risk in the metapopulation model, while

acknowledging that it may be violated (Hanski 1994b), is that the density of a species remains

constant over varying habitat area. This relationship has alternatively been termed the density-

area relationship (DAR) when density is related to habitat area or the individuals-area relationship when relating the number of individuals to habitat area (Connor et al. 2000, Gaston

and Matter 2002). In either case, the assumption of a constant DAR or a linearly proportionate

increase of individuals with area is incorporated into the metapopulation model since w, density

of a species, is assumed to be constant (Hanski and Gyllenberg 1997).

This relationship, where a linearly proportionate increase of individuals with area, has

been found to be violated for a variety of taxa in both island-mainland systems and fragmented

habitat patches (Bowers and Matter 1997, Bender et al. 1998, Connor et al. 2000, Gaston and

Matter 2002, Wilder and Meikle 2005, Zhao et al. 2012, Schnell et al. 2013, Lancaster and

Downes 2014). Since the DAR has been shown to vary among species, taxa, and scale of study; it would seem the assumption of a constant DAR can be easily violated, potentially skewing results when applying metapopulation models to extinction risk. Previous simulations have shown that a variable DAR can alter the expected shape of the species-area curve, population growth estimates, the relative importance of certain habitat patches within a metapopulation in terms of connectedness, and estimates of local extinction (Matter 2000, Donovan and Lamberson

2001, Yamaura et al. 2016). Therefore, it is important to incorporate varying DAR when estimating metapopulation dynamics, extinction risk, and attendant community level patterns

(Schnell et al. 2013, Yamaura et al. 2016).

We evaluated whether the constant DAR assumption is violated and, if so, how it affects estimates of extinction risk. The focus of our research was to explicitly incorporate the DAR into

the metapopulation hypothesis calculation of species-specific extinction rate. Our study incorporated data from a single island-mainland system for a variety of functional taxa and we predicted that the DAR will vary for individual species as well as have taxon-specific differences for small mammals, tree species, and moths.

METHODS System Within the metapopulation matrix, non-habitat patches can influence connectivity and therefore persistence of habitat patches (Åberg et al. 1995, Weins 1997, Moilanen et al. 1998).

Ideally, to improve estimates of the interplay of density and area on the rate of extinction in a system, non-habitat should be areas with no chance for long-term survival and reproduction.

Therefore, we chose an island mainland system, Pymatuning reservoir, which has discrete habitat patches (i.e. islands) surrounded by an inhabitable matrix (i.e. reservoir) for certain species.

Pymatuning reservoir is located on the border of Ohio and Pennsylvania (41° 29′ 54″ N, 80° 27′

41″ W). The reservoir was created in 1932 and contains 32 homogeneous, forested islands.

Current island sizes range from 0.0001 to 68.0313 ha and isolation varies from 9.2 to 670.8 m from the mainland.

Data Collection Three taxa were considered for study during May through August 2012 to 2014; small mammals, trees, and moths. For small mammals, the density and species richness on each island was estimated using standard mark-recapture methodology (Nichols 1992, Hoffmann et al.

2010). Mammals were captured using live-traps for five consecutive days per island (Conard et al. 2008). Islands were sampled once and five islands were resampled each year to monitor for annual differences in capture rates, which were minimal. Mammal surveys employed small live traps (H.B. Sherman Trap, Inc., Tallahassee Fla.; 7.6 x 8.9 x 22.9 cm) and large live traps

(Tomahawk Live Traps Co., Tomahawk, WI; 81.3 x 25.4 x 30.5 cm), baited, and placed in the

habitats during May-August. The number of traps/grids used was proportional to island area.

Small islands with an area < 1 ha had a minimum of five small traps and two large traps evenly distributed across the landmass to increase sampling effort in case of disturbance. Larger island sampling was conducted using grids with effective trapping area of 1ha comprised of 25 small traps using 20 m spacing and 5 large traps placed on the corners and center of the grid. The number of 1 ha grids was proportional to island size with a minimum 250 m spacing between grid edges. Captured individuals were uniquely marked by either toe clipping (Blarina and Sorex

sp.) or Monel fingerling ear tags for species with large external pinnae. All mammal work was

done in accordance with UC IACUC protocol 13-02-22-01 and by the American Society of

Mammalogists (Sikes et al. 2011). Density was calculated as number of unique individuals per

ha.

Tree species were surveyed using a 10 m radius circle plots to estimate mean density.

Woody plant species with a diameter at breast height (DBH) ≥5 cm and taller than 0.5 m were

identified using Rhoads and Block (2007). Density of a plot was calculated as number of

qualifying stems per ha. Plot locations were determined by stratified sampling based on the area

percentage of dominant habitat types. Plots spaced 250 m apart and 100 m away from roadways

and trails. Islands with a diameter < 20 m had irregularly shaped plots to fit the island’s natural

shape but maintained plot area of 314.16 m2. Islands with an area less than the standard plot area

received total island surveys. Vegetation plots were conducted in conjunction with moth trap

locations and mammal grids to link vegetation data to the other taxa. To better estimate species

richness of trees, a timed meander method was employed between plots of the same habitat patch

(Goff et al. 1982, Huebner 2007). Distance to nearest plot was recorded as well as the

identification of any species that were not recorded within plots.

Moth sampling was conducted using 12-volt battery-powered, ultra-violet (UV) light funnel traps with automatic light sensors (BioQuip Inc., Rancho Dominguez, CA) during dark hours for two consecutive nights. Locations were sampled at least twice during May-August to capture species’ emergence times. Traps were hung from natural vegetation or shepherd hooks

1.5-2.5 m off the ground and a proportional number of light traps were placed on each island with 250 m between traps. To estimate density, an effective trapping size of 20m radius around the trap was estimated due to the radius of attraction for UV traps (Plaut 1971, Truxa and Fiedler

2012). Moon phase was taken into account and trapping was suspended during full and new moon phases. Habitat type and dominant plant species in a 20 m radius around the point center were noted. Traps contained Dichlorvos strips for the collection of specimens which were used to identify species with total length greater than 1cm.

Data Analysis We explicitly incorporated the DAR into the metapopulation calculation of species- specific extinction rate rather than assume a constant DAR. We broke down the metapopulation parameter x to where it no longer represented only the scaling of extinction risk with area, but also was adjusted for changes in density with area. The scaling parameter (Xi) would now be

described by two estimable parameters, the relationship between density and area and how

extinction risk varies with abundance for species i:

Equation 4-2

X = x B

where B represents the slopei ofi ∗ thei DAR for species i.

To test if the slope of DAR was significantly different than 1, and therefore violated the

assumption of constant density, a generalized linear model (GLM) with Poisson error was fit to

abundance of each species using log(area) and compared to a model with log(area) as an offset;

i.e., assuming the slope is constant (Connor et al. 1997, Matter 1997). First, the abundance data

for each species of each taxon were fit in the GLM to see the relationship between number of

unique individual captures on an island and log of the island area. Second, to account for over

dispersion, the dispersion parameter was extracted from the summary results of the GLM and the

dependent variable was divided by the dispersion parameter, i.e., jointly modeling the mean and

dispersion (McCullagh and Nelder 1989). Then the GLM was refitted with the new independent variable both with log(area) as a dependent variable and as an offset to compare the slope of the

DAR to a value of 1. Significance testing to compare models used a likelihood ratio test with

df=1 and α=0.05. To estimate the scaling parameter , the slope of the density-area relationship

𝑖𝑖 was extracted from the GLMs using log(area). 𝑋𝑋

To find the relative contribution of the relationship between extinction risk varying with abundance and the scaling parameter, the parameter needed to be estimated. The value of

𝑖𝑖 𝑖𝑖 can be extracted from the incidence function𝑥𝑥 ( ) model since it describes the relationship 𝑥𝑥

𝑖𝑖𝑖𝑖 between patch area and when a species is no longer𝑃𝑃 present. This estimate of was then used in

𝑖𝑖 the estimation of : 𝑥𝑥

𝑋𝑋𝑖𝑖

Equation 4-3

e P = e K+ij 1 ij Kij where Kij is:

Equation 4-4 p K = c + (1 + x ) w + x A d 1 ijp ij i i i j i j 𝑙𝑙𝑙𝑙𝑙𝑙 ij 𝑙𝑙𝑙𝑙𝑙𝑙 𝑙𝑙𝑙𝑙𝑙𝑙 𝑙𝑙𝑙𝑙𝑙𝑙 − α where αi describes the dispersal− ability of species i in the community and wi is the constant density of species i (Hanski and Gyllenberg 1997, Matter et al. 2002). c is a constant parameter.

Incidence data was fit using a quasibinomial GLM. To tease apart the influence of unoccupied patches on the DAR slope (Loman 1991, Bowers and Matter 1997), we also compared the slopes using the full set of islands and using a subset of only occupied islands.

We also tested if moth densities may best be described by habitat heterogeneity because of the host specialization of many herbivorous insects, including moths (Strong et al. 1984,

Thompson and Pellmyr 1991). We predicted that the abundance of tree-dependent moth species could be described by diversity of vegetation since many of our tree-dependent species are tree generalists. To parse out if host plant diversity is related to moth abundance in our system, we added tree species richness as a predictor variable to the species specific GLMs. Only moth species that have trees as known host plants were considered (Robinson et al. 2010).

RESULTS The assumption of a constant DAR was violated for 63% of species with adequate capture data across all three taxa (Table 4-1). All four mammal species with adequate capture data had slopes significantly less than the assumed constant of 1, indicating that their densities were higher on smaller islands than on larger islands. Only three of the 13 tree species with adequate capture data to analyze did not violate the assumption of constant density; Fagus grandifolia, Fraxinus nigra, and Pinus resinosa. Nine tree species had DAR slopes significantly less than one; no tree species showed increasing density as island area increased. One tree species, Salix nigra, had a significantly negative DAR slope indicating higher density and

63 abundance on smaller than on larger islands. The moth taxon had the most varied response with

DAR slopes significantly differing from one for 59 out of the 98 species with adequate capture data to analyze; again, all these species showed decreasing density as island area increased.

Additionally, 15 of these species had negative slope estimates indicating that there was higher abundance and density on smaller islands than on larger islands.

Table 4-1. Results of log-likelihood test between GLM with log(area) as a dependent variable and as an offset in order to compare the slope of the density-area relationship (DAR) to a value of 1. Slope of the density-area relationship (B) was extracted from the results of the GLM and used to adjust estimates of extinction risk. The DAR was significantly different (bold) for all mammal and the majority of tree and moth species, indicating that the DAR slope may affect the calculation of metapopulation extinction risk and should be incorporated into the scaling parameter.

Mammal Species Deviance df p-value B ±SE Blarina brevicauda -13.17 1 2.84E-04 0.459 0.135 Peromyscus leucopus -77.94 1 1.06E-18 0.504 0.051 Procyon lotor -56.81 1 4.80E-14 0.254 0.092 Tamias striatus -35.73 1 2.27E-09 0.659 0.052 Mature Tree Species Deviance df p-value B ±SE Acer rubrum -283.18 1 1.52E-63 0.214 0.043 Acer saccharinum -94.60 1 2.33E-22 0.024 0.089 Acer saccharum -20.23 1 6.85E-06 0.690 0.064 Fagus grandifolia -0.09 1 0.76 0.970 0.096 Fraxinus americana -12.68 1 3.70E-04 0.484 0.132 Fraxinus nigra -2.50 1 0.11 0.649 0.204 Fraxinus pennsylvanica -32.14 1 1.44E-08 0.237 0.125 Nyssa sylvatica -32.31 1 1.31E-08 0.297 0.114 Pinus resinosa 0.00 1 0.97 1.011 0.298 Prunus serotina -33.02 1 9.10E-09 0.621 0.060 Quercus alba -4.67 1 0.03 0.427 0.242 Quercus rubra -15.36 1 8.88E-05 0.457 0.126 Salix nigra -204.08 1 2.69E-46 -0.058 0.061 Moth Species Deviance df p-value B ±SE Achyra rantalis -0.26 1 0.61 1.186 0.385 Acronicta grisea -9.90 1 1.65E-03 0.412 0.170

Acronicta hasta -5.70 1 0.02 0.163 0.326 Aethiophysa invisalis -2.47 1 0.12 0.755 0.146 Aglossa disciferalis -25.77 1 3.85E-07 0.361 0.115 Agriphila vulgivagellus -39.00 1 4.24E-10 0.238 0.113 Agrotis ipsilon -25.99 1 3.43E-07 0.063 0.167 Apamea dubitans -0.26 1 0.61 1.186 0.385 Athetis tarda -11.08 1 8.71E-04 0.723 0.077 Autographa precationis -34.88 1 3.51E-09 -0.232 0.145 Biston betularia -1.24 1 0.27 0.740 0.218 Cabera erythemaria -31.75 1 1.75E-08 0.217 0.129 Cabera variolaria -17.24 1 3.29E-05 0.624 0.083 Callosamia promethea -22.32 1 2.30E-06 -0.184 0.181 Catocala ultronia 0.00 1 0.99 1.002 0.324 Choristoneura rosaceana -28.69 1 8.51E-08 0.314 0.118 Chytolita morbidalis -6.80 1 0.01 0.682 0.113 Costaconvexa 1 0.424 centrostrigaria -3.53 0.06 0.279 Crambus saltuellus -12.12 1 5.00E-04 -0.118 0.250 Datana drexelii -36.51 1 1.52E-09 0.029 0.143 Desmia funeralis -2.17 1 0.14 0.786 0.137 Desmia maculalis -3.12 1 0.08 0.353 0.336 Digrammia ocellinata -0.06 1 0.80 1.086 0.351 Dryocampa rubicunda -33.09 1 8.79E-09 -0.217 0.149 Dysstroma citrata -0.02 1 0.89 0.970 0.222 Ectropis crepuscularia -4.26 1 0.04 0.378 0.275 Ennomos subsignaria -6.09 1 0.01 0.139 0.324 Epirrhoe alternata -24.59 1 7.10E-07 0.246 0.141 Euchlaena irraria -8.51 1 3.54E-03 0.329 0.211 Euclea delphinii -2.09 1 0.15 0.537 0.291 Eulithis diversilineata -14.56 1 1.36E-04 0.483 0.123 Euphyia intermediata -2.82 1 0.09 0.682 0.174 Eupithecia sp. -95.80 1 1.27E-22 0.580 0.039 Eupithecia tripunctaria -11.28 1 7.83E-04 0.456 0.147 Eutrapela clemataria -1.81 1 0.18 0.792 0.146 Feltia subterranea -22.16 1 2.50E-06 0.328 0.131 Halysidota tessellaris -55.55 1 9.12E-14 0.508 0.060 Haploa clymene -2.76 1 0.10 0.634 0.202 Helicoverpa zea -17.64 1 2.68E-05 0.345 0.143 Helotropha reniformis -8.02 1 4.62E-03 0.461 0.173 Heterocampa guttivitta -18.77 1 1.47E-05 0.230 0.165 Heterophleps refusaria -0.79 1 0.37 0.752 0.260 Heterophleps triguttaria -20.93 1 4.76E-06 0.296 0.142 Homophoberia cristata -36.17 1 1.81E-09 0.142 0.132 Hypagyrtis piniata -1.27 1 0.26 1.388 0.391 Hypena manalis -17.15 1 3.45E-05 -0.098 0.211

Hypenodes fractilinea -5.85 1 0.02 0.153 0.325 Hyphantria cunea -11.73 1 6.16E-04 0.153 0.230 Idia americalis -5.54 1 0.02 0.644 0.139 Ledaea perditalis -14.11 1 1.73E-04 0.460 0.131 Lymantria dispar -10.48 1 1.21E-03 0.451 0.154 Macaria signaria -0.28 1 0.60 0.893 0.198 Macrurocampa marthesia -32.59 1 1.14E-08 0.113 0.143 Malacosoma americana -27.14 1 1.89E-07 -0.080 0.168 Melanolophia canadaria -0.06 1 0.81 0.969 0.128 Melanolophia signataria -12.47 1 4.13E-04 0.410 0.152 Metalectra discalis -0.41 1 0.52 0.897 0.155 Moth169 -0.78 1 0.38 0.635 0.378 Moth251 -15.13 1 1.00E-04 0.298 0.166 Moth360 -9.96 1 1.60E-03 0.210 0.232 Moth96 -0.25 1 0.62 0.777 0.419 Mythimna unipuncta -76.83 1 1.86E-18 -0.136 0.099 Nadata gibbosa -5.90 1 0.02 0.683 0.120 Nematocampa resistaria -1.12 1 0.29 0.684 0.276 Nemoria rubrifrontaria -0.78 1 0.38 0.635 0.378 Noctua pronuba -3.36 1 0.07 0.671 0.165 Nomophila nearctica -17.51 1 2.86E-05 -0.234 0.205 Notodonta torva -0.20 1 0.65 0.892 0.232 Ochropleura implecta -20.58 1 5.73E-06 0.272 0.148 Olethreutes fasciatana -21.01 1 4.58E-06 0.482 0.103 Olethreutes glaciana -80.76 1 2.55E-19 0.314 0.070 Olethreutes quadrifidum -13.09 1 2.97E-04 0.588 0.104 Oligocentria semirufescens -0.24 1 0.62 1.202 0.437 Orthodes cynica -0.91 1 0.34 0.737 0.257 Orthodes detracta -1.81 1 0.18 0.483 0.348 Paonias excaecatus -0.05 1 0.82 0.963 0.160 Paonias myops -1.00 1 0.32 0.832 0.160 Parallelia bistriaris -0.02 1 0.90 1.035 0.282 Pero ancetaria -0.80 1 0.37 0.838 0.173 Pleuroprucha insulsaria -0.50 1 0.48 0.845 0.210 Polygrammate hebraeicum -14.80 1 1.20E-04 -0.183 0.223 Polygrammodes flavidalis -0.58 1 0.45 0.885 0.146 Prochoerodes lineola -0.79 1 0.37 0.787 0.226 Prolimacodes badia -22.53 1 2.07E-06 -0.093 0.184 Proxenus miranda -3.42 1 0.06 0.573 0.210 Pyrrharctia isabella -2.10 1 0.15 0.451 0.344 Renia factiosalis -15.48 1 8.33E-05 0.132 0.204 Scopula limboundata -21.29 1 3.94E-06 0.010 0.189 Speranza pustularia -313.33 1 4.11E-70 0.309 0.036 Spilosoma congrua -59.80 1 1.05E-14 -0.049 0.114

Spilosoma virginica -4.41 1 0.04 0.369 0.275 Spodoptera ornithogalli -28.65 1 8.69E-08 -0.259 0.161 Trichodezia albovittata -0.01 1 0.90 0.971 0.235 Tricholita signata -7.53 1 0.01 0.058 0.311 Xestia dolosa -10.14 1 1.45E-03 0.099 0.260 Xestia normanianus -32.85 1 9.97E-09 -0.214 0.149 Yponomeuta multipunctella -12.98 1 3.14E-04 -0.141 0.240 Zale horrida -2.95 1 0.09 0.368 0.337

When the slopes of the DAR were incorporated into the metapopulation scaling

parameter (X) estimates, the magnitude of X decreased when the relationship between density and area increased less than expected; i.e., a DAR slope less than one (Table 4-2). The largest

difference in X when correcting for a significant DAR was found in the pest moth species,

Malacosoma americanum (Eastern tent caterpillar). The slope of the DAR was -0.080 which greatly increased the value of X from -51.205 to 4.091 because of the negative slope of the DAR

(Table 4-2). Malacosoma americanum was captured at least once during all survey years from

June-July on three islands whose areas ranged from 0.043 to 9.612 ha.

Table 4-2. Change in the estimate of the metapopulation scaling parameter (X) for those species when accounting for density-area slopes. The extinction risk per area scaling parameter (x) is also the uncorrected metapopulation scaling parameter. The majority of species had density- area relationships less than the assumed constant density-area relationship indicating lower densities than expected on larger islands. This resulted in lower than estimated values for X.

Mammal Species X ±SE X Blarina brevicauda 0.200 2.861 0.092 Peromyscus leucopus 0.581 0.098 0.293 Procyon lotor 0.687 0.021 0.174 Tamias striatus 0.095 2.914 0.062 Mature Tree Species X ±SE X Acer rubrum -0.862 2.918 -0.185 Acer saccharinum 1.066 0.561 0.025 Acer saccharum -0.980 0.334 -0.676 Fagus grandifolia -0.053 0.053 -0.052

Fraxinus americana -0.040 0.862 -0.019 Fraxinus nigra 0.681 0.206 0.442 Fraxinus pennsylvanica 0.890 0.321 0.211 Nyssa sylvatica -0.665 0.191 -0.197 Pinus resinosa -1.433 0.941 -1.449 Prunus serotina -1.749 1.198 -1.086 Quercus alba 0.552 0.332 0.235 Quercus rubra 0.454 3.857 0.207 Salix nigra 1.063 0.569 -0.061 Moth Species X ±SE X Achyra rantalis -2.967 1.485 -3.520 Acronicta grisea 0.667 2.705 0.275 Acronicta hasta 0.479 3.010 0.078 Aethiophysa invisalis 0.229 1.227 0.173 Aglossa disciferalis 0.367 0.546 0.132 Agriphila vulgivagellus 0.820 1.878 0.195 Agrotis ipsilon -2.967 1.485 -0.188 Apamea dubitans 0.227 0.321 0.269 Athetis tarda 1.409 1.206 1.018 Autographa precationis -0.011 0.335 0.003 Biston betularia 0.634 0.035 0.470 Cabera erythemaria 0.362 0.212 0.079 Cabera variolaria 1.352 0.870 0.844 Callosamia promethea -1.135 0.215 0.209 Catocala ultronia 0.585 0.281 0.586 Choristoneura rosaceana 0.697 0.010 0.219 Chytolita morbidalis 0.475 4.548 0.324 Costaconvexa 1.150 1.567 0.488 centrostrigaria Crambus saltuellus 0.729 3.316 -0.086 Datana drexelii 0.604 0.743 0.018 Desmia funeralis 1.292 2.049 1.015 Desmia maculalis -0.697 0.274 -0.246 Digrammia ocellinata 0.546 0.129 0.593 Dryocampa rubicunda 0.894 5.820 -0.194 Dysstroma citrata 0.706 3.500 0.684 Ectropis crepuscularia 0.542 7.569 0.205 Ennomos subsignaria 0.738 7.865 0.102 Epirrhoe alternata 0.267 0.628 0.066 Euchlaena irraria 0.266 0.274 0.088 Euclea delphinii 0.711 0.626 0.382 Eulithis diversilineata 0.616 2.092 0.297 Euphyia intermediata 0.535 0.139 0.365

Eupithecia sp. 1.082 0.311 0.627 Eupithecia tripunctaria 0.166 0.355 0.076 Eutrapela clemataria 0.042 0.426 0.033 Feltia subterranea 0.559 1.674 0.183 Halysidota tessellaris 0.791 1.419 0.402 Haploa clymene 0.125 1.160 0.079 Helicoverpa zea 0.551 0.943 0.190 Helotropha reniformis 0.744 0.153 0.343 Heterocampa guttivitta 1.228 1.224 0.283 Heterophleps refusaria 0.875 0.607 0.658 Heterophleps triguttaria 0.219 1.578 0.065 Homophoberia cristata 0.712 1.000 0.101 Hypagyrtis piniata 0.431 3.305 0.598 Hypena manalis 0.789 1.339 -0.077 Hypenodes fractilinea 1.077 1.995 0.165 Hyphantria cunea 0.183 10.888 0.028 Idia americalis 1.108 0.412 0.713 Ledaea perditalis 0.985 0.210 0.453 Lymantria dispar 0.216 0.074 0.097 Macaria signaria 0.430 0.411 0.384 Macrurocampa marthesia 0.216 0.074 0.024 Malacosoma americana -51.205 0.542 4.091 Melanolophia canadaria 0.338 0.661 0.328 Melanolophia signataria 0.860 0.726 0.353 Metalectra discalis 0.200 2.034 0.179 Moth169 0.544 1.079 0.345 Moth251 -0.094 0.433 -0.028 Moth360 0.413 1.577 0.087 Moth96 1.253 1.449 0.973 Mythimna unipuncta 0.874 1.771 -0.119 Nadata gibbosa 0.306 1.031 0.209 Nematocampa resistaria 1.004 2.632 0.686 Nemoria rubrifrontaria 1.416 1.682 0.899 Noctua pronuba 0.596 0.549 0.400 Nomophila nearctica 1.284 2.670 -0.300 Notodonta torva -0.007 0.005 -0.007 Ochropleura implecta 1.193 0.080 0.325 Olethreutes fasciatana -0.142 0.014 -0.068 Olethreutes glaciana -0.411 0.587 -0.129 Olethreutes quadrifidum -0.325 0.133 -0.191 Oligocentria semirufescens -0.239 0.290 -0.287 Orthodes cynica 0.509 2.107 0.375 Orthodes detracta 0.772 0.180 0.373 Paonias excaecatus 0.603 0.079 0.581

Paonias myops -0.007 0.005 -0.006 Parallelia bistriaris 0.780 0.088 0.807 Pero ancetaria 0.542 7.569 0.454 Pleuroprucha insulsaria 0.313 10.083 0.264 Polygrammate hebraeicum -0.116 2.451 0.021 Polygrammodes flavidalis -0.060 0.196 -0.053 Prochoerodes lineola 1.341 1.821 1.056 Prolimacodes badia 0.038 1.172 -0.004 Proxenus miranda 0.542 7.569 0.311 Pyrrharctia isabella 0.738 7.865 0.333 Renia factiosalis 0.473 0.475 0.063 Scopula limboundata 1.044 1.481 0.011 Speranza pustularia 1.103 0.056 0.341 Spilosoma congrua 0.861 0.346 -0.042 Spilosoma virginica 1.298 0.696 0.479 Spodoptera ornithogalli 0.894 5.820 -0.232 Trichodezia albovittata 1.445 2.188 1.403 Tricholita signata 0.435 1.416 0.025 Xestia dolosa 1.009 4.574 0.100 Xestia normanianus 0.928 0.899 -0.199 Yponomeuta multipunctella 1.284 2.670 -0.181 Zale horrida 0.584 1.134 0.215

The change in magnitude for X, in turn, altered the extinction rate estimates for species whose DAR slopes violated the assumption of constant density. A decrease in X was usually found in species with smaller than expected DAR, such as found in members of the mammal taxon. This produced lower estimates of extinction risk on large islands and higher than expected extinction on small islands (Figure 2-1). There was one tree, Salix nigra, and 14 moth species where the incorporation of DAR slope reversed the sign of X, which has the potential to greatly impact the resulting estimate of extinction rate, such as in Malacosoma americanum (Table 4-2).

Four moth species, Autographa precationis, Polygrammate hebraeicum, Callosamia promethean, and Malacosoma americanum, had a X value change from a positive to negative value, indicating that these species may be more prone to extinction on large islands than would otherwise be estimated.

Mammal

Mature Tree

Moth

Figure 4-1. Comparisons of the metapopulation extinction risk estimate (µ) when corrected for variable density-area relationship (red) compared to the uncorrected extinction risk estimate (black) that assumes a constant density-area relationship. Corrected estimates produce reduced estimates of extinction risk on large islands and increased on small islands for the majority of species. Lines were smoothed using locally weighted scatterplot smoothing.

Despite the significant impacts of incorporating DAR into the calculation of extinction rate, island area was not always an important predictor of abundance (Table 4-3). Island area was not a significant predictor of abundance for four tree and 45 moth species. Our alternative predictor, host tree richness, also was not found to be a significant predictor of abundance for 18 out of 24 species (Table 4-4).

Table 4-3. As expected, island area is a significant driver for the abundance distribution for most species in the mammal and tree taxa studied located in the Pymatuning system. This is indicated by the results of individual species GLM where log(area) (Area) was a significant (bold) predictor of abundance for the majority of species at an alpha of 0.05. Area was less important for the members of the moth taxon; Area was not a significant predictor of abundance for 45 moth species.

Mammal Std T Species Parameter Estimate P-value Dev value Intercept -1.09 0.34 -3.21 1.32E-03 Blarina brevicauda Area 0.46 0.14 3.39 6.98E-04 Intercept 0.83 0.13 6.27 3.52E-10 Peromyscus leucopus Area 0.50 0.05 9.89 4.76E-23 Intercept -0.19 0.20 -0.95 0.34 Procyon lotor Area 0.25 0.09 2.76 0.01 Intercept 0.65 0.15 4.30 1.71E-05 Tamias striatus Area 0.66 0.05 12.56 3.42E-36 Mature Tree Std T Species Parameter Estimate P-value Dev value Intercept 1.31 0.09 13.89 7.69E-44 Acer rubrum Area 0.21 0.04 4.93 8.03E-07 Intercept -0.32 0.21 -1.47 0.14 Acer saccharinum Area 0.02 0.09 0.27 0.79 Intercept 0.24 0.19 1.27 0.21 Acer saccharum Area 0.69 0.06 10.85 2.06E-27 Intercept -0.87 0.32 -2.69 0.01 Fagus grandifolia Area 0.97 0.10 10.13 4.01E-24 Intercept -1.05 0.34 -3.13 1.74E-03 Fraxinus americana Area 0.48 0.13 3.67 2.41E-04 Intercept -2.06 0.58 -3.53 4.19E-04 Fraxinus nigra Area 0.65 0.20 3.19 1.44E-03 Fraxinus pennsylvanica Intercept -0.80 0.27 -2.94 3.33E-03

Area 0.24 0.12 1.90 0.06 Intercept -0.64 0.26 -2.51 0.01 Nyssa sylvatica Area 0.30 0.11 2.60 0.01 Intercept -3.19 1.02 -3.13 1.74E-03 Pinus resinosa Area 1.01 0.30 3.39 7.03E-04 Intercept 0.40 0.17 2.37 0.02 Prunus serotina Area 0.62 0.06 10.30 7.20E-25 Intercept -2.22 0.59 -3.76 1.70E-04 Quercus alba Area 0.43 0.24 1.77 0.08 Intercept -0.94 0.32 -2.99 2.76E-03 Quercus rubra Area 0.46 0.13 3.63 2.88E-04 Intercept 0.17 0.17 1.01 0.31 Salix nigra Area -0.06 0.06 -0.94 0.35 Moth Taxon Std T Species Parameter Estimate P-value Dev value Intercept -3.94 1.39 -2.85 4.42E-03 Achyra rantalis Area 1.19 0.39 3.08 2.06E-03 Intercept -1.51 0.41 -3.67 2.44E-04 Acronicta grisea Area 0.41 0.17 2.42 0.02 Intercept -2.73 0.71 -3.85 1.18E-04 Acronicta hasta Area 0.16 0.33 0.50 0.62 Intercept -1.48 0.44 -3.33 8.62E-04 Aethiophysa invisalis Area 0.76 0.15 5.18 2.20E-07 Intercept -0.70 0.27 -2.60 0.01 Aglossa disciferalis Area 0.36 0.12 3.13 1.75E-03 Intercept -0.61 0.25 -2.45 0.01 Agriphila vulgivagellus Area 0.24 0.11 2.10 0.04 Intercept -1.49 0.38 -3.88 1.04E-04 Agrotis ipsilon Area 0.06 0.17 0.38 0.70 Intercept -3.94 1.39 -2.85 4.42E-03 Apamea dubitans Area 1.19 0.39 3.08 2.06E-03 Intercept -0.18 0.23 -0.79 0.43 Athetis tarda Area 0.72 0.08 9.35 9.11E-21 Intercept -2.44 0.63 -3.88 1.04E-04 Autographa precationis Area -0.23 0.14 -1.60 0.11 Intercept -2.27 0.66 -3.45 5.64E-04 Biston betularia Area 0.74 0.22 3.40 6.74E-04 Intercept -0.87 0.28 -3.08 2.04E-03 Cabera erythemaria Area 0.22 0.13 1.68 0.09 Intercept -0.24 0.23 -1.01 0.31 Cabera variolaria Area 0.62 0.08 7.54 4.80E-14 Callosamia promethea Intercept -2.61 0.69 -3.78 1.58E-04

Area -0.18 0.18 -1.02 0.31 Intercept -3.34 1.10 -3.03 2.44E-03 Catocala ultronia Area 1.00 0.32 3.09 1.99E-03 Intercept -0.72 0.27 -2.68 0.01 Choristoneura rosaceana Area 0.31 0.12 2.66 0.01 Intercept -0.90 0.33 -2.73 0.01 Chytolita morbidalis Area 0.68 0.11 6.06 1.37E-09 Intercept -2.51 0.68 -3.68 2.32E-04 Costaconvexa centrostrigaria Area 0.42 0.28 1.52 0.13 Intercept -2.90 0.80 -3.62 2.90E-04 Crambus saltuellus Area -0.12 0.25 -0.47 0.64 Intercept -1.25 0.34 -3.65 2.61E-04 Datana drexelii Area 0.03 0.14 0.20 0.84 Intercept -1.38 0.42 -3.26 1.10E-03 Desmia funeralis Area 0.79 0.14 5.73 1.00E-08 Intercept -2.83 0.78 -3.63 2.86E-04 Desmia maculalis Area 0.35 0.34 1.05 0.29 Intercept -3.61 1.23 -2.94 3.25E-03 Digrammia ocellinata Area 1.09 0.35 3.10 1.95E-03 Intercept -2.40 0.62 -3.88 1.04E-04 Dryocampa rubicunda Area -0.22 0.15 -1.46 0.14 Intercept -2.55 0.75 -3.41 6.50E-04 Dysstroma citrata Area 0.97 0.22 4.36 1.30E-05 Intercept -2.45 0.65 -3.76 1.67E-04 Ectropis crepuscularia Area 0.38 0.28 1.37 0.17 Intercept -2.73 0.71 -3.85 1.16E-04 Ennomos subsignaria Area 0.14 0.32 0.43 0.67 Intercept -1.05 0.31 -3.38 7.16E-04 Epirrhoe alternata Area 0.25 0.14 1.75 0.08 Intercept -1.89 0.48 -3.91 9.21E-05 Euchlaena irraria Area 0.33 0.21 1.56 0.12 Intercept -2.68 0.77 -3.47 5.20E-04 Euclea delphinii Area 0.54 0.29 1.84 0.07 Intercept -0.92 0.31 -2.92 3.48E-03 Eulithis diversilineata Area 0.48 0.12 3.92 8.90E-05 Intercept -1.77 0.51 -3.48 4.98E-04 Euphyia intermediata Area 0.68 0.17 3.91 9.15E-05 Intercept 1.30 0.11 12.16 5.32E-34 Eupithecia sp. Area 0.58 0.04 14.81 1.28E-49 Intercept -1.25 0.37 -3.41 6.61E-04 Eupithecia tripunctaria Area 0.46 0.15 3.10 1.91E-03 Intercept -1.51 0.45 -3.34 8.26E-04 Eutrapela clemataria Area 0.79 0.15 5.44 5.43E-08

Intercept -0.94 0.30 -3.12 1.79E-03 Feltia subterranea Area 0.33 0.13 2.51 0.01 Intercept 0.50 0.16 3.23 1.24E-03 Halysidota tessellaris Area 0.51 0.06 8.48 2.32E-17 Intercept -2.02 0.57 -3.54 3.99E-04 Haploa clymene Area 0.63 0.20 3.14 1.67E-03 Intercept -1.12 0.33 -3.39 7.07E-04 Helicoverpa zea Area 0.35 0.14 2.42 0.02 Intercept -1.58 0.43 -3.64 2.74E-04 Helotropha reniformis Area 0.46 0.17 2.67 0.01 Intercept -1.36 0.36 -3.77 1.64E-04 Heterocampa guttivitta Area 0.23 0.16 1.40 0.16 Intercept -2.63 0.79 -3.33 8.65E-04 Heterophleps refusaria Area 0.75 0.26 2.89 3.82E-03 Intercept -1.08 0.32 -3.38 7.15E-04 Heterophleps triguttaria Area 0.30 0.14 2.09 0.04 Intercept -0.93 0.29 -3.23 1.22E-03 Homophoberia cristata Area 0.14 0.13 1.08 0.28 Intercept -4.32 1.47 -2.94 3.30E-03 Hypagyrtis piniata Area 1.39 0.39 3.55 3.85E-04 Intercept -2.47 0.64 -3.83 1.26E-04 Hypena manalis Area -0.10 0.21 -0.47 0.64 Intercept -2.73 0.71 -3.85 1.17E-04 Hypenodes fractilinea Area 0.15 0.33 0.47 0.64 Intercept -2.03 0.50 -4.06 4.84E-05 Hyphantria cunea Area 0.15 0.23 0.66 0.51 Intercept -1.28 0.40 -3.24 1.18E-03 Idia americalis Area 0.64 0.14 4.64 3.43E-06 Intercept -1.02 0.33 -3.11 1.89E-03 Ledaea perditalis Area 0.46 0.13 3.53 4.22E-04 Intercept -1.34 0.38 -3.49 4.76E-04 Lymantria dispar Area 0.45 0.15 2.93 3.37E-03 Intercept -2.23 0.64 -3.46 5.48E-04 Macaria signaria Area 0.89 0.20 4.52 6.31E-06 Intercept -1.12 0.32 -3.53 4.18E-04 Macrurocampa marthesia Area 0.11 0.14 0.79 0.43 Intercept -1.93 0.49 -3.93 8.47E-05 Malacosoma americana Area -0.08 0.17 -0.48 0.63 Intercept -1.45 0.43 -3.36 7.81E-04 Melanolophia canadaria Area 0.97 0.13 7.55 4.34E-14 Intercept -1.29 0.37 -3.50 4.71E-04 Melanolophia signataria Area 0.41 0.15 2.70 0.01 Metalectra discalis Intercept -1.75 0.51 -3.45 5.64E-04

Area 0.90 0.16 5.78 7.37E-09 Intercept -3.28 1.07 -3.06 2.19E-03 Moth169 Area 0.63 0.38 1.68 0.09 Intercept -1.40 0.37 -3.74 1.87E-04 Moth251 Area 0.30 0.17 1.79 0.07 Intercept -2.04 0.51 -4.04 5.37E-05 Moth360 Area 0.21 0.23 0.90 0.37 Intercept -3.61 1.29 -2.80 0.01 Moth96 Area 0.78 0.42 1.85 0.06 Intercept -1.14 0.33 -3.43 6.03E-04 Mythimna unipuncta Area -0.14 0.10 -1.38 0.17 Intercept -1.03 0.35 -2.94 3.32E-03 Nadata gibbosa Area 0.68 0.12 5.67 1.42E-08 Intercept -2.69 0.81 -3.34 8.46E-04 Nematocampa resistaria Area 0.68 0.28 2.48 0.01 Intercept -3.28 1.07 -3.06 2.19E-03 Nemoria rubrifrontaria Area 0.63 0.38 1.68 0.09 Intercept -1.65 0.48 -3.45 5.52E-04 Noctua pronuba Area 0.67 0.17 4.07 4.72E-05 Intercept -3.14 0.89 -3.52 4.27E-04 Nomophila nearctica Area -0.23 0.20 -1.14 0.25 Intercept -2.54 0.75 -3.37 7.53E-04 Notodonta torva Area 0.89 0.23 3.85 1.18E-04 Intercept -1.16 0.33 -3.51 4.40E-04 Ochropleura implecta Area 0.27 0.15 1.84 0.07 Intercept -0.55 0.26 -2.12 0.03 Olethreutes fasciatana Area 0.48 0.10 4.69 2.70E-06 Intercept 0.32 0.16 1.98 0.05 Olethreutes glaciana Area 0.31 0.07 4.46 8.13E-06 Intercept -0.66 0.29 -2.30 0.02 Olethreutes quadrifidum Area 0.59 0.10 5.67 1.44E-08 Intercept -4.22 1.58 -2.67 0.01 Oligocentria semirufescens Area 1.20 0.44 2.75 0.01 Intercept -2.60 0.77 -3.35 8.04E-04 Orthodes cynica Area 0.74 0.26 2.87 4.14E-03 Intercept -3.00 0.89 -3.37 7.46E-04 Orthodes detracta Area 0.48 0.35 1.39 0.17 Intercept -1.89 0.54 -3.51 4.48E-04 Paonias excaecatus Area 0.96 0.16 6.00 1.92E-09 Intercept -1.75 0.51 -3.43 5.97E-04 Paonias myops Area 0.83 0.16 5.18 2.16E-07 Intercept -3.11 0.97 -3.20 1.38E-03 Parallelia bistriaris Area 1.03 0.28 3.66 2.48E-04

Intercept -1.90 0.55 -3.46 5.41E-04 Pero ancetaria Area 0.84 0.17 4.84 1.32E-06 Intercept -2.29 0.67 -3.43 6.01E-04 Pleuroprucha insulsaria Area 0.85 0.21 4.03 5.50E-05 Intercept -3.02 0.85 -3.57 3.64E-04 Polygrammate hebraeicum Area -0.18 0.22 -0.82 0.41 Intercept -1.61 0.47 -3.40 6.81E-04 Polygrammodes flavidalis Area 0.88 0.15 6.08 1.22E-09 Intercept -2.39 0.70 -3.41 6.53E-04 Prochoerodes lineola Area 0.79 0.23 3.48 5.00E-04 Intercept -2.17 0.56 -3.91 9.10E-05 Prolimacodes badia Area -0.09 0.18 -0.50 0.61 Intercept -2.06 0.57 -3.60 3.22E-04 Proxenus miranda Area 0.57 0.21 2.73 0.01 Intercept -2.95 0.86 -3.44 5.87E-04 Pyrrharctia isabella Area 0.45 0.34 1.31 0.19 Intercept -1.81 0.45 -4.04 5.23E-05 Renia factiosalis Area 0.13 0.20 0.65 0.52 Intercept -1.85 0.46 -3.99 6.68E-05 Scopula limboundata Area 0.01 0.19 0.05 0.96 Intercept 1.66 0.08 20.40 1.53E-92 Speranza pustularia Area 0.31 0.04 8.61 7.49E-18 Intercept -1.02 0.31 -3.29 9.87E-04 Spilosoma congrua Area -0.05 0.11 -0.43 0.67 Intercept -2.44 0.65 -3.78 1.57E-04 Spilosoma virginica Area 0.37 0.27 1.34 0.18 Intercept -2.80 0.75 -3.74 1.81E-04 Spodoptera ornithogalli Area -0.26 0.16 -1.61 0.11 Intercept -2.66 0.79 -3.37 7.58E-04 Trichodezia albovittata Area 0.97 0.23 4.14 3.53E-05 Intercept -2.74 0.72 -3.82 1.34E-04 Tricholita signata Area 0.06 0.31 0.19 0.85 Intercept -2.32 0.58 -4.01 6.07E-05 Xestia dolosa Area 0.10 0.26 0.38 0.70 Intercept -2.39 0.62 -3.88 1.04E-04 Xestia normanianus Area -0.21 0.15 -1.44 0.15 Intercept -2.94 0.82 -3.60 3.16E-04 Yponomeuta multipunctella Area -0.14 0.24 -0.59 0.56 Intercept -2.85 0.79 -3.60 3.18E-04 Zale horrida Area 0.37 0.34 1.09 0.27

Table 4-4. The results of individual moth species GLMs when tree species richness on each island (Tree S) was added as a predictor. Moth species with known tree host plants and adequate captures on islands were analyzed using log(area) (Area) and tree species richness. Host tree plant richness was not a significant (bold) predictor of moth abundance for most species.

Moth Taxon

Species Parameter Estimate Std Dev T value P-value

Intercept -2.14 1.16 -1.85 0.06 Acronicta grisea Area 0.34 0.41 0.82 0.41 Tree S 0.02 0.11 0.20 0.84 Intercept -3.36 1.04 -3.24 1.22E-03 Cabera erythemaria Area -0.28 0.21 -1.34 0.18 Tree S 0.18 0.07 2.51 0.01 Intercept -3.00 0.88 -3.40 6.86E-04 Cabera variolaria Area -0.02 0.26 -0.09 0.93 Tree S 0.17 0.07 2.60 0.01 Intercept -3.53 1.38 -2.55 0.01 Callosamia promethea Area -0.35 0.21 -1.66 0.10 Tree S 0.12 0.11 1.11 0.27 Intercept -0.65 0.63 -1.03 0.30 Catocala ultronia Area 2.76 0.33 8.43 3.47E-17 Tree S -0.30 0.04 -7.28 3.46E-13 Intercept 0.00 1.62 0.00 1.00 Datana drexelii Area 0.75 0.70 1.06 0.29 Tree S -0.28 0.22 -1.28 0.20 Intercept -4.13 1.86 -2.21 0.03 Dryocampa rubicunda Area -0.37 0.28 -1.35 0.18 Tree S 0.12 0.15 0.79 0.43 Intercept -5.28 1.87 -2.82 4.75E-03 Euchlaena irraria Area -0.41 0.33 -1.26 0.21 Tree S 0.25 0.12 2.14 0.03 Intercept -7.34 2.79 -2.63 0.01 Euclea delphinii Area -0.63 0.42 -1.50 0.13 Tree S 0.37 0.16 2.29 0.02 Intercept -2.33 1.03 -2.26 0.02 Heterocampa guttivitta Area 0.00 0.28 -0.01 0.99 Tree S 0.08 0.08 0.95 0.34 Intercept -0.39 1.05 -0.37 0.71 Heterophleps triguttaria Area 0.73 0.42 1.73 0.08 Tree S -0.14 0.12 -1.15 0.25 Intercept -0.42 1.15 -0.37 0.71 Macrurocampa marthesia Area 0.52 0.44 1.16 0.25

Tree S -0.15 0.14 -1.09 0.27 Intercept -4.05 1.46 -2.77 0.01 Malacosoma americana Area -0.38 0.23 -1.65 0.10 Tree S 0.17 0.10 1.66 0.10 Intercept -0.11 1.75 -0.06 0.95 Melanolophia signataria Area 1.35 0.78 1.72 0.09 Tree S -0.29 0.24 -1.23 0.22 Intercept -1.10 0.64 -1.71 0.09 Nadata gibbosa Area 0.80 0.29 2.76 0.01 Tree S -0.03 0.06 -0.47 0.64 Intercept -2.44 1.20 -2.03 0.04 Notodonta torva Area 1.39 0.65 2.13 0.03 Tree S -0.10 0.11 -0.93 0.35 Intercept -2.92 2.05 -1.42 0.15 Olethreutes glaciana Area 0.34 0.73 0.47 0.64 Tree S -0.01 0.20 -0.05 0.96 Intercept -3.04 1.15 -2.64 0.01 Olethreutes quadrifidum Area 0.16 0.38 0.42 0.67 Tree S 0.11 0.09 1.22 0.22 Intercept -5.35 1.69 -3.16 1.58E-03 Paonias excaecatus Area -0.19 0.44 -0.42 0.68 Tree S 0.27 0.12 2.33 0.02 Intercept -2.85 1.27 -2.25 0.02 Parallelia bistriaris Area 1.68 0.72 2.33 0.02 Tree S -0.12 0.10 -1.12 0.26 Intercept -4.45 1.73 -2.57 0.01 Polygrammate hebraeicum Area -0.44 0.25 -1.77 0.08 Tree S 0.17 0.12 1.41 0.16 Intercept -5.36 2.29 -2.34 0.02 Prolimacodes badia Area -0.47 0.34 -1.39 0.16 Tree S 0.21 0.15 1.40 0.16 Intercept -3.49 1.75 -1.99 0.05 Xestia normanianus Area -0.28 0.28 -0.98 0.33 Tree S 0.05 0.16 0.32 0.75 Intercept -4.32 1.67 -2.58 0.01 Zale horrida Area -0.21 0.38 -0.56 0.58 Tree S 0.18 0.12 1.56 0.12

When evaluating the impacts of unoccupied islands using the full set of islands versus

using a subset of only occupied islands, we found that removing unoccupied islands reduced the

estimated DAR slope. For mammals, this was especially true for Blarina brevicauda

(B=0.459±0.135 to B=0.038±0.069) and Procyon lotor (B=0.254±0.092 to B=0.084±0.085) while Peromyscus leucopus and Tamias striatus also had decreases in estimated slopes but to a lesser degree (B=0.504±0.051 to B=0.303±0.092; B=0.659±0.052 to B=0.380±0.158). Despite the decrease in DAR slope estimates, they were still significantly different than a constant slope of 1 when analyzing occupied-only islands, indicating that unoccupied small islands are not the sole driver behind the patterns. For trees, the density pattern for Acer saccharinum, Fraxinus americana, and Nyssa sylvatica was heavily influenced by the effect of unoccupied small islands. When these islands were removed from analysis, the DAR slope became negative indicating that when the species is present, it is both more abundant and dense on smaller islands than larger islands. Similarly, 16 moth species changed the sign of their DAR slopes with 11 species having higher density and abundance on smaller islands when present.

DISCUSSION Our study confirms the findings of previous studies that the DAR is variable across

species and taxa (Bowers and Matter 1997, Bender et al. 1998, Connor et al. 2000, Matter 2000).

Most species in this study violated the assumption of constant density assumed by

metapopulation theory. Failing to incorporate the slope of the DAR can result in both over and

under estimation of extinction risk on islands.

In this system, smaller islands would generally have lower extinction risk and larger

islands higher extinction risk than would be assumed under constant density. Inaccurate

extinction risk estimates can result in poor management decisions and alter the priority for

applied species conservation. For instance, in the Pymatuning system not incorporating estimates

of density would lead to an overvaluation of the conservation value of large islands and an

undervaluation of small islands. Original estimates for extinction risk would also not have

factored in the higher abundance and densities found on smaller islands for species like Salix

niger and Malacosoma americanum. When feasible, determining the relationship between density and area should be applied to estimates of metapopulation extinction risk.

While we used the data collected at Pymatuning reservoir to illustrate the importance of incorporating variable DAR into metapopulation estimates of extinction risk, we do not assume that metapopulation dynamics are indeed taking place in this system. There is evidence that certain species can be structured according to metapopulation dynamics (Harrison and Taylor

1997) but that can only be confirmed after extensive evaluations. It appears that in our system the mammal, tree, and moth communities (Chapter 3 pg.37), as well as song bird community

(Coleman et al. 1982) are structured according to the random placement of species rather than being described by metapopulation dynamics. However, the driving forces behind the occurrence and abundance of individual species has not yet been studied. We acknowledge that metapopulation dynamics may not be the main driver for abundance patterns.

While previous studies found that density increases with increasing area for insects and to a lesser degree, mammals (Bowers and Matter 1997, Connor et al. 2000), no species in this study showed increasing density with increasing island area. Negative DAR have been found in mammals (Wilder and Meikle 2005) and at small spatial scales (Bowers and Matter 1997). It is suspected that species exhibiting negative DAR may be able to utilize non-suitable habitat or have higher reproductive rates in edge habitat (Foster and Gaines 1991, Wilder and Meikle

2005). Insect taxa have been found to have strong correlations between density and area (Bender

et al. 1998, Connor et al. 2000); other research indicates individual insect species may follow

more variable responses (Kareiva 1983). We found high variability in the magnitude of species

responses in the moth taxon which may be related to higher numbers of species included in the

taxon. We found that abundance for the majority of moth species was not described well by

either island area or tree species richness as a surrogate for habitat heterogeneity. Out of the 27

candidate species, the abundance of only 6 species were predicted by tree species richness;

Cabera erythemaria, Cabera variolaria, Catocala ultronia, Euchlaena irraria, Euclea delphinii,

and Paonias excaecalus (Table 4). Since we were unable to determine a predominant driving

force for moth abundance, we conclude that the moth DAR may be driven by the combination of

hypotheses as proposed by Matter (1999).

The negative DAR slope for Salix nigra indicates higher densities and abundance on

small habitat patches which may be a response to higher availability of resources. This species

requires high light levels and water availability which are in greater abundance on smaller habitat

patches (McLeod et al. 1986). This species was often found on the periphery of islands and

smaller islands have a higher proportion of edge habitat to area, further supporting the

importance of small habitat patches in this system. The pattern matches two hypotheses, the

resources availability hypothesis as well as the sampling hypothesis, whereas sampling increases

the amount of unsuitable habitat increases (Smallwood and Schonewald 1996, Gaston et al.

1999, Gaston and Matter 2002).

While the metapopulation model requires few measured variables for input (Hanski

1994b), imperiled species often have limited available data that upon which to base conservation measures (Drechsler et al. 2003). Estimates of abundance across a system in multiple habitat patches can be difficult to achieve and occurrence data is often the only available information

(Gotelli and Colwell 2001, Brooks et al. 2004). However, the results of our research illustrate the importance of incorporating variable DAR into metapopulation estimates of extinction risk when feasible and determining the relationship between density and area should be applied to future estimates of metapopulation extinction risk.

5. Conclusions The simulations in Chapter 2 highlighted the conditions where the community-level metapopulation, neutral, and null models excelled or failed at describing data generated following their own model assumptions. The range of variables where the models could accurately describe data derived under their respective conditions was limited and investigators wanting to parse process from pattern may not be able to for a wide variety of taxa and systems.

Somewhat surprisingly, the two unified mechanistic models had varying levels of success

and the neutral model often did not exceed the descriptive ability of competing models, despite

not varying greatly from the null. While the neutral model has been proposed as a null model in

which to compare individual versus species differences or test for niches or mechanisms that

may account for the patterns observed in data (Rosindell et al. 2011, Rosindell et al. 2012), the

neutral model is not a traditional null model containing no assumed mechanisms and constrained

by observable data (Gotelli and Graves 1996, Gotelli and Ellison 2002, Gotelli and McGill

2006). The results of this simulation, even though there was a narrow set of conditions where the

null model was ranked “best”, suggest against using the neutral model as a baseline null model at

least in the context of community investigations occurring over ecological timescales. Even

when the assumption of neutrality was built into the simulation, our null model based on

Williams (1995) extreme value function was better able to repeatedly describe the data in a wider range of simulated system structures. Part of this may be due to the EVF null model’s success at describing sparse data (few species, few islands) for null and neutrally-derived datasets. Since

the neutral model should have been able to rank higher when describing data constructed

following neutral assumptions it may not work as a reliable baseline model.

While the assumed mechanisms in the simulations for each theory were explicitly

incorporated, model selection did not always match the assumptions. This indicates that the

mechanisms in a system are not as important in determining community structure as the basic

abiotic and biotic structure of the system. Care must be taken when ranking empirical data since

it may not necessarily reflect the true mechanisms that are actually occurring or the mechanisms

may not be the main driving force in determining species richness in all circumstances. Patterns

observed in nature can be generated by multiple processes (Cale et al. 1989).

The patterns of species richness found at Pymatuning reservoir for small mammals, trees,

and moths were described by the community-level metapopulation and EVF null models equivalently. This may be because the communities there are not structured solely by metapopulation dynamics. The inherently sparse set of explanatory variables found in mechanistic models may not be capturing the important drivers in the Pymatuning system. As seen for the moth taxon in Chapter 3, alternative theories like the diversity of habitat can be incorporated to improve model descriptive ability. This result indicates that the base unified mechanistic models may have utility for describing species richness patterns, but may be less mechanistic than assumed (Kalmykov and Kalmykov 2012).

The lack of evidence for metapopulation dynamics driving community structure does not preclude there being individual species in Pymatuning reservoir who are influenced by population dynamics. Previous studies have found evidence that metapopulation dynamics structure individual species (Eriksson 1996, Harrison and Taylor 1997, Wright et al. 2006).

Different functional taxa may also be more susceptible to metapopulation dynamics, especially

when comprised of species that are susceptible to extinction events and are limited in dispersal

ability. Shrew species (Soricomorpha: Soricidae) have previously been used to study metapopulation dynamics (Hanski 1986, Peltonen and Hanski 1991, Hanski 1994a; 1998a) and

may be a better focal taxon in future studies than all small mammals. The methods for small

mammal capture in this study did not maximize effort for the capture of the smaller-bodied shrew species belonging to the genus Sorex. Only the large-bodied Blarina brevicauda was found on islands and only two Sorex species, S. cinereus and S. fumeus, were found in low occurrence on the mainland.

The limited descriptive ability of the community-level metapopulation model may also be due to a violation of model assumptions. As demonstrated in Chapter 4, the majority of species in all three taxa at Pymatuning reservoir had density-area relationships that were significantly different than the assumed constant. Variability in the density-area relationship has the potential to vastly change the expected presence and absence of individual species. Future studies wanting to apply metapopulation dynamic models should first test for variability of species’ densities in the system. Additionally, incorporating this variability in the community structuring of the simulation discussed in Chapter 2 may change the appropriate range of testing conditions or may alter model descriptive capabilities.

These studies demonstrated that there is little utility in the community-level metapopulation model beyond its null-like assumptions when trying to understand what structures ecological communities. The ability to simply and accurately describe and predict species richness would be beneficial to conservation applications. Mechanistic hypotheses attempting to explain patterns in the distribution and abundance of species can further be developed for this purpose. Accounting for basic system structure and assumption violations are steps towards a useful unified theory for community ecology.

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