EcoSim: Null Models Software for Ecologists

EcoSim: Null Models Software for Ecologists Nicholas J. Gotelli Department of Biology University of Vermont Burlington, VT USA

Limitations of Ecological Data • Non-normality • Small sample sizes • Non-independence

Null Model Analysis • Monte Carlo simulation of ecological data • Generates patterns expected in the absence of a mechanism • Allows for statistical tests of patterns • Wide applicability to community data

Steps in Null Model Analysis • Define community metric X • Calculate Xobs for observed data • Randomize data subject to constraints • Calculate Xsim for randomized data • Repeat 1000 randomizations • Compare Xobs to histogram of Xsim • Measure P(Xobs£ Xsim)

Niche Overlap Data

Quantify Pattern as a single metric Average pairwise niche overlap = 0.17

Randomize Overlap Data

Null Assemblage

Niche Overlap of A Single Null Community

Histogram of Niche Overlaps from Null Communities

Statistical Comparison with Observed Niche Overlap • Observed = 0.17

Features of Null Models • Distinction between pattern/process • Possibility of no effect • Principle of parsimony • Principle of falsification • Potential importance of stochastic mechanisms

Criticisms of Null Models • Ecological hypotheses cannot be stated in a way for formal proof/disproof • Interactions between factors may confound null model tests • Understanding only increased when null hypothesis is rejected • Using same data to build and test model is circular

Controversy over Null Model Analysis • Early studies challenged conventional examples • Philosophical debate over falsification • Statistical debate over null model construction • Lack of powerful software

EcoSim Software • Programmed in Delphi • Object-oriented design • Graphical user interface • Optimized for Windows • Supported by NSF • Created by Acquired Intelligence, Inc.

Analysis of MacArthur’s (1958) warblers • 5 coexisting species of warblers in NE forests • Insectivores • Similar body sizes, diets • Paradox for classical niche theory • How could all species co-occur?

MacArthur’s resolution

Spatial niche segregation 2 6 25 25 25 25 25 49 18 Cape May warbler Myrtle warbler

How much niche overlap of MacArthur’s warblers would be expected in the absence of species interactions?

Guided Tour of EcoSim

Diamond’s (1975) Assembly Rules • Not all species combinations found in nature • Those that are not found are “forbidden” • Competition and niche adjustment lead to a small number of stable species combinations

Connor and Simberloff’s (1979) challenge • Assembly rules are tautologies • How much coexistence would be expected in the absence of competition • Construction of a null model to test community patterns

Presence-Absence Matrix

Connor and Simberloff’s (1979) null model • Species by site co-occurrence matrix • Create random matrices that maintain row totals (= species occurrences) and column totals (= number of species per site)

Criticisms of C&S null model • Competitive effects “smuggled in” with row and column totals • Cannot detect certain checkerboard distributions • Constraints guarantee that simulated matrices are very similar to observed matrices

Co-occurrence Analysis with EcoSim

Evaluating Co-occurrence Algorithms • Type I error (incorrectly rejecting null) • Type II error (incorrectly accepting null)

Evaluating Type I Error • Use null model tests on “random matrices” • A well-behaved model should reject the null hypothesis 5% of the time

Evaluating Type II Error • Begin with perfectly “structured” data set • Add increasing amounts of random noise • Determine how much noise the test can tolerate and still detect non-randomness

Type II Error P-value Ideal Curve 0.05 Type I Error % Noise Added

Summary of Error Analyses • Best algorithm depends on co-occurrence index • Maintaining row totals (= species occurrences) necessary to control Type I error • Modified version of C&S (fixed,fixed) has low Type I, Type II errors for C-score

Meta-analyses of co-occurrence • 98 presence-absence matrices from literature • analyzed for # of checkerboards, # combinations, C-score • standardized effect size using fixed,fixed null model

Results • Larger C-score than expected by chance • More checkerboard species pairs than expected by chance • Fewer species combinations than expected by chance

Conclusions • Published presence-absence matrices are highly non-random • Patterns match the predictions of Diamond’s assembly rules model! • Consistent with small-scale experimental studies demonstrating importance of species interactions

Causes of Non-random Co-occurrence Patterns • Negative species interactions • Habitat checkerboards • Historical, evolutionary processes

Statistical covariates of effect size • Number of species in matrix • Number of sites in matrix • % fill of matrix

Biological correlates of effect size • Area (patch, geographic extent) • Insularity (island, mainland) • Biogeographic Province (Nearctic, Palearctic) • Latitude, Longitude • Taxonomic group (plants, mammals, birds)

Ectoparasites of marine fishes Gotelli & Rohde 2002

Conclusion • Homeotherm matrices highly structured • Poikilotherm matrices random co-occurrence • Ants, plant matrices highly structured • Energetic constraints may affect community co-occurrence patterns

Conclusions • Null models are useful tools for analyses of community structure • Species co-occurrence in published matrices is less than expected by chance • Patterns match the predictions of Diamond’s (1975) assembly rules model • Co-occurrence patterns differ for homeotherm vs. poikilotherm matrices • EcoSim software available for analysis

EcoSim Website http://homepages.together.net/~gentsmin/ecosim.htm

EcoSim: Null Models Software for Ecologists