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 X obs for observed data Randomize data subject to constraints Calculate X sim for randomized data Repeat 1000 randomizations Compare X obs to histogram of X sim Measure P(X obs  X sim )

Niche Overlap Data SpeciesForest Canopy Leaf Litter Ground Nesting Old Field UrbanWetland Solenopsis invicta Camponotus floridanus Crematogaster punctulata Tapinoma sessile

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

Randomize Overlap Data SpeciesForest Canopy Leaf Litter Ground Nesting Old Field UrbanWetland Solenopsis invicta Camponotus floridanus Crematogaster punctulata Tapinoma sessile

Null Assemblage SpeciesForest Canopy Leaf Litter Ground Nesting Old Field UrbanWetland Solenopsis invicta Camponotus floridanus Crematogaster punctulata Tapinoma sessile

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 Cape May warblerMyrtle 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

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

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

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)

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

Plant AssemblageSitesSource Flowering plantsVacant Chicago lotsCrowe (1979) Subcanopy plantsMahogany woodlots of BarbadosWatts (1978) Vascular plantsBaja IslandsCody et al. (1983) Vascular plantsGreater, Lesser AntillesBeard (1948) Vascular plantsOceanic Islands, Gulf of GuineaExell (1944) Genus PeleaHawaiian IslandsStone (1969) Vascular plantsOceanic islets near Perth, AustraliaAbbott & Black (1980) Mangrove forestsGreat Barrier Reef, AustraliaStoddart (1980) Trees (Dry Zone)Greater, Lesser AntillesBeard (1948) Trees (Montane)Greater, Lesser AntillesBeard (1948) Trees (Tropical Forest)Greater, Lesser AntillesBeard (1948) Trees (Swamps)Greater, Lesser AntillesBeard (1948) TreesWoodlot fragments, OntarioWeaver & Kellman (1981)

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