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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

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## EcoSim: Null Models Software for Ecologists

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

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