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

2. Limitations of Ecological Data Non-normality Small sample sizes Non-independence

3. 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

4. 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 )

5. Niche Overlap Data SpeciesForest Canopy Leaf Litter Ground Nesting Old Field UrbanWetland Solenopsis invicta 0.300.220.00 0.440.04 Camponotus floridanus 0.25 0.300.200.00 Crematogaster punctulata 0.980.020.00 Tapinoma sessile 0.000.070.500.110.220.10

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

7. Randomize Overlap Data SpeciesForest Canopy Leaf Litter Ground Nesting Old Field UrbanWetland Solenopsis invicta 0.300.220.00 0.440.04 Camponotus floridanus 0.25 0.300.200.00 Crematogaster punctulata 0.980.020.00 Tapinoma sessile 0.000.070.500.110.220.10

8. Null Assemblage SpeciesForest Canopy Leaf Litter Ground Nesting Old Field UrbanWetland Solenopsis invicta 0.000.220.300.040.000.44 Camponotus floridanus 0.00 0.200.25 0.30 Crematogaster punctulata 0.00 0.980.00 0.02 Tapinoma sessile 0.100.220.110.500.070.00

9. Niche Overlap of A Single Null Community

10. Histogram of Niche Overlaps from Null Communities

11. Statistical Comparison with Observed Niche Overlap Observed = 0.17

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

13. 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

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

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

16. 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?

17. MacArthur’s resolution

18. Spatial niche segregation 25 6 2 1849 25 Cape May warblerMyrtle warbler

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

20. Guided Tour of EcoSim

21. 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

22. 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

23. Presence-Absence Matrix

24. 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)

25. 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

26. Co-occurrence Analysis with EcoSim

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

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

29. 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

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

31. 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

32. 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

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

37. 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

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

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

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

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

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

45. Ectoparasites of marine fishes Gotelli & Rohde 2002

46. 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)

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

48. 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

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