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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)


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


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


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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