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

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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

Limitations of Ecological Data

  • Non-normality

  • Small sample sizes

  • Non-independence


Null model analysis

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

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

Niche Overlap Data


Quantify pattern as a single metric

Quantify Pattern as a single metric

Average pairwise niche overlap = 0.17


Randomize overlap data

Randomize Overlap Data


Null assemblage

Null Assemblage


Niche overlap of a single null community

Niche Overlap of A Single Null Community


Histogram of niche overlaps from null communities

Histogram of Niche Overlaps from Null Communities


Statistical comparison with observed niche overlap

Statistical Comparison with Observed Niche Overlap

  • Observed = 0.17


Features of null models

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

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

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

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

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

MacArthur’s resolution


Spatial niche segregation

Spatial niche segregation

2

6

25

25

25

25

25

49

18

Cape May warbler

Myrtle warbler


Ecosim null models software for ecologists

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


Guided tour of ecosim

Guided Tour of EcoSim


Diamond s 1975 assembly rules

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

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

Presence-Absence Matrix


Connor and simberloff s 1979 null model

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

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

Co-occurrence Analysis with EcoSim


Evaluating co occurrence algorithms

Evaluating Co-occurrence Algorithms

  • Type I error (incorrectly rejecting null)

  • Type II error (incorrectly accepting null)


Evaluating type i error

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

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


Ecosim null models software for ecologists

Type II Error

P-value

Ideal Curve

0.05

Type I Error

% Noise Added


Summary of error analyses

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

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

Results

  • Larger C-score than expected by chance

  • More checkerboard species pairs than expected by chance

  • Fewer species combinations than expected by chance


Conclusions

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

Causes of Non-random Co-occurrence Patterns

  • Negative species interactions

  • Habitat checkerboards

  • Historical, evolutionary processes


Statistical covariates of effect size

Statistical covariates of effect size

  • Number of species in matrix

  • Number of sites in matrix

  • % fill of matrix


Statistical covariates of effect size1

Statistical covariates of effect size

  • Number of species in matrix

  • Number of sites in matrix

  • % fill of matrix


Biological correlates of effect size

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 size1

Biological correlates of effect size

  • Area (patch, geographic extent)

  • Insularity (island, mainland)

  • Biogeographic Province (Nearctic, Palearctic)

  • Latitude, Longitude

  • Taxonomic group (plants, mammals, birds)


Ecosim null models software for ecologists

Ectoparasites of marine fishes Gotelli & Rohde 2002


Conclusion

Conclusion

  • Homeotherm matrices highly structured

  • Poikilotherm matrices random co-occurrence

  • Ants, plant matrices highly structured

  • Energetic constraints may affect community co-occurrence patterns


Conclusions1

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

EcoSim Website

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


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