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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)
quantify pattern as a single metric

Quantify Pattern as a single metric

Average pairwise niche overlap = 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?
spatial niche segregation
Spatial niche segregation

2

6

25

25

25

25

25

49

18

Cape May warbler

Myrtle warbler

slide19
How much niche overlap of MacArthur’s warblers would be expected in the absence of species interactions?
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
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
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
slide30
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)
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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