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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


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 expected in the absence of species interactions?


Diamond s 1975 assembly rules
Diamond’s (1975) Assembly Rules expected in the absence of species interactions?

  • 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 expected in the absence of species interactions?

  • 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 expected in the absence of species interactions?


Connor and simberloff s 1979 null model
Connor and Simberloff’s (1979) null model expected in the absence of species interactions?

  • 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 expected in the absence of species interactions?

  • 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 expected in the absence of species interactions?


Evaluating co occurrence algorithms
Evaluating Co-occurrence Algorithms expected in the absence of species interactions?

  • Type I error (incorrectly rejecting null)

  • Type II error (incorrectly accepting null)


Evaluating type i error
Evaluating Type I Error expected in the absence of species interactions?

  • 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 expected in the absence of species interactions?

  • 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 expected in the absence of species interactions?

P-value

Ideal Curve

0.05

Type I Error

% Noise Added


Summary of error analyses
Summary of Error Analyses expected in the absence of species interactions?

  • 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 expected in the absence of species interactions?

  • 98 presence-absence matrices from literature

  • analyzed for # of checkerboards, # combinations, C-score

  • standardized effect size using fixed,fixed null model


Results
Results expected in the absence of species interactions?

  • Larger C-score than expected by chance

  • More checkerboard species pairs than expected by chance

  • Fewer species combinations than expected by chance


Conclusions
Conclusions expected in the absence of species interactions?

  • 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 expected in the absence of species interactions?

  • Negative species interactions

  • Habitat checkerboards

  • Historical, evolutionary processes


Statistical covariates of effect size
Statistical covariates of effect size expected in the absence of species interactions?

  • Number of species in matrix

  • Number of sites in matrix

  • % fill of matrix


Statistical covariates of effect size1
Statistical covariates of effect size expected in the absence of species interactions?

  • Number of species in matrix

  • Number of sites in matrix

  • % fill of matrix


Biological correlates of effect size
Biological correlates of effect size expected in the absence of species interactions?

  • 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 expected in the absence of species interactions?

  • Area (patch, geographic extent)

  • Insularity (island, mainland)

  • Biogeographic Province (Nearctic, Palearctic)

  • Latitude, Longitude

  • Taxonomic group (plants, mammals, birds)


Ectoparasites of marine fishes expected in the absence of species interactions?Gotelli & Rohde 2002


Conclusion
Conclusion expected in the absence of species interactions?

  • Homeotherm matrices highly structured

  • Poikilotherm matrices random co-occurrence

  • Ants, plant matrices highly structured

  • Energetic constraints may affect community co-occurrence patterns


Conclusions1
Conclusions expected in the absence of species interactions?

  • 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 expected in the absence of species interactions?

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


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