Transcript 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
• 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
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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
Species
Forest
Canopy
Leaf
Litter
Ground
Nesting
Old
Field
Urban
Wetland
Solenopsis
invicta
0.30
0.22
0.00
0.00
0.44
0.04
Camponotus
floridanus
0.25
0.25
0.30
0.20
0.00
0.00
Crematogaster
punctulata
0.98
0.02
0.00
0.00
0.00
0.00
Tapinoma
sessile
0.00
0.07
0.50
0.11
0.22
0.10
Quantify Pattern as a single
metric
Average pairwise niche
overlap = 0.17
Randomize Overlap Data
Species
Forest
Canopy
Leaf
Litter
Ground
Nesting
Old
Field
Urban
Wetland
Solenopsis
invicta
0.30
0.22
0.00
0.00
0.44
0.04
Camponotus
floridanus
0.25
0.25
0.30
0.20
0.00
0.00
Crematogaster
punctulata
0.98
0.02
0.00
0.00
0.00
0.00
Tapinoma
sessile
0.00
0.07
0.50
0.11
0.22
0.10
Null Assemblage
Species
Forest
Canopy
Leaf
Litter
Ground
Nesting
Old
Field
Urban
Wetland
Solenopsis
invicta
0.00
0.22
0.30
0.04
0.00
0.44
Camponotus
floridanus
0.00
0.00
0.20
0.25
0.25
0.30
Crematogaster
punctulata
0.00
0.00
0.98
0.00
0.00
0.02
Tapinoma
sessile
0.10
0.22
0.11
0.50
0.07
0.00
Niche Overlap of A Single
Null Community
10
Frequency
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4
2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Niche Overlap
0.7
0.8
0.9
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Histogram of Niche Overlaps
from Null Communities
300
Frequency
250
200
150
100
50
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Niche Overlap
0.7
0.8
0.9
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Statistical Comparison with
Observed Niche Overlap
300
Frequency
250
200
150 •
100
Observed =
0.17
50
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Niche Overlap
0.7
0.8
0.9
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Features of Null Models
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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
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Early studies challenged conventional examples
Philosophical debate over falsification
Statistical debate over null model construction
Lack of powerful software
EcoSim Software
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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
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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
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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
SPECIES
Solenopsis wagneri
Camponotus chromaoides
Lasius neoniger
Myrmica fracticornis
SITE
1F 2F 3F 4F 5F 6F
1 1 1 0 1 1
0 0 0 1 0 0
1 1 0 1 1 0
0 0 1 0 0 1
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 cooccurrence
• 98 presence-absence matrices from literature
• analyzed for # of checkerboards, # combinations,
C-score
• standardized effect size using fixed,fixed null
model
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C-SCORE
20
15
10
5
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-10
-5
0
Standardized Effect Size
5
10
40
CHECKERBOARD
PAIRS
30
20
10
0
-10
-5
0
5
STANDARDIZED EFFECT SIZE
10
75
NUMBER OF
SPECIES
COMBINATIONS
60
45
30
15
0
-10
-5
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5
Standardized effect size
10
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 Cooccurrence Patterns
• Negative species interactions
• Habitat checkerboards
• Historical, evolutionary processes
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C-SCORE
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Standardized Effect Size
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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
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Area (patch, geographic extent)
Insularity (island, mainland)
Biogeographic Province (Nearctic, Palearctic)
Latitude, Longitude
Taxonomic group (plants, mammals, birds)
Biological correlates of effect
size
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Area (patch, geographic extent)
Insularity (island, mainland)
Biogeographic Province (Nearctic, Palearctic)
Latitude, Longitude
Taxonomic group (plants, mammals, birds)
Standardized effect size
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Standardized effect size
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Ectoparasites of
marine fishes
Gotelli & Rohde 2002
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Plant Assemblage
Sites
Source
Flowering plants
Vacant Chicago lots
Crowe (1979)
Subcanopy plants
Mahogany woodlots of Barbados
Watts (1978)
Vascular plants
Baja Islands
Cody et al. (1983)
Vascular plants
Greater, Lesser Antilles
Beard (1948)
Vascular plants
Oceanic Islands, Gulf of Guinea
Exell (1944)
Genus Pelea
Hawaiian Islands
Stone (1969)
Vascular plants
Oceanic islets near Perth, Australia
Abbott & Black (1980)
Mangrove forests
Great Barrier Reef, Australia
Stoddart (1980)
Trees (Dry Zone)
Greater, Lesser Antilles
Beard (1948)
Trees (Montane)
Greater, Lesser Antilles
Beard (1948)
Trees (Tropical Forest)
Greater, Lesser Antilles
Beard (1948)
Trees (Swamps)
Greater, Lesser Antilles
Beard (1948)
Trees
Woodlot fragments, Ontario
Weaver & Kellman (1981)
Conclusion
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Homeotherm matrices highly structured
Poikilotherm matrices random co-occurrence
Ants, plant matrices highly structured
Energetic constraints may affect community cooccurrence 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