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The Past, Present, and Future of Null Model Analysis in Biogeography
Nicholas J. GotelliDepartment of BiologyUniversity of Vermont
Burlington VT 05405 USA
“The past is never dead. It's not even past”
William Faulkner 1950 Requiem For A Nun
“Data! Data! Data!” he cried impatiently. “I can't make bricks without clay”.
Sherlock Holmes, The Adventure Of The Copper Breeches Sir Arthur Conan Doyle 1892
What Is A Null Model?“A null model is a pattern-generating model thatIs based on randomization of ecological data or
random sampling from a known or imagineddistribution...The randomization is designed to
produce a pattern that would he expected in theabsence of a particular ecological mechanism.”
Gotelli & Graves (1996)
Steps In Null Model Analysis
Define metric X Measure Xobs for empirical data Randomize data, subject to constraints (H0) Calculate Xsim for simulated data Repeat simulation many times (n = 1000) Estimate p(Xobs | H0) Make inferences & draw conclusions
MacArthur's (1958) Warblers:
Segregation of foraging microhabitats allows for species coexistence.
More overlap than expected by chance!!
The Origins Of Null Model Analysis
Diamond (1975)
Community assembly rules (checkerboard distributions, incidence functions, forbidden
species combinations)
Connor & Simberloff (1979)
What patterns would be expected in the absence of competition? (null model randomizations,
probability tests)
Species/Genus Ratios
Elton (1946): low S/G ratios on islands reflect reduced resources, increased competition among species within a genus
Williams (1947): low S/G ratios are expected based on random sampling – a property of numbers, not of biology
Hairston (1964): S/G ratios might increase because related species have common habitat requirements & dispersal characteristics
Deeper Roots...
Maillefier (1929) G/S ratios tested with draws from a deck of marked cards. Ordered vs. randomized
diversity accumulation curves
Null Models As A Benchmark
Simberloff (1970) S/G ratios on islands were actually larger than expected by chance
“The past is never dead. It's not even past”
William Faulkner 1950 Requiem For A Nun
The past is never dead...
Community phylogenetics, habitat filtering, niche differentiation
Technical Criticisms Of Null Models “Not truly null with respect to processes”
(“Narcissus Effect” and other smuggled processes) “Drowns the baby in a tub too deep”
(= “Dilution Effect”) “Not a mechanistic stochastic model”
(contra neutral model, HW Equilibrium) “Circular to use same data for hypothesis
testing and creating null distributions” (standard to condition on marginal variables, as in
contingency table analysis)
Philosophical Criticisms Of Null Models
“Ecological / biogeographic theory does not generate simple predictions” (perhaps a problem with the theory!!)
“Results depend on the particular null model” (we certainly hope so!)
“Multiple processes are in operation” (test a suite of null models)
“Difficult to program” (perhaps ultimately a feature not a flaw)
Features Of Null Models
Clarity of Assumptions Tailored to Available Data (= ease of parameter
estimation) Hypothesis Testing Framework Parsimony
It is interesting to contemplatea tangled bank,
clothed with many plantsof many kinds...
TangledBank
Fever!!
A Bivariate Map of Models
Statistical Mechanistic
Simple
Complex
A Bivariate Map of Models
Statistical Mechanistic
Simple
Complex
t-test
A Bivariate Map of Models
Statistical Mechanistic
Simple
Complex
t-test
Hierarchical Model
A Bivariate Map of Models
Statistical Mechanistic
Simple
Complex
t-testNeutralModel
Hierarchical Model
A Bivariate Map of Models
Statistical Mechanistic
Simple
Complex
t-testNeutralModel
Hierarchical Model
CommunityMatrix
A Bivariate Map of Models
Statistical Mechanistic
Simple
Complex
t-testNeutralModel
Hierarchical Model
CommunityMatrix
NULL MODELS
A Bivariate Map of Models
Statistical Mechanistic
Simple
Complex
t-testNeutralModel
Hierarchical Model
CommunityMatrix
NULL MODELS
RANDOMIZATIONTESTS
A Bivariate Map of Models
Statistical Mechanistic
Simple
Complex
t-testNeutralModel
Hierarchical Model
CommunityMatrix
NULL MODELS
MID-DOMAIN EFFECT
RANDOMIZATIONTESTS
A Bivariate Map of Models
Statistical Mechanistic
Simple
Complex
t-testNeutralModel
Hierarchical Model
CommunityMatrix
NULL MODELS
MID-DOMAIN EFFECT
COMMUNITY PHYLOGENETICS &
TRAIT ANALYSES
RANDOMIZATIONTESTS
A Bivariate Map of Models
Statistical Mechanistic
Simple
Complex
t-testNeutralModel
Hierarchical Model
CommunityMatrix
NULL MODELS
MID-DOMAIN EFFECT
COMMUNITY PHYLOGENETICS &
TRAIT ANALYSES
CO-OCCURENCEANALYSIS
RANDOMIZATIONTESTS
Prevedello et al., in review
Current Challenges in Null Model Analysis
Choosing a null model algorithm
“Isotropic” Null Model
“Fixed-Fixed” Null Model
Current Challenges in Null Model Analysis
Choosing a null model algorithm Matrix-wide versus pairwise metrics
Null Model Analyses of Segregated and Aggregated Species Pairs
Gotelli & Ulrich (2010)
Current Challenges in Null Model Analysis
Choosing a null model algorithm Matrix-wide versus pairwise metrics Benchmark testing BEFORE empirical analysis
and publication
Benchmark Testing
Type I error (incorrectly rejecting a true null hypothesis)
Feed the test a series of “random” matrices Incorporate heterogeneity in row and
column totals (~ beta distribution) Type II error (incorrectly accepting a false null hypothesis)
“Progressive noise test”: adding random noise to a structured matrix
“Embedded structure test”: adding a structured sub-matrix to a random matrix
Future Challenges In Null Model Analysis
Future Challenges
Big Data The more data, the smaller the p value AIC, likelihood not a solution
GUIs and the failure of imagination Efficient and convenient The “canalisation” of data analysis
Moving from pattern to mechanism
“Data! Data! Data!” he cried impatiently. “I can't make bricks without clay”.
Sherlock Holmes, The Adventure Of The Copper Breeches Sir Arthur Conan Doyle 1892
Causes Of Segregated Patterns
Species Interactions Habitat/Climate Associations Dispersal Barriers
Spatial Test
Climate Test
Pairwise NullModel Analysis
Blois et al., (2014) Ecography
Habitats
Species
Barrier
Dispersal Barrier
Habitat Barrier
Both
Diamond
Checkerboard
Spatial Test
Climate Test
Pairwise NullModel Analysis
Blois et al., (2014) Ecography
Co-occurrence of fossil woody plant genera
• 106 fossil pollen genera• 527 pollen cores throughout eastern North
America• 21 1000-year time slices, present to late
Quaternery
Spatial Test
Climate Test
Pairwise NullModel Analysis
Blois et al., (2014) Ecography
Spatial Test
Climate Test
Pairwise NullModel Analysis
Blois et al., (2014) Ecography
Most associations do not persist through (paleo) time
The Past, Present, and Future of Null Model Analysis in Biogeography
The Past Taxonomic ratios in biogeography An antidote for “Tangled Bank Fever”
The Present Benchmark testing of null model procedures Classifying patterns of co-occurrence (fossil plants)
The Future Big Data New methods
