null model analyses of presence-absence data

8/11/2019 Null Model Analyses of Presence-Absence Data

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Null Model Analyses of Presence-Absence Data in Ecology:

Combining Generalized Linear Modelsand Monte Carlo Testing for the

Detection of Non-Random Patterns

Applied Statistics 2007 International Conference

Ribno, Slovenia

Jorge Navarro-AlbertoUADY. Yucatn, Mxico

Bryan F. J. ManlyWEST, Inc. Wyoming, USA


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Outline

Why ecologists use null models?

Statistical approaches for null model analyses

of presence-absence data (e.g. speciesoccurrences on locations)

Generalized linear models as a tool

Testing non random patterns via Monte Carlo

Properties of the combined GLM-Monte Carlomethod

Comparison to other approaches

Conclusions


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From an ecological point of view, NMs are useful forpattern detection.

How? Compare a realization of an observed

ecological process and an associated model thataims to eliminate the effect of that particularecological process: the null model (Harvey et al.1983).

Tools for analysis of data generated by non-experimental procedures, typical of community andbiogeographical studies, in an experimental setting.

The usual terminology and interpretation ofhypothesis testing of experimental data, like Type I

and Type II errors, are applicable Ecolo ists use null models to com are observed data


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Null model analyses of presence/absencedata in ecology (e.g., occurrences of specieson particular locations) can be characterizedinto two broad categories: those where thesimulation protocols keep row (species) andcolumn (location) totals fixed in the nullmatrices, and those where row and/or column

totals are allowed to vary. In contrast to theresearch devoted to the first type of nullmodels, relatively little research has beendone to study the properties of the latter.


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we describe a strategy for null modelconstruction by means of generalized linearmodels for presence-absence data.

Assumptions for the generalized linearmodels (GLMs) are that (1) occurrences areindependent of each other; (2) species andisland effects are the only explanatory

variables for each observation in the matrix;and (3) the relationship between theoccurrence of each species-locationcombination and the species and location

effects is non-linear.


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For model definition, observable presence-

absence data are related with unobservable

hypothetical distributions of the number ofelements (called the "quasiabundance") of

each species-location combination; these

distributions are interpreted as different

scenarios of species occurrences from wherethe best fitting model is selected among a

range of competitor null models.


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Themethod produces fitted cell probabilities,which are subsequently used for thedetection of non-random patterns in theobserved matrices, via parametric bootstrap.

As a consequence, the simulation protocolallows both row and column totals to varyfrom one simulation to the other.

Monte Carlo tests applied to suitable metricsfor the observed and simulated matrices arethen used to evaluate the adequacy ofspecies and location effects for the prediction

of each species-location combination.


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Properties of the observed data matrices (e.g.,sparseness and degeneracy) and constraints in thesimulation protocols are also evaluated.

Finally, using as statistic the estimated proportion ofallocated presences in each cell of randomlygenerated matrices, it is shown that the set of nullmatrices in the GLM approach can be different fromthe set of null matrices obtained with three algorithms

keeping row and column totals fixed. It is confirmed also that there may be differences in

the null universe of matrices produced by differentversions of this latter simulation protocol.

null model analyses of presence-absence data

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