The architecture and design of ecological null models

Abstract

Many questions in ecology are best addressed using observational data because they concern spatial or temporal scales where experimentation is impractical. Null models, which make predictions in the absence of a particular ecological mechanism, are instrumental for making inferences in these situations, but which null models to use or how to best test them is often unclear; this ambiguity is problematic because different null models and tests can yield different results, suggesting contradictory ecological mechanisms. To address these challenges, this paper presents an overar ching framework for the development and testing of null models, in which desirable models and tests are obtained as solutions to mathematical optimization problems. As an example of how the framework can be applied, this paper shows how it can be used to design null model tests to check for effects of interspecific interactions on species co-occurrence patterns. A minimal sufficient statistic (metric) for effects of interspecific interactions is derived, which achieves the maximal level of data compression without losing information present in the data about interspecific in teractions. Existing, intuitive statistics are shown to lack this property. The paper then derives a statistical hypothesis test that has the greatest possible power (sen sitivity) for detecting effects of competition and facilitation given a controlled false positive rate. This test is shown numerically to improve greatly over existing tests. The optimization paradigm allows the most accurate inferences possible, and should be applicable throughout ecology where null models are used to make inferences.