Joshua Ladau

Validation of null model tests using Neyman–Pearson hypothesis testing theory

A long-standing question in ecology is whether interspecific competition affects co-occurrence patterns of species. Null model tests of presence–absence data (NMTPAs) constitute an important approach to address the question, but different tests often give conflicting results when applied to the same data. Neyman–Pearson hypothesis testing theory provides a rigorous and well accepted framework for assessing the validity and optimality of statistical tests. Here, I treat NMTPAs within this framework, and measure the robustness and bias of 72 representative tests. My results indicate that, when restrictive assumptions are met, existing NMTPAs are adequate, but for general testing situations, the use of all existing NMTPAs is unjustified — the tests are nonrobust or biased. For many current applications of NMTPAs, restrictive assumptions appear unmet, so these results illustrate an area in which existing NMTPAs can be improved. In addition to highlighting useful improvements to existing NMTPAs, the results here provide a rigorous framework for developing improved methods.

Robust hypothesis tests for independence in community assembly

The extent to which competition affects the distributions of species at large spatial scales is unclear. To evaluate this question, hypothesis tests that do not depend on parametric assumptions are needed. Here, we develop a broadly applicable test that requires only one parametric assumption. Letting i and j denote the ith and jth colonists to arrive at a site, respectively, and

Competition in the savanna: Models of species assemblages in Kruger National Park, South Africa

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The architecture and design of ecological null models

the event that i and j belong to the same “unit” (e.g., functional group, genus), we show how colonists will be partitioned into units if for all i and j,

The ecology of Malware

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Phylogenetically Novel Uncultured Microbial Cells Dominate Earth Microbiomes

is independent of whether i and j share unit membership with the other colonists, conditional on other information about shared units. Our distribution of partitions is useful for inferring competitive effects, because these effects predict that for at least one i and j,