Permutation tests for hypothesis testing with animal social network data: Problems and potential solutions.

Permutation tests are widely used to test null hypotheses with animal social network data, but suffer from high rates of type I and II error when the permutations do not properly simulate the intended null hypothesis.Two common types of permutations each have limitations. Pre-network (or datastream) permutations can be used to control 'nuisance effects' like spatial, temporal or sampling biases, but only when the null hypothesis assumes random social structure. Node (or node-label) permutation tests can test null hypotheses that include nonrandom social structure, but only when nuisance effects do not shape the observed network.We demonstrate one possible solution addressing these limitations: using pre-network permutations to adjust the values for each node or edge before conducting a node permutation test. We conduct a range of simulations to estimate error rates caused by confounding effects of social or non-social structure in the raw data.Regressions on simulated datasets suggest that this 'double permutation' approach is less likely to produce elevated error rates relative to using only node permutations, pre-network permutations or node permutations with simple covariates, which all exhibit elevated type I errors under at least one set of simulated conditions. For example, in scenarios where type I error rates from pre-network permutation tests exceed 30%, the error rates from double permutation remain at 5%.The double permutation procedure provides one potential solution to issues arising from elevated type I and type II error rates when testing null hypotheses with social network data. We also discuss alternative approaches that can provide robust inference, including fitting mixed effects models, restricted node permutations, testing multiple null hypotheses and splitting large datasets to generate replicated networks. Finally, we highlight ways that uncertainty can be explicitly considered and carried through the analysis.