Avoiding spurious findings of nonrandom social structure in association data

Researchers studying animal societies often begin by testing whether a population shows nonrandom social structure, by comparing observed social associations with the predictions of a null model. Association data comprises observations of individuals in groups, which are observed through repeated surveys. Each survey is conducted on a discrete occasion, for example, within 1 day or 1 week. Current null models randomize the interactions among individuals, while preserving two key elements of the data: the number of times that each individual has been seen, and the sizes of observed groups. A critical assumption of existing permutation methods is that each observed group is independent. However, this assumption is often violated. Typically, researchers search a large study area, relative to the distances moved by animals within the sampling occasion. Thus, most individuals will not have had opportunity to change their group associations during a sampling occasion. We show how randomization tests should be modified to account for this nonindependence of group membership. We generated association data sets in which we randomly assigned individuals to groups. We tested these data sets for nonrandom structure using the generally accepted ‘trial swap’ algorithm. We found that spurious conclusions of nonrandom structure occur when we allowed permutation of individuals across sampling occasions, but not when we ‘blocked’ the data by sampling occasion, and constrained our randomizations to permute individuals only among groups within each block.