Mixture models as a method for comparative sociality: social networks and demographic change in resident killer whales

Abstract: In studies of social behaviour, social bonds are usually inferred from rates of interaction or association. This approach has revealed many important insights into the proximate formation and ultimate function of animal social structures. However, it remains challenging to compare social structure between systems or time-points because extrinsic factors, such as sampling methodology, can also influence the observed rate of association. As a consequence of these methodological challenges, it is difficult to analyse how patterns of social association change with demographic processes, such as the death of key social partners. Here we develop and illustrate the use of binomial mixture models to quantitatively compare patterns of social association between networks. We then use this method to investigate how patterns of social preferences in killer whales respond to demographic change. Resident killer whales are bisexually philopatric, and both sexes stay in close association with their mother in adulthood. We show that mothers and daughters show reduced social association after the birth of the daughter's first offspring, but not after the birth of an offspring to the mother. We also show that whales whose mother is dead associate more with their opposite sex siblings and with their grandmother than whales whose mother is alive. Our work demonstrates the utility of using mixture models to compare social preferences between networks and between species. We also highlight other potential uses of this method such as to identify strong social bonds in animal populations. Significance statement: Comparing patters of social associations between systems, or between the same systems at different times, is challenging due to the confounding effects of sampling and methodological differences. Here we present a method to allow social associations to be robustly classified and then compared between networks using binomial mixture models. We illustrate this method by showing how killer whales change their patterns of social association in response to the birth of calves and the death of their mother. We show that after the birth of her calf, females associate less with their mother. We also show that whales' whose mother is dead associate more with their opposite sex siblings and grandmothers than whales' whose mother is alive. This clearly demonstrates how this method can be used to examine fine scale temporal processes in animal social systems.