Analysis of sparse animal social networks

Low-density social networks can be common in animal societies, even among species generally considered to be highly social. Social network analysis is commonly used to analyse animal societal structure, but edge weight (strength of association between two individuals) estimation methods designed for dense networks can produce biased measures when applied to low-density networks. Frequentist methods suffer when data availability is low, because they contain an inherent flat prior that will accept any possible edge weight value, and contain no uncertainty in their output. Bayesian methods can accept alternative priors, so can provide more reliable edge weights that include a measure of uncertainty, but they can only reduce bias when sensible prior values are selected. Currently, neither accounts for zero-inflation, so they produce edge weight estimates biased towards stronger associations than the true social network, which can be seen through diagnostic plots of data quality against output estimate. We address this by adding zero-inflation to the model, and demonstrate the process using group-based data from a population of male African savannah elephants. We show that the Bayesian approach performs better than the frequentist to reduce the bias caused by these problems, though the Bayesian requires careful consideration of the priors. We recommend the use of a Bayesian framework, but with a conditional prior that allows the modelling of zero-inflation. This reflects the fact that edge weight derivation is a two-step process: i) probability of ever interacting, and ii) frequency of interaction for those who do. Additional conditional priors could be added where the biology requires it, for example in a society with strong community structure, such as female elephants in which kin structure would create additional levels of social clustering. Although this approach was inspired by reducing bias observed in sparse networks, it could have value for networks of all densities.