Spatial utilization predicts animal social contact networks are not scale-free

While heterogeneity in social behaviour has been described in many human contexts it is often assumed to be less common in the animal kingdom even though scale-free networks are observed. This homogeneity raises the question of whether the patterns of behaviour necessary to account for scale-free social contact networks, where the degree distribution follows a power law, i.e. a few individuals are very highly connected but most have only a few connections, occur in animals, or whether other mechanisms are needed to produce realistic contact network architectures. We develop a space-utilization model for individual animal behaviour to predict the individuals' social contact network. Using basic properties of the χ(2) distribution we present a simple analytical result that allows the model to give a range of predictions with minimal computational effort. The model results are tested on data collected in New Zealand for the social contact networks of the wild brushtail possum (Trichosurus vulpecula). Our model provides a better prediction of network architecture than other simple models, including a scale-free model.