The role of weighted and topological network information to understand animal social networks: a null model approach

Network null models are important to drawing conclusions about individual- and population-(or graph) level metrics. While the null models of binary networks are well studied, recent literature on weighted networks suggests that: (1) many so-called 'weighted metrics' do not actually depend on weights, and (2) many metrics that supposedly measure higher-order social structure actually are highly correlated with individual-level attributes. This is important for behavioural ecology studies where weighted network analyses predominate, but there is no consensus on how null models should be specified. Using real social networks, we developed three null models that address two technical challenges in the networks of social animals: (1) how to specify null models that are suitable for 'proportion-weighted networks' based on indices such as the half-weight index; and (2) how to condition on the degree- and strength-sequence and both. We compared 11 metrics with each other and against null-model expectations for 10 social networks of bottlenose dolphin, Tursiops aduncus, from Shark Bay, Australia. Observed metric values were similar to null-model expectations for some weighted metrics, such as centrality measures, disparity and connectivity, whereas other metrics such as affinity and clustering were informative about dolphin social structure. Because weighted metrics can differ in their sensitivity to the degree-sequence or strength-sequence, conditioning on both is a more reliable and conservative null model than the more common strength-preserving null-model for weighted networks. Other social structure analyses, such as community partitioning by weighted Modularity optimization, were much less sensitive to the underlying null-model. Lastly, in contrast to results in other scientific disciplines, we found that many weighted metrics do not depend trivially on topology; rather, the weight distribution contains important information about dolphin social structure.