Measuring the complexity of social associations using mixture models

Abstract

Abstract: We propose a method for examining and measuring the complexity of animal social networks that are characterized using association indices. The method focusses on the diversity of types of dyadic relationship within the social network. Binomial mixture models cluster dyadic relationships into relationship types, and variation in the preponderance and strength of these relationship types can be used to estimate association complexity using Shannon’s information index. We use simulated data to test the method and find that models chosen using integrated complete likelihood give estimates of complexity that closely reflect the true complexity of social systems, but these estimates can be downwardly biased by low-intensity sampling and upwardly biased by extreme overdispersion within components. We also illustrate the use of the method on two real datasets. The method could be extended for use on interaction rate data using Poisson mixture models or on multidimensional relationship data using multivariate mixture models. Significance statement: Animals from many species interact socially with multiple individuals, and these interactions form a social network. Pairs of individuals have social relationships that differ in their strength and type. This social complexity has long interested behavioural biologists, particularly in the context of social cognition. Measuring social complexity, however, presents challenges. We propose a new method for measuring the complexity of animal social networks. Our approach is based on quantifying variation in the strengths of social connections (measured using association indices) which we use to classify different types of pairwise relationships. We, then, use the number, strength and prevalence of these different types of relationships to measure association complexity. Our approach can be used to compare association complexity between populations and/or species. We provide code that researchers can use with their own datasets.