Inferring networks from multivariate symbolic time series to unravel behavioural interactions among animals

A traditional way to quantify synchronous interactions between animals has been to use concordance indices, which commonly do not take into account the effects of the length of the sampling time and of behaviour driven by third parties. We overcame these issues by casting the process of investigating behavioural interactions into a network inference methodology. We summarized multivariate time series using a complex network whose construction depends on a surrogate hypothesis testing data analysis of synchronous interactions between animals. The method accounts for the effect of third parties on pairwise comparisons, allows one to test the effect of the size of the sampling window on the interactions between animals, and allows one to test behavioural models of increasing complexity. We used a continuous 1-month behavioural data set of the foraging activity of a mixed-sex group of 40 Soay sheep, Ovis aries. We uncovered underlying patterns of behavioural interaction between individual sheep by applying our inferential approach to the symbolic multivariate time series of activity, that is grazing, not grazing. Our findings clearly indicate that animals of the same sex are more synchronized than animals of different sex independent of body size. We advocate that the method proposed is more general and more efficient at detecting patterns of synchronization than traditional concordance indices. We provide the reader with a comprehensive software toolbox to apply the methodology proposed.