  The internal behaviour of a population is an important feature to take
account of when modelling their dynamics. In line with kin selection theory,
many social species tend to cluster into distinct groups in order to enhance
their overall population fitness. Temporal interactions between populations are
often modelled using classical mathematical models, but these sometimes fail to
delve deeper into the, often uncertain, relationships within populations. Here,
we introduce a stochastic framework that aims to capture the interactions of
animal groups and an auxiliary population over time. We demonstrate the model's
capabilities, from a Bayesian perspective, through simulation studies and by
fitting it to predator-prey count time series data. We then derive an
approximation to the group correlation structure within such a population,
while also taking account of the effect of the auxiliary population. We finally
discuss how this approximation can lead to ecologically realistic
interpretations in a predator-prey context. This approximation also serves as
verification to whether the population in question satisfies our various
assumptions. Our modelling approach will be useful for empiricists for
monitoring groups within a conservation framework and also theoreticians
wanting to quantify interactions, to study cooperation and other phenomena
within social populations.
