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 can also serve as verification to whether the population in question satisfies our various simplifying 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.

翻译：群体内部行为是建模其动态时需考虑的重要因素。根据亲缘选择理论，许多社会性物种倾向于聚集成不同群体以增强整体种群适应性。群体间的时间交互通常采用经典数学模型进行建模，但这些模型有时难以深入探究群体内部往往具有不确定性的关系。本文提出一个随机框架，旨在捕捉动物群体与辅助群体随时间变化的交互。我们通过模拟研究以及将模型拟合到捕食者-猎物计数时间序列数据，从贝叶斯视角展示了该模型的能力。随后，我们推导出此类群体内部相关结构的近似表达，同时考虑辅助群体的影响。最后，我们讨论了该近似如何在捕食者-猎物情境下产生具有生态学意义的解释。该近似还可用于验证所研究群体是否满足我们的各项简化假设。我们的建模方法将对保护框架下监测群体的实证研究者以及希望量化交互、研究社会群体内合作等现象的理论研究者具有实用价值。