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力学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提升整体种群适应性。种群间的时间动态交互常采用经典数学模型建模，但这些模型有时难以深入探究种群内部往往具有不确定性的关系。本文提出一种随机框架，旨在捕捉动物群体与辅助种群随时间变化的交互模式。我们通过仿真研究，并从贝叶斯视角将该模型拟合至捕食者-猎物计数时间序列数据，验证了其能力。随后，在考虑辅助种群效应的前提下，推导出此类群体内部相关结构的近似解。最后，我们讨论了该近似解如何在捕食者-猎物情境中产生具有生态学意义的解释，同时可作为检验研究群体是否满足各项简化假设的验证工具。本建模方法对在保护框架下监测群体的实证研究者，以及旨在量化交互、研究社会性群体合作及其他现象的理论工作者均具有应用价值。