Georgiou Fillipe, Buhl Camille, Green J E F, Lamichhane Bishnu, Thamwattana Ngamta
Institute for Mathematical Innovation, University of Bath, Bath, United Kingdom.
School of Agriculture, Food and Wine, University of Adelaide, Adelaide, South Australia, Australia.
PLoS Comput Biol. 2025 Apr 15;21(4):e1011469. doi: 10.1371/journal.pcbi.1011469. eCollection 2025.
Collective behaviour occurs at all levels of the natural world, from cells aggregating to form tissues, to locusts interacting to form large and destructive plagues. These complex behaviours arise from relatively simple interactions amongst individuals and between individuals and their environment. For simplicity, mathematical models of these phenomena often assume that the population is homogeneous. However, population heterogeneity arising due to the internal state of individuals can affect these interactions and thus plays a role in the dynamics of group formation. In this paper, we present a partial differential equation model that accounts for this heterogeneity by introducing a state space that models an individual's internal state (e.g. age, level of hunger) which affects its movement characteristics. We then apply the model to a concrete example of locust foraging to investigate the dynamic interplay of food availability, hunger, and degree of gregarisation (level of sociability) on locust group formation and structure. We find that including hunger lowers group density and raises the percentage of the population that needs to be gregarious for group formation. Within the group structure itself we find that the most gregarious and satiated locusts tend to be located towards the centre with hunger driving locusts towards the edges of the group. These two effects may combine to give a simple mechanism for locust group dispersal, in that hunger lowers the group density, which in turn lowers the gregarisation, further lowering density and creating a feedback loop. We also note that a previously found optimal food patch size for group formation may be driven by hunger. In addition to our locust results, we provide more general results and methods in the attached appendices.
群体行为在自然界的各个层面都会发生，从细胞聚集形成组织，到蝗虫相互作用形成大规模的破坏性蝗灾。这些复杂行为源于个体之间以及个体与环境之间相对简单的相互作用。为了简化起见，这些现象的数学模型通常假设种群是同质的。然而，由于个体内部状态产生的种群异质性会影响这些相互作用，从而在群体形成的动态过程中发挥作用。在本文中，我们提出了一个偏微分方程模型，该模型通过引入一个状态空间来考虑这种异质性，该状态空间对影响个体运动特征的内部状态（如年龄、饥饿程度）进行建模。然后，我们将该模型应用于蝗虫觅食的具体例子，以研究食物可获得性、饥饿程度和群居化程度（社交性水平）对蝗虫群体形成和结构的动态相互作用。我们发现，考虑饥饿因素会降低群体密度，并提高群体形成所需的群居个体的百分比。在群体结构内部，我们发现最具群居性且饱腹的蝗虫往往位于群体中心，而饥饿则驱使蝗虫向群体边缘移动。这两种效应可能共同作用，形成一种蝗虫群体分散的简单机制，即饥饿降低了群体密度，进而降低了群居化程度，进一步降低密度并形成一个反馈循环。我们还注意到，先前发现的群体形成的最佳食物斑块大小可能受饥饿驱使。除了蝗虫研究结果外，我们还在附录中提供了更一般的结果和方法。
