Department of Biology, University of Maryland, College Park, MD 20742, USA.
Graduate Program in Applied Mathematics and Scientific Computing, University of Maryland, College Park, MD 20742, USA.
J R Soc Interface. 2023 Mar;20(200):20220700. doi: 10.1098/rsif.2022.0700. Epub 2023 Mar 29.
How memory shapes animals' movement paths is a topic of growing interest in ecology, with connections to planning for conservation and climate change. Empirical studies suggest that memory has both temporal and spatial components, and can include both attractive and aversive elements. Here, we introduce reinforced diffusions (the continuous time counterpart of reinforced random walks) as a modelling framework for understanding the role that memory plays in determining animal movements. This framework includes reinforcement via functions of time before present and of distance away from a current location. Focusing on the interplay between memory and central place attraction (a component of home ranging behaviour), we explore patterns of space usage that result from the reinforced diffusion. Our efforts identify three qualitatively different behaviours: bounded wandering behaviour that does not collapse spatially, collapse to a very small area, and, most intriguingly, convergence to a cycle. Subsequent applications show how reinforced diffusion can create movement trajectories emulating the learning of movement routes by homing pigeons and consolidation of ant travel paths. The mathematically explicit manner with which assumptions about the structure of memory can be stated and subsequently explored provides linkages to biological concepts like an animal's 'immediate surroundings' and memory decay.
记忆如何塑造动物的运动路径是生态学中日益受到关注的一个主题，它与保护和气候变化规划有关。实证研究表明，记忆既有时间成分，也有空间成分，并且可以包括有吸引力和厌恶的元素。在这里，我们引入强化扩散（强化随机游走的连续时间对应物）作为理解记忆在决定动物运动中所起作用的建模框架。该框架包括通过当前位置之前的时间和距离的函数进行强化。我们专注于记忆和中心位置吸引（家庭范围行为的一个组成部分）之间的相互作用，探索强化扩散产生的空间使用模式。我们的努力确定了三种不同的行为：有界漫游行为不会在空间上崩溃，崩溃到一个非常小的区域，最有趣的是，收敛到一个循环。随后的应用表明，强化扩散如何创建模仿归巢鸽子学习运动路线和蚂蚁旅行路径巩固的运动轨迹。可以用数学上明确的方式来陈述关于记忆结构的假设，并随后进行探索，这为动物的“周围环境”和记忆衰减等生物学概念提供了联系。
