Abstract

This paper considers the patch selection by a population without having full information about the utility of the patch, i.e., the amount of its energy resources. This problem is related to the optimal foraging theory. According to U. Dieckmann’s suggestion, the population distribution by patches should be modeled according to the utility function that takes into account the amount of resources per patch, the population–patch distance, and the extent to which the population is aware of the amount of resources in the patch. In this case, the population distribution by patches is described using the Boltzmann distribution. Dieckmann considers a static problem without taking into account the change in the position of the population over time. In this paper, we suggest a dynamic system that describes the population distribution by patches, which depends on the utility of patches that changes over time as a result of variations in the population–patch distance. That said, the Boltzmann distribution is a particular solution of the derived system of ordinary differential equations. The Lyapunov stability condition for the Boltzmann distribution is derived. The patch utility functions dependent on the distance to and the population’s awareness of the patch are introduced. As a result, in the 2D case the R² space in divided in preferential utility domains. This partition generalizes G.F. Voronoy’s diagram.

中文翻译：

---

斑块分布人口动态

摘要

本文考虑了人群的补丁选择，而没有关于补丁效用（即其能量资源的数量）的完整信息。这个问题与最优觅食理论有关。根据U. Dieckmann的建议，应根据效用函数对斑块的种群分布进行建模，该函数应考虑到每个斑块的资源量，种群到斑块的距离以及种群对种群数量的了解程度。补丁中的资源。在这种情况下，使用玻耳兹曼分布描述了斑块的种群分布。迪克曼（Dieckmann）认为是一个静态问题，没有考虑到人口随时间的变化。在本文中，我们建议使用一个动态系统来描述补丁的人口分布，这取决于斑块的效用，而斑块的效用是由于种群－斑块距离的变化而随时间变化的。也就是说，玻耳兹曼分布是导出的常微分方程组的一种特殊解。推导了玻尔兹曼分布的Lyapunov稳定性条件。介绍了补丁实用程序功能，该功能取决于到补丁的距离和人群的意识。结果，在2D情况下 介绍了补丁实用程序功能，该功能取决于到补丁的距离和人群的意识。结果，在2D情况下 介绍了补丁实用程序功能，该功能取决于到补丁的距离和人群的意识。结果，在2D情况下R ²空间分为优先效用域。该分区概括了GF Voronoy的图。