Three-patch Models for the Evolution of Dispersal in Advective Environments: Varying Drift and Network Topology

• Published in: Bulletin of mathematical biology Vol. 83; no. 10; p. 109
• Main Authors: Jiang, Hongyan, Lam, King-Yeung, Lou, Yuan
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2021; Springer Nature B.V
• Subjects: Biological Evolution; Carrying capacity; Cell Biology; Diffusion; Diffusion rate; Dispersal; Dispersion; Drift; Drift rate; Ecosystem; Environment models; Evolution; Infinity; Life Sciences; Mathematical and Computational Biology; Mathematical Concepts; Mathematics; Mathematics and Statistics; Models, Biological; Network topologies; Original Article; Population Dynamics; Varying drift; River patch model; Network topology; Evolution of dispersal; 92D15; 34D20; 92D40
• ISSN: 0092-8240; 1522-9602; 1522-9602
• DOI: 10.1007/s11538-021-00939-8

We study the evolution of dispersal in advective three-patch models with distinct network topologies. Organisms can move between connected patches freely and they are also subject to the passive, directed drift. The carrying capacity is assumed to be the same in all patches, while the drift rates could vary. We first show that if all drift rates are the same, the faster dispersal rate is selected for all three models. For general drift rates, we show that the infinite diffusion rate is a local Convergence Stable Strategy (CvSS) for all three models. However, there are notable differences for three models: For Model I, the faster dispersal is always favored, irrespective of the drift rates, and thus the infinity dispersal rate is a global CvSS. In contrast, for Models II and III a singular strategy will exist for some ranges of drift rates and bi-stability phenomenon happens, i.e., both infinity and zero diffusion rates are local CvSSs. Furthermore, for both Models II and III, it is possible for two competing populations to coexist by varying drift and diffusion rates. Some predictions on the dynamics of n -patch models in advective environments are given along with some numerical evidence.