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Resource-driven pattern formation in consumer-resource systems with asymmetric dispersal on a plane

January 28, 2024
This paper considers resource-driven pattern formation in consumer-resource systems. Here, a planar pattern consists of many big patches, and a big patch can be regarded as combination of many patches on the plane. The consumer moves between patches asymmetrically, while the asymmetry is driven by the resource abundance. Based on experimental models with linearly-linked patches, we propose a planarly-linked-patch model with asymmetric dispersal. Using dynamical systems theory, we show global stability of equilibria in the model, and demonstrate how the resource-driven dispersal forms patterns. It is shown that appropriate asymmetry in dispersal would make the consumer persist in the system, even in sink patches. The asymmetry could also make the consumer’s total population abundance larger than that without dispersal. However, inappropriate asymmetry would make the consumer go into extinction, even in source patches. Dispersal rates are also shown to play a role in the persistence and abundance increase. Our results are consistent with experimental observations and provide new insights. Numerical simulations by the model reproduce various vegetation patterns in the real world. This work has potential applications in spatial pattern formation in biological research.
Publication Year 2024
Title Resource-driven pattern formation in consumer-resource systems with asymmetric dispersal on a plane
DOI 10.1137/22M1506006
Authors Weiting Song, Shikun Wang, Yuanshi Wang, Don DeAngelis
Publication Type Article
Publication Subtype Journal Article
Series Title SIAM Journal on Applied Mathematics
Index ID 70251681
Record Source USGS Publications Warehouse
USGS Organization Wetland and Aquatic Research Center