Spatio-temporal pattern formation in predator-prey systems with fitness taxis
Autor: | Mads Peter Sørensen, Irene Heilmann, Uffe Høgsbro Thygesen |
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Rok vydání: | 2018 |
Předmět: |
0106 biological sciences
0301 basic medicine Well-posed problem Computer simulation Computer science Ecological Modeling Chaotic Taxis Pattern formation 01 natural sciences Stability (probability) Term (time) 010601 ecology 03 medical and health sciences 030104 developmental biology Spatial ecology Statistical physics Ecology Evolution Behavior and Systematics |
Zdroj: | Ecological Complexity. 34:44-57 |
ISSN: | 1476-945X |
Popis: | We pose a spatial predator–prey model in which the movement of animals is not purely diffusive, but also contains a drift term in the direction of higher specific growth rates. We refer to this as fitness taxis. We conduct a linear stability analysis of the resulting coupled reaction–advection–diffusion equations and derive conditions under which spatial patterns form. We find that for some parameters the problem is ill posed and short waves grow with unbounded speeds. To eliminate this, we introduce spatial kernels in the model, yielding coupled integro-differential equations, and conduct a similar stability analysis for this system. Through numerical simulation, we find that a variety of patterns can emerge, including stationary spatial patterns, standing and travelling waves, and seemingly chaotic spatio-temporal patterns. We argue that fitness taxis represents a simple and generic extension of diffusive motion, is ecologically plausible, and provides an alternative mechanism for formation of patterns in spatially explicit ecosystem models, with emphasis on non-stationary spatio-temporal dynamics. |
Databáze: | OpenAIRE |
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