Journal article
Spatio-temporal pattern formation in predator-prey systems with fitness taxis
Department of Applied Mathematics and Computer Science, Technical University of Denmark1
Centre for Ocean Life, National Institute of Aquatic Resources, Technical University of Denmark2
National Institute of Aquatic Resources, Technical University of Denmark3
Dynamical Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark4
Technical University of Denmark5
Center for Intelligent Drug Delivery and Sensing Using Microcontainers and Nanomechanics, Department of Health Technology, Technical University of Denmark6
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.
Language: | English |
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Year: | 2018 |
Pages: | 44-57 |
ISSN: | 14769840 and 1476945x |
Types: | Journal article |
DOI: | 10.1016/j.ecocom.2018.04.003 |
ORCIDs: | Heilmann, Irene T. , Thygesen, Uffe Høgsbro and Sørensen, Mads Peter |