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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Revisiting the stability of spatially heterogeneous predator-prey systems under eutrophication
Authors: Farkas, Jozsef Zoltan
Morozov, Andrew
Arashkevich, Elena G
Nikishina, Anastasia
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Keywords: Spatially structured populations
Partial integro-differential equations
Paradox of enrichment
Top-down control
Issue Date: Oct-2015
Citation: Farkas JZ, Morozov A, Arashkevich EG & Nikishina A (2015) Revisiting the stability of spatially heterogeneous predator-prey systems under eutrophication, Bulletin of Mathematical Biology, 77 (10), pp. 1886-1908.
Abstract: We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction–diffusion models, this framework allows us to more realistically describe the situation where movement of individuals occurs on a faster time scale than on the demographic (population) time scale, and we cannot determine population growth based on local density. However, most of the results reported so far for such systems have only been verified numerically and for a particular choice of model functions, which obviously casts doubts about these findings. In this paper, we analyse a class of integro-differential predator–prey models with a highly mobile predator in a heterogeneous environment, and we reveal the main factors stabilizing such systems. In particular, we explore an ecologically relevant case of interactions in a highly eutrophic environment, where the prey carrying capacity can be formally set to ‘infinity’. We investigate two main scenarios: (1) the spatial gradient of the growth rate is due to abiotic factors only, and (2) the local growth rate depends on the global density distribution across the environment (e.g. due to non-local self-shading). For an arbitrary spatial gradient of the prey growth rate, we analytically investigate the possibility of the predator–prey equilibrium in such systems and we explore the conditions of stability of this equilibrium. In particular, we demonstrate that for a Holling type I (linear) functional response, the predator can stabilize the system at low prey density even for an ‘unlimited’ carrying capacity. We conclude that the interplay between spatial heterogeneity in the prey growth and fast displacement of the predator across the habitat works as an efficient stabilizing mechanism. These results highlight the generality of the stabilization mechanisms we find in spatially structured predator–prey ecological systems in a heterogeneous environment.
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Rights: This item has been embargoed for a period. During the embargo please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study. Publisher policy allows this work to be made available in this repository. Published in Bulletin of Mathematical Biology, October 2015, Volume 77, Issue 10, pp 1886-1908; The final publication is available at Springer via

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