Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays

Eide, Ragna M.; Krause, Andrew L.; Fadai, Nabil T.; Van Gorder, Robert A.

Abstract

We examine the role of the travel time of a predator along a spatial network on predator-prey population interactions, where the predator is able to partially or fully sustain itself on a resource subsidy. The impact of access to food resources on the stability and behaviour of the predator-prey-subsidy system is investigated, with a primary focus on how incorporating travel time changes the dynamics. The population interactions are modelled by a system of delay differential equations, where travel time is incorporated as discrete delay in the network diffusion term in order to model time taken to migrate between spatial regions. The model is motivated by the Arctic ecosystem, where the Arctic fox consumes both hunted lemming and scavenged seal carcass. The fox travels out on sea ice, in addition to quadrennially migrating over substantial distances. We model the spatial predator-prey-subsidy dynamics through a “stepping-stone” approach. We find that a temporal delay alone does not push species into extinction, but rather may stabilize or destabilize coexistence equilibria. We are able to show that delay can stabilize quasi-periodic or chaotic dynamics, and conclude that the incorporation of dispersal delay has a regularizing effect on dynamics, suggesting that dispersal delay can be proposed as a solution to the paradox of enrichment.

Citation

Eide, R. M., Krause, A. L., Fadai, N. T., & Van Gorder, R. A. (2018). Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays. Journal of Theoretical Biology, 451, 19-34. https://doi.org/10.1016/j.jtbi.2018.04.038

• Journal Article Type: Article
• Acceptance Date: Apr 20, 2018
• Online Publication Date: May 1, 2018
• Publication Date: Aug 14, 2018
• Deposit Date: May 29, 2020
• Publicly Available Date: Aug 7, 2020
• Journal: Journal of Theoretical Biology
• Print ISSN: 0022-5193
• Electronic ISSN: 1095-8541
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 451
• Pages: 19-34
• DOI: https://doi.org/10.1016/j.jtbi.2018.04.038
• Public URL: https://nottingham-repository.worktribe.com/output/4531457
• Publisher URL: https://www.sciencedirect.com/science/article/abs/pii/S0022519318302066
• Additional Information: This article is maintained by: Elsevier; Article Title: Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays; Journal Title: Journal of Theoretical Biology; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.jtbi.2018.04.038; Content Type: article; Copyright: © 2018 Elsevier Ltd. All rights reserved.