Homogenization techniques for population dynamics in strongly heterogeneous landscapes

Yurk, B. P. and Cobbold, C. A. (2018) Homogenization techniques for population dynamics in strongly heterogeneous landscapes. Journal of Biological Dynamics, 12(1), pp. 171-193. (doi: 10.1080/17513758.2017.1410238) (PMID:29228877)

Abstract

An important problem in spatial ecology is to understand how population-scale patterns emerge from individual-level birth, death, and movement processes. These processes, which depend on local landscape characteristics, vary spatially and may exhibit sharp transitions through behavioural responses to habitat edges, leading to discontinuous population densities. Such systems can be modelled using reaction–diffusion equations with interface conditions that capture local behaviour at patch boundaries. In this work we develop a novel homogenization technique to approximate the large-scale dynamics of the system. We illustrate our approach, which also generalizes to multiple species, with an example of logistic growth within a periodic environment. We find that population persistence and the large-scale population carrying capacity is influenced by patch residence times that depend on patch preference, as well as movement rates in adjacent patches. The forms of the homogenized coefficients yield key theoretical insights into how large-scale dynamics arise from the small-scale features.

• Item Type: Articles
• Additional Information: This work was supported by the American Institute of Mathematics SQuaREs Program.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Cobbold, Professor Christina
• Authors: Yurk, B. P., and Cobbold, C. A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Biological Dynamics
• Publisher: Taylor & Francis
• ISSN: 1751-3758
• ISSN (Online): 1751-3766
• Published Online: 11 December 2017
• Copyright Holders: Copyright © 2018 The Authors
• First Published: First published in Journal of Biological Dynamics 12(1): 171-193
• Publisher Policy: Reproduced under a Creative Commons License