A necessary condition for dispersal driven growth of populations with discrete patch dynamics

Guiver, Christopher; Packman, David; Townley, Stuart

Abstract

We revisit the question of when can dispersal-induced coupling between discrete sink populations cause overall population growth? Such a phenomenon is called dispersal driven growth and provides a simple explanation of how dispersal can allow populations to persist across discrete, spatially heterogeneous, environments even when individual patches are adverse or unfavourable. For two classes of mathematical models, one linear and one non-linear, we provide necessary conditions for dispersal driven growth in terms of the non-existence of a common linear Lyapunov function, which we describe. Our approach draws heavily upon the underlying positive dynamical systems structure. Our results apply to both discrete- and continuous-time models. The theory is illustrated with examples and both biological and mathematical conclusions are drawn.

Citation

Guiver, C., Packman, D., & Townley, S. (2017). A necessary condition for dispersal driven growth of populations with discrete patch dynamics. Journal of Theoretical Biology, 424, 11-25. https://doi.org/10.1016/j.jtbi.2017.03.030

• Journal Article Type: Article
• Acceptance Date: Mar 8, 2017
• Online Publication Date: Apr 18, 2017
• Publication Date: Jul 7, 2017
• Deposit Date: Jul 23, 2020
• Publicly Available Date: Jul 29, 2020
• Journal: Journal of Theoretical Biology
• Print ISSN: 0022-5193
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 424
• Pages: 11-25
• DOI: https://doi.org/10.1016/j.jtbi.2017.03.030
• Keywords: Common linear Lyapunov function; Dispersal driven growth; Patch dynamics; Positive dynamical system; Population ecology; Population persistence
• Public URL: http://researchrepository.napier.ac.uk/Output/2677305