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

JOURNAL OF THEORETICAL BIOLOGY

卷:424

Article

Guiver, Chris¹  Packman, David²  Townley, Stuart² 

[1] Univ Bath, Dept Math Sci, Bath, Avon, England

[2] Univ Exeter, Environm & Sustainabil Inst, Coll Engn Math & Phys Sci, Penryn Campus, Exeter, Cornwall, England

关键词: Common linear Lyapunov function;    Dispersal driven growth;    Patch dynamics;    Positive dynamical system;    Population ecology;    Population persistence;   

DOI  :  10.1016/j.jtbi.2017.03.030

来源: Elsevier

【 摘 要 】

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. 2017 The Authors. Published by Elsevier Ltd.

【 授权许可】

Free