title: Role of seasonality on predator-prey-subsidy population dynamics.
abstract: The role of seasonality on predator-prey interactions in the presence of a resource subsidy is examined using a system of non-autonomous ordinary differential equations (ODEs). The problem is motivated by the Arctic, inhabited by the ecological system of arctic foxes (predator), lemmings (prey), and seal carrion (subsidy). We construct two nonlinear, nonautonomous systems of ODEs named the Primary Model, and the n-Patch Model. The Primary Model considers spatial factors implicitly, and the n-Patch Model considers space explicitly as a "Stepping Stone" system. We establish the boundedness of the dynamics, as well as the necessity of sufficiently nutritional food for the survival of the predator. We investigate the importance of including the resource subsidy explicitly in the model, and the importance of accounting for predator mortality during migration. We find a variety of non-equilibrium dynamics for both systems, obtaining both limit cycles and chaotic oscillations. We were then able to discuss relevant implications for biologically interesting predator-prey systems including subsidy under seasonal effects. Notably, we can observe the extinction or persistence of a species when the corresponding autonomous system might predict the opposite.
authors.affiliation: Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK.
authors.forename: Dorian
authors.initials: D
authors.lastname: Levy
authors.affiliation: Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK.
authors.forename: Heather A
authors.initials: HA
authors.lastname: Harrington
authors.affiliation: Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK. Electronic address: Robert.VanGorder@maths.ox.ac.uk.
authors.forename: Robert A
authors.initials: RA
authors.lastname: Van Gorder
mesh_terms: D025041:Animal Migration; D000818:Animals; D001110:Arctic Regions; D020387:Food Chain; D008954:Models, Biological; D011157:Population Dynamics; D012621:Seasons
keywords: Allochthonous resource subsidy; Chaotic oscillations; Non-equilibrium dynamics; Population dynamics; Predator–prey dynamics