Population models with partial migration

Abstract

Abstract. Populations exhibiting partial migration consist of two groups of individuals: Those that migrate between habitats, and those that remain fixed in a single habitat. We propose several discrete-time population models to investigate the coexistence of migrants and residents. The first class of models is linear, and we distinguish two scenarios. In the first, there is a single egg pool to which both populations contribute. A fraction of the eggs is destined to become migrants, and the remainder become residents. In a second model, there are two distinct egg pools to which the two types contribute, one corresponding to residents and another to migrants. The asymptotic growth or decline in these models can be phrased in terms of the value of the basic reproduction number being larger or less than one respectively. A second class of models incorporates density dependence effects. It is assumed that increased densities in the various life history stages adversely affect the success of transitioning of individuals to subsequent stages. Here too we consider models with one or two egg pools. Although these are nonlinear models, their asymptotic dynamics can still be classified in terms of the value of a locally defined basic reproduction number: If it is less than one, then the entire population goes extinct, whereas it settles at a unique fixed point consisting of a mixture of residents and migrants, when it is larger than one. Thus, the value of the basic reproduction number can be used to predict the stable coexistence or collapse of populations exhibiting partial migration.

The evolutionary stability of partial migration with Allee effects

“…Several mechanisms are studied in association with partial migration which include genetic control, density-dependence, and exogenous stochastic effects in environmental variables [6,17,23,29,30]. In general, partial migration population models with negative density dependence effects are studied and neglecting the populations that experience Allee effects [17,21,26,29]. One of the most common examples of Allee effects occur when a species is subject to predation with a saturating functional response, meaning that increased population levels decrease the risk of predation.…”