Population models with partial migration

TL;DR

This paper develops discrete-time population models to analyze the coexistence and dynamics of migrant and resident groups in populations, incorporating linear and density-dependent nonlinear effects, with outcomes predicted by a basic reproduction number.

Contribution

It introduces novel discrete-time models for partial migration, including linear and density-dependent types, and demonstrates how the basic reproduction number predicts population stability or extinction.

Findings

Basic reproduction number determines population fate.

Models predict coexistence or extinction based on reproduction number.

Density dependence influences long-term population dynamics.

Abstract

Populations exhibiting partial migration consist of two groups of individuals: Those that mi- grate 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.