A Fragmented Population in a Varying Environment

Abstract

When speaking about spatially distributed populations, a conceptual distinction is made between two spatial scales and, hence, between two classes of populations which are termed as “pure” metapopulation structures and {puod}pure{pucd} within-population structures. We study a model which belongs to an intermediate type named a “patchy population”. It is characterized by independent density fluctuations in patches and by a “fast” migration flow. The model includes the Allee effect for density dependence in order to allow (deterministically) for population extinction when reaching very low levels of abundance. We study equilibrium points and their stability in the case of a constant external influence which is modelled by a density-independent death rate. In a variable environment, we obtain explicit expressions for fluctuations and calculate their lags behind environmental changes. Regarding the influence of the migration rate, we obtain that, under the assumptions made in this model, particularly the Allee effect in local population dynamics, an increase of the migration rate is not always profitable for the persistence of the population.