Density-dependent migration and stability in a system of linked populations

Abstract

The effect of adding density-dependent migration between nearest neighbour populations of a single discrete-generation species in a chain of habitat fragments is investigated. The larger the population on a particular habitat fragment, the greater the fraction of inhabitants who migrate before reproducing. It has previously been shown for similar models with density-independent migration that coupling populations in this way has no effect on the stability of these populations. Here, it is demonstrated that this effect is also generally true if migration is density-dependent. However, if the migration rate is large enough and has density dependence of the correct form, then the steady state (with all the populations remaining at the same constant value through time) can be destabilised. The conditions for this to occur are obtained analytically. When this “destabilisation” occurs, the system settles down to an alternative steady state where half of the populations take one constant value which is below that of an equivalent isolated system, and the other populations all share a population value which is greater than the steady state of the isolated populations. Once this configuration is reached, the population size on each patch remains constant over time. hence the change might more properly be described as a decrease in homogeneity rather than in stability.