The effect of migration on metapopulation stability is qualitatively unaffected by demographic and spatial heterogeneity

Coupled map lattices (CMLs), using two coupled logistic equations, have been extensively used to model the dynamics of two-patch ecological systems. Such studies have revealed that migration rate plays an important role in determining the dynamics of the system, particularly when the two maps differ in their intrinsic growth rate parameter, r. However, under more realistic assumptions, a metapopulation can be expected to consist of more than two subpopulations, each with its own demographic parameters, which will in part be a function of the environment of that patch. The role of the spatial arrangement of heterogeneous (i.e. with different r values) subpopulations in shaping the dynamics of such a metapopulation has rarely been investigated. Here, we study the effect of demographic and spatial heterogeneity on the stability of one- and two-dimensional systems of 64 coupled Ricker maps with different r values, under periodic and absorbing boundary conditions. We show that the effects of migration rate on metapopulation stability do not depend upon either the precise spatial arrangement of the subpopulations in the lattice, or on the presence of a moderate proportion of vacant (uninhabitable) patches in the lattice. The results, thus, suggest that metapopulation models are robust to variation in spatial arrangement of patch quality and, hence, of demographic parameters. We also show that for any given arrangement of the patches, maximum stability of the metapopulation occurs when the migration levels are intermediate, a result that agrees well with previous studies on two-map CML systems.