Neighbourhood size, dispersal distance and the complex dynamics of the spatial Ricker model

Amongst the most frequently made assumptions in simple population models are that individuals interact equally with every other individual and that dispersal occurs with equal likelihood to any location. This is especially true for models of a single population (as opposed to a patchy population or metapopulation). For many species of animals and probably for all plant species these assumptions are unlikely to hold true. Here one much-studied population model-the Ricker model-is reformulated such that interactions occur only between individuals located within a certain distance of each other and dispersal distance is finite. Two alternative reformulations are presented. Results demonstrate that both limiting the interaction neighbourhood and reducing dispersal distance tend to stabilise the global population dynamics, although the extent to which this occurs depends upon the reformulation used. Spatial pattern formation is a feature of the simulated population. At lower intrinsic rates of growth (r) these patterns tend to be static, while for higher r, they are dynamic. Both the stabilisation of global dynamics and spatial pattern formation are well-described features of metapopulation models. Here, similar effects are shown to occur on a single contiguous patch of habitat.