Application of a diffusion model to the spread of an invasive species: The coypu in Great Britain

Abstract

A discrete diffusion model, based on that of Dobzhansky et al., is adapted for the spread of an invasive species through the cells of a grid. As a case-study, the model is parameterised to simulate the spread of the coypu, Myocastor coypus Molina, in East Anglia, Great Britain. The model parameters are K, the carrying capacity of the environment, D, diffusivity, and r, the population growth rate; these three parameters are estimated from published data that were collected in the field. In order to implement the model, a detection threshold, local diffusivity, an initial population size and an initial population focus had to be specified. Experimental runs of the model are analysed to determine the relative importance of each of the parameters. The model, with a constant value of r, gave a good approximation to the observed coypu distribution. Contrary to expection, a model with variable values of r gave unsatisfactory results. A diffusion model such as this gives a ‘front’ to the spread of a species that is ‘solid’; in reality some colonies exist ahead of the front and some areas behind the front remain uncolonized for a substantial period of time.