COMPETITION IN A SPATIALLY HETEROGENEOUS ENVIRONMENT - MODELING THE RISK OF SPREAD OF A GENETICALLY-ENGINEERED POPULATION

In recent years regulations have been developed to address the risks o f releasing genetically engineered organisms into the natural environm ent. These risks are generally considered to be proportional to the ex posure multiplied by the hazard. Exposure is, in part, determined by t he spatial spread of the organisms, a component of risk suited to math ematical analysis. In this paper we examine a mathematical model descr ibing the spread of organisms introduced into a hetereogeneous environ ment, focusing on the risk of spread and plausibility of containment s trategies. Two competing populations are assumed, one the natural spec ies and the other an engineered species or strain, both of which move randomly in a spatially heterogenous environment consisting of alterna ting Favourable and unfavourable patches. The classical Lotka-Volterra competition model with diffusion is used. Analyses of the possible sp read and invasion of engineered organisms are thus reduced to finding periodic travelling wave solutions to the model equations. We focus on whether a very small number of engineered organisms can spatially inv ade a natural population. Initially we investigate the problem for spa tially periodic diffusion coefficients and demonstrate that, under the right circumstances and a large enough unfavourable patch, invasion d oes not succeed. However, if spatially periodic carrying capacities ar e assumed along with spatially varying diffusion rates, the situation is far more complex. In this case containment of the engineered specie s is no longer only a simple function of the unfavourable parch length . BS using perturbation solutions to the nonuniform steady states. app roximate invasion conditions are obtained. (C) 1996 Academic Press, In c.