SPATIAL HETEROGENEITY IN 3-SPECIES, PLANT-PARASITE-HYPERPARASITE, SYSTEMS

This paper addresses the question of bow heterogeneity may evolve due to interactions between the dynamics and movement of three-species sys tems involving hosts, parasites and hyperparasites in homogeneous envi ronments. The models are motivated by the spread of soil-borne parasit es within plant populations, where the hyperparasite is used as a biol ogical control agent but where patchiness in the distribution of the p arasite occurs, even when environmental conditions are apparently homo geneous. However, the models are introduced in generic form as three-s pecies reaction-diffusion systems so that they have broad applicabilit y to a range of ecological systems. We establish necessary criteria fo r the occurrence of population-driven patterning via diffusion-driven instability Sufficient conditions are obtained for restricted cases wi th no host movement. The criteria are similar to those for the well-do cumented two-species reaction-diffusion system, although more possibil ities arise for spatial patterning with three species. In particular, temporally varying patterns, that may be responsible for the apparent drifting of hot-spots of disease and periodic occurrence of disease at a given location, are possible when three species interact. We propos e that the criteria can be used to screen population interactions, to distinguish those that cannot cause patterning from those that may giv e rise to population-driven patterning. This establishes a basic dynam ical 'landscape' against which other perturbations, including environm entally driven variations, can be analysed and distinguished from popu lation-driven patterns. By applying the theory to a specific model exa mple for host-parasite-hyperparasite interactions both with and withou t host movement, we show directly how the evolution of spatial pattern is related to biologically meaningful parameters. In particular, we d emonstrate that when there is strong density dependence limiting host growth, the pattern is stable over time, whereas with less stable unde rlying host growth, the pattern varies with time.