On the Inadequacy of Simple Models of Mutual Interference for Parasitism and Predation

Mutual interference between searching arthropod parasites (i.e. parasitoids) is a beguilingly simple process, with apparently far-reaching implications for the stability of parasite-host interactions. The widely held view is that as parasite density increases, behavioural interactions (mutual interference) between searching individuals cause a reduction in the parasites' searching efficiency. In consequence, interference tends to confer stability on parasite-host interactions by reducing the death rate per parasite imposed on the hosts (and so the recruitment of parasites in the next generation) when parasite densities are high. The stabilizing effects of interference have recently been incorporated into a wide variety of ecological models (e.g. Austin & Cook 1974; Bulmer 1977; De Angelis, Goldstein & O'Neill 1975; Hassell & May 1973; Rogers & Hubbard 1974). It is often assumed (e.g. Beddington 1975) that similar considerations apply to predator-prey interactions. This paper is concerned primarily with parasitism, but possible extensions to predation are considered in the Discussion. The paper is divided into three sections. First, we re-examine the empirical model of interference proposed by Hassell & Varley (1969). This model postulates a linear relationship in logarithmic form between parasites' searching efficiency and density, with the degree of mutual interference given by the gradient. The model is already known to be oversimplified in one important respect. Thus, both a priori considerations (Royama 1971) and more detailed behavioural models (Beddington 1975; Rogers & Hassell 1974) require that the relationship should be curvilinear, with interference becoming negligible at low parasite densities. We later show that the behavioural models themselves indicate pitfalls in extrapolating from laboratory experiments conducted at higher parasite densities than prevail in the field. The second part, dealing with a host-parasite model written in difference equations, suggests that behavioural considerations largely preclude the possibility of significant mutual interference when the parasite is at or close to its equilibrium density. The behavioural models discussed assume that parasites search randomly. This assumption is relaxed in the last section. The implications of this change are that due to differential exploitation of the richer patches, searching efficiency measured over the whole environment is found to decline with parasite density (indicating interference) when there are no behavioural interactions. We call this effect 'pseudo-interference'. Accordingly we argue that 'interference' in the field can arise from both behavioural interactions and the effect of non-random search for aggregated hosts.