This paper investigates the local dynamical behaviour of a deterministic model describing two host species experiencing three forms of competition: direct competition, apparent competition mediated by macroparasites, and intra-specific (density-dependent) competition. The problem of algebraic intractability is sidestepped by adopting a geometric approach, in which an array of maps is constructed in parameter space, each structured by bifurcation surfaces which mark qualitative changes in system behaviour. The maps provide both a succinct and a comprehensive overview of the stability and feasibility structure of the system equilibria, from which can be deduced the possible modes of local dynamical behaviour. A detailed examination of these maps shows that (i) the system is highly sensitive to the effect of infection on fecundity with synchronous sustained cycles readily generated by Hopf bifurcations; (ii) for a broad range of parameter values, pertinent to actual biological systems, apparent competition mediated by macroparasites is sufficient, on its own, to explain host exclusion; (iii) direct competition reinforces parasite-mediated competition to expand the host exclusion region; and (iv) the condition for host exclusion can be expressed simply in a form which holds for both micro- and macroparasite models and which involves just two key indices, measuring tolerance to the infection and the strength of direct competition. The techniques used in this paper are not restricted to the analysis of host-parasite systems but can be applied to a wide range of nonlinear population models. They are therefore as relevant to the analysis of such general issues as exploitative competition and trophic interactions as they are to specific epidemiological problems. (C) 2000 Academic Press.
All Science Journal Classification (ASJC) codes
- Ecology, Evolution, Behavior and Systematics