Stability, Variability, and Persistence in Host‐Parasitoid Systems

Abstract

Insect parasitoids are ubiquitous members of natural insect communities, as well as being important agents of biological control. Because of their economic importance and relatively simple life cycles, host-parasitoid systems have received much theoretical effort. In this essay, I first review the theory available for hostparasitoid systems, and in particular explore the effects of environmental variability, spatial subdivision, and migration. These factors are often thought to influence dynamics in the field, but until recently have not received much attention in theory. I then make some recommendations for empirical work that could assess the effects of these factors in the field, and especially how they influence the persistence (through time) of host and parsitoid populations. Using the unstable Nicholson-Bailey model (Nicholson and Bailey 1935) as a starting point, theory has sought mechanisms that stabilize its dynamics; the rationale is that stability should ensure the persistence of the host and parasitoid (an apparent feature of real systems, at least on large spatial scales). Many stabilizing mechanisms have been identified, including mutual interference among parasitoids (Hassell and Varley 1969), several types of parasitoid aggregation (Hassell and May 1973, 1974, May 1978, Hassell 1984, Chesson and Murdoch 1986), density-dependent parasitoid sex ratios (Hassell et al. 1983, Comins and Wellings 1985), and competition among parasitoid larvae (Taylor 1988a). However, Morrison and Barbosa (1987) have questioned the idea that stability leads to persistence, when the population is subject to environmental variability. They used a standard host-parasitoid model, the negative-binomial model (May 1978), and simulated a fluctuating environment by allowing parameters in the model to be random variables. They found that perilously low densities could arise even when the model was strongly stable. Although stability ensures that