Refuge evolution and the population dynamics of coupled host—parasitoid associations

Summary

We have investigated the theoretical consequences of character evolution for the population dynamics of a host—parasitoid interaction, assuming a monophagous parasitoid. In the purely ecological model it is assumed that hosts can escape parasitism by being in absolute refuges. A striking property of this model is a threshold effect in control of the host by the parasitoid, when host density dependence is weak. The approximate criteria for the parasitoid to regulate the host to low densities are (1) that the parasitoid's maximum population growth rate should exceed the host's and (2) that the maximum growth rate of the host in the refuge should be less than unity. We then use this ecological framework as a basis for a model which considers evolutionary changes in quantitative characters influencing the size of the absolute refuge. For each species, an increase in its refuge-determining character comes at a cost to maximum population growth rate. We show that refuge evolution can substantially alter the population dynamics of the purely ecological model, resulting in a number of emergent and sometimes counter-intuitive properties. In general, when the host has a high carrying capacity, systems are polarized either with low or minor refuge and ‘top-down’ control of the host by the parasitoid or with a refuge and ‘bottom-up’ control of the host by a combination of its own density dependence and the parasitoid. A particularly tantalizing result is that co-evolutionary dynamics can modify ecologically unstable systems into ones which are either stable or quasi-stable (with bouts of unstable dynamics, punctuating long-term periods of quasi-stable behaviour). We present five quantitative criteria which must all be met for the parasitoid to be the agent responsible for control of the host at a co-evolutionary equilibrium. The apparent stringency of this full set of requirements supports the empirically-based suggestion that monophagous parasitoid-driven systems should be less common in nature than those driven by multiple forms of density dependence. Further, we apply our theory to the question of whether exploiters may ‘harvest’ their victims at maximum sustainable yields and to the evolutionary stability of biological control. Finally, we present a series of testable predictions of our theory and methods useful for testing them.