Variable Parasitoid Sex Ratios and their Effect on Host-Parasitoid Dynamics

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Abstract
(1) Three forms of density-dependent parasitoid sex ratios are discussed: (a) where sex ratio is a function of the size of the adult female population (P), (b) where sex ratio depends on the ratio of females to hosts (P/N) and (c) the case of heteronomous hyperparasitoids, where sex ratio is related to the frequency of encounters with parasitized and unparasitized hosts (yielding male and female progeny, respectively). (2) The dynamic properties of difference equation models including each of these mechanisms in turn are displayed. Sex ratios as a function of P or P/N are considered within the framework of conventional host-parasitoid models. Heteronomous hyperparasitoids, however, require a new model structure. In each case, models are explored in which encounters with hosts are either assumed to be random (Poisson) or contagiously distributed with the probability of parasitism given by the negative binomial distribution. (3) With random host encounters, sex ratios as a function of P or P/N can be sufficient to be the sole cause of stability of the interaction, but only with `fine tuning' of the relevant parameters. These critical parameters values, however, broaden considerably when some additional stability is added via contagion in the distribution of parasitism. (4) In the special case of randomly acting heteronomous hyperparasitoids, the unusual result occurs of a neutrally stable interaction over a wide range of host rates of increase. The slightest additional stability added to the interaction (e.g. by some contagion in the host attacks) is sufficient to `tip the balance' and convert the neutral stability to a locally stable equilibrium. We conclude that such interactions should be highly stable in the real world.