Density-related parasitoid sex-ratio: influence on host- parasitoid dynamics
We briefly review several mechanisms which suggest that sex-ratio in arrhenotokous parasitoids may be density-related. Four models incorporating density-related parasitoid sex-ratio are presented. We consider the cases where sex-ratio is a function of (i) male parasitoid population density, (ii) female parasitoid population density, (iii) host population density, and (iv) the ratio of females to hosts. We display the near-equilibrium dynamic properties of simple difference equation models which incorporate density-related sex-ratios. Each model is framed to incorporate the same parameter, zeta, defined as the fractional change in the proportion of female progeny per fractional change in the controlling population density or density ratio. Two constraints are shown to operate on the natural parameter combinations in these models: (i) there are strong theoretical reasons for believing that the sex-ratio is 0.5 in the absence of local mate competition, and (ii) a simple global model suggests that zeta may be limited to between -0.5 and +0.5. Models incorporating sex-ratio are shown to be locally stable over a broad range of host depression below carrying capacity. Some of the models generate large host depressions, which are a characteristic feature of successful biological control programmes using natural enemies.