Mate finding, dispersal, number released, and the success of biological control introductions

Abstract. An analysis of published data and a mathematical model of the population dynamics of introduced parasitoids were used to explore the possibility that biological control introductions fail because an Allee effect drives small, introduced populations extinct. Such an Allee effect would arise because low densities, resulting from dispersal into a new environment, lead to failure to mate, which leads to a male‐biased sex ratio, which, if extreme enough, could cause population extinction. For chalcidoids, ichneumonoids and tachinids, the proportion of parasitoid populations that established when introduced for control of lepidopteran pests increased with the number of parasitoids per release, the total number released, and the number collected when each variable was analysed separately. For chalcidoids alone, establishment increased with the number of releases for this variable analysed separately. However, stepwise logistic regression of establishment on these variables included only the total number released for chalcidoids and the number per release for ichneumonoids and tachinids. This suggests that an Allee effect may limit the establishment of introduced parasitoids more than stochastic environmental variation or lack of genetic variation. A reaction‐diffusion model of parasitoid introductions was developed, which included mate finding, dispersal, reproduction and survival. Sensitivity analysis showed that the critical number of females needed to establish a population decreased hyperbolically as mate detection distance and net reproductive rate were increased, but the critical number increased linearly as mean‐square displacement was increased. The critical number of females did not change when the gross distance traversed per generation was varied. This was because increased area searched by males compensated for increased displacement. Changing from virgin females producing all males (arrhenotoky) to virgin females producing no progeny increased the critical number of females by over 30%. The analysis of past introductions and the sensitivity analysis of the reaction‐diffusion model both suggested a threshold of about 1000 insects per release to ensure establishment of introduced parasitoids. The implications of our results for the design of biological control introductions are discussed. Limitations in retrospective analyses and current knowledge indicate the need for an experimental approach to introductions.