Optimising the sex ratio of translocation for genetic rescue as a function of invested resources

Translocation of individuals between isolated populations is practised, or envisaged, for a variety of reasons but requires careful consideration. Linklater [Linklater, W.L., 2003. A novel application of the Trivers-Willard model to the problem of genetic rescue. Conserv. Biol. 17, 906-909] proposed that the number of individuals of each sex translocated into a target population for the purposes of maintaining genetic diversity could be chosen using parental investment theory when the manager is allocating limited resources between the sexes as a parent invests in offspring of different sex. In this paper, by adapting basic ideas in the parental investment literature, we formulate a model to capture Linklater's proposal and provide a thorough mathematical analysis of the model. Granted the necessary species-specific biological information and translocation protocols to determine the model parameters in any instance in which the model is applied, the analysis indicates that a practical algorithm can be constructed to generate predictions of the optimal number, sex ratio, and division of resources for translocation with the goal of genetic rescue. This work is in line with recent calls for a more theoretical approach to translocation by providing quantitative models which can be subjected to scientific scrutiny and provide protocols for translocation planning. In particular, our model is intended to promote the design of translocations which study means of investment and the measurement of response to that investment.