Dispersal and settling of translocated populations: a general study and a New Zealand amphibian case study.

Translocations are widely used to reintroduce threatened species to areas where they have disappeared. A continuum multi-species model framework describing dispersal and settling of translocated animals is developed. A variety of different dispersal and settling mechanisms, which may depend on local population density and/or a pheromone produced by the population, are considered. Steady state solutions are obtained using numerical techniques for each combination of dispersal and settling mechanism and for both single and double translocations at the same location. Each combination results in a different steady state population distribution and the distinguishing features are identified. In addition, for the case of a single translocation, a relationship between the radius of the settled region and the population size is determined, in some cases analytically. Finally, the model is applied to a case study of a double translocation of the Maud Island frog, Leiopelma pakeka. The models suggest that settling occurs at a constant rate, with repulsion evidently playing a significant role. Mathematical modelling of translocations is useful in suggesting design and monitoring strategies for future translocations, and as an aid in understanding observed behaviour.