How large a managed area is needed to protect a threatened animal species? Combining simple dispersal and population models

The size and shape of the managed area for a threatened species to have a stable or growing population is a central issue for conservation management, for example for kiwi, Apteryx sp. Combining geometric probability results for retention of juveniles to breed in the protected area with a standard matrix population model allows the creation of an explicit relationship between the minimum area needed and how far juveniles of the species disperse to establish breeding territories. For a given set of demographic parameters for the population, and a rectangular protected area, there is a quadratic relationship between area and dispersal distance. Extensions for a circular protected area, and for a probability distribution on dispersal distance, are considered. The results are applied to kiwi, using established population parameters, giving results that match closely those from a previously published simulation. This approach can provide simple tools, readily implemented in a spreadsheet, for assessment of the size and shape of protected areas needed in conservation management of animals that disperse before breeding.