Stochastic Extinction and Reserve Size: A Focal Species Approach

Abstract

Chance population fluctuations may carry endangered animal species to extinction. Model populations of a focal rare species, whose abundance fluctuates according to a stochastic analog of the logistic, were examined to determine whether 1 large (OLR) or 2 small (TSR) reserves of the same total area are better able to prevent or delay extinction of the focal species. The preferred conservation strategy varies with immigration. When the model reserve is closed to outside immigrants of the focal species, OLR is preferable. Extinction is inevitable, but it takes longer and potentially much longer, in OLR than in TSR. This is true even when the TSR are connected by inter-reserve immigration. When the model reserve is open to outside immigrants of the focal species, the difference between OLR and TSR is usually negligible. It is possible to specify a minimum critical reserve size above which the focal species will nearly always be present in the reserve. There is a narrow range of reserve sizes for which the focal species switches from being absent almost always to almost always present. The open-reserve model mimics islands receiving immigrants from nearby continents and a prediction is tested with island data. The open-reserve model predicts a tight sigmoidal relationship between persistence of the focal species in a reserve (or on an island) and the coefficient of variation (CV) of its abundance. The prediction is closely matched by bird data from Farne and Skokholm Islands. The relationship between persistence and CV''s of abundance should help conservationists in estimating critical minimum reserve sizes for focal species of particular interest. Increasing numbers of endangered species are restricted solely to reserves, for which there is not possibility of immigration. For such species, OLR is preferable to TSR; and reserve size should be as large as possible. Recommendations are based just on considerations of extinction caused by demographic stochasticity and do not consider other problems facing rare and endangered species. This analysis should be considered a favorable-case scenario.