The application of the Dennis et al. (Ecol. Monogr., 61, 1991) model to data from 12 herbivore populations from the Kruger National Park, South Africa, introduces "risk assessment' procedures into the conservation management of free-ranging species. The model enables one to predict the probability of reaching an arbitrarily defined threshold population size using census figures from censused and unmanaged populations. It also provides an objective evaluation of population persistence based on past performance. Of the 12 species investigated, five (impala Aepyceros melampus, blue wildebeest Con- nochaetes taurinus, zebra Equus burchelli, white rhinoceros Ceratotherium simum, giraffe Giraffa camelopardalis) appear to be secure, four (kudu Tragelaphus strepsiceros, waterbuck Kobus ellipsiprymnus, warthog Phacochoerus aethiopicus, sable antelope Hippotragus niger) are vulnerable and three species (tsessebe Damaliscus lunatus, eland Taurotragus oryx, roan antelope Hippotragus equinus) are at risk of declining by an order of magnitude within 100 years. Therefore, within data limitations, the KNP appears not to offer "sufficient suitable habitat for a number of herbivore species despite its considerable size, and a metapopulation approach may be required for the effective conservation of some species. The model also allows the principle of 'complementarity' to be extended beyond that of species composition. Objective evaluations of population persistence, of censused and unmanaged populations, as demonstrated here, mean that the principle of 'population viability' can help the design of efficient regional reserve networks.