SummaryAnnual and monthly rainfall records (1969‐72) for the southern section of Tsavo National Park (East) were used to estimate net primary production above ground. Annual estimates of mean primary production varied between 210 g nr‐2a‐1(1971) and 545 g nr‐2a‐1(1969). The distribution limits of elephant deaths during 1970‐71 showed good correlation with the annual 200 g nr‐2a‐1contours.The calculated food consumption of the elephant population indicated txhat 4–7% of the primary production was eaten in years of good rainfall and 8–12% in drought years. Monthly food consumption was used to demonstrate that in a year where 4 to 5 consecutive months fell below the large mammal food requirement some mortality occurred.Maps showing the probability of a given level of primary production occurring in a specific region in any one month related very well to recorded elephant distributions. Further maps showing the probability with time of 4 and 5 consecutive months with primary production below the food requirements of the large mammals predicted 5 and 10 year and 43–50 year periodicities in primary production. The influence of the annual and longer term periodicities is discussed, and illustrated by generalized models which predict the ‘carrying capacities’ of the habitat for the different faunal categories.The potential of the probability maps for management purposes was demonstrated by reference to the ‘elephant problem’ and the much discussed recommendations of culling and non‐interference. On the available evidence it is believed that, in Tsavo (East), non‐interferenc