The theoretical maximum rate of increase for the African elephant is calculated at 7%. This figure agrees closely with the rate of increase observed at Addo Elephant Park, the highest rate of increase reported for elephants living under natural conditions. An elephant population increasing at the maximum rate soon reaches a stable age distribution in which 48% of the animals are older than 11 years of age, (the age of first reproduction) and 6.7% are calves (less than one year old). Several papers have reported frequencies of calves in natural populations of up to twice this percentage. Calculations are presented to show that such high calf frequencies are both theoretically impossible on a sustained basis, and internally inconsistent with the population data presented in these papers.