A Mathematical Model with a Modified Logistic Approach for Singly Peaked Population Processes

Abstract

When a small number of individuals of a single species are confined in a closed space with a limited amount of indispensable resources, breeding may start initially under suitable conditions, and after peaking, the population should go extinct as the resources are exhausted. Starting with the logistic equation and assuming that the carrying capacity of the environment is a function of the amount of resources, a mathematical model describing such a pattern of population change is obtained. An application of this model to a typical set of population records, that of deer herds by V. B. Scheffer (1951, Sci. Monthly 73, 356–362) and E. C. O'Roke and F. N. Hamerstrom (1948, J. Wildlife Management 12, 78–86), yields estimates of the initial amount of indispensable food and its availability or nutritional efficiency which were previously unspecified.