A simple population model consisting of one adult and two larval stages with cannibalism or competition among the larval stages is presented. The solutions are found to be either periodic or of a steady state nature depending on the ratios of fertility and cannibalism among the larvae. Two similar cannibalism pressure functions are compared and the conditions that lead to steady or periodic solutions, or to extinction, are examined.
Studies of ecological communities require various assumptions concerning the number of species that make up the community, their interrelationships, abundances, and spatial distributions. In m a n y studies, the definition of the investigators community is determined by convenience and intuition (Pielou, 1969) which is based, among other things, on the investigators experience with the individual species. In this note we examine the simplest prototype of a single species population (e.g., insects) t h a t consists of adults and several larval stages where a weighted cannibalism exists among the larval stages. Even in this simple system rather complicated solutions arise that would not be intuitively obvious a l~riori. It is hoped that the system may give some insight into the cyclic variations in certain insect populations.
The following model is a representation of a three stage population with age dependent cannibalism. For convenience, the stages are designated the adults (A'), which live for only one season, those larvae (LI') which h a t c h from eggs 11
LITERATURE
An Introduction to Mathematical Ecology. New York: Wiley,