REGULAR AND CHAOTIC CYCLING IN MODELS FROM POPULATION AND ECOLOGICAL GENETICS

Abstract

This chapter discusses regular and chaotic cycling in models from population and ecological genetics, and describes the biological issues in population genetics. Population genetics is the genetic composition of populations, including the forces affecting this composition and the way it changes over time. Many loci in living organisms are polymorphic, meaning that they are represented by multiple forms. For example, in most human populations, there are three different alleles present at the locus determining basic blood types, namely, A, B, and 0. The single most important issue in population genetics is that of genetic variation in natural populations. A major aim of mathematical genetic models is to determine under what conditions a given force or combination of forces can maintain more than one allele at a locus. The gene frequency in successive generations is specified by the iterates of the transformation. Genetic variation is preserved only if heterozygotes have a higher fitness than the two homozygotes. There are never any oscillations in the gene frequency under the classical model. The genetic system is inherently stable.