PROPERTIES OF EQUILIBRIA IN MULTI-LOCUS GENETIC SYSTEMS

Warren J. Ewens ¹ and Glenys Thomson ²

¹ Department of Biology, University of Pennsylvania and Department of Mathematics, Monash University, Victoria, Australia
² Genetics Laboratory, University of Oxford, England

The classical mathematical theory of population genetics considered, for simplicity, almost exclusively one-locus systems. In the last two decades much work has been done on two-locus and, less frequently, multi-locus systems. This research has usually involved investigating properties of systems with given, and usually rather special, fitness parameters. Real genetic fitness systems are undoubtedly multi-locus and seldom will possess simplifying characteristics. One aim of this paper is to study generalized systems where no special assumptions are made about fitness structure, the number of alleles at each locus, the number of loci involved or the recombination structure between loci. A second aim is to consider marginal properties (often one-locus properties) of complex systems: the fact that many observations involve data from only one locus makes this second aim relevant.