The Maintenance of Genetic Variation: A Functional Analytic Approach to Quantitative Genetic Models

Abstract

If one tries to understand phenomena of quantitative genetics in terms of classical population genetics one is faced with several problems. On the one hand, the genetic structure underlying quantitative traits is usually very complex and not well understood. On the other hand, models that have been treated mathematically on the basis of classical population genetics usually depend on a number of special assumptions like a very limited number of alleles or loci, special types of fitness functions, particular mutation schemes, etc. However, for describing dynamic and equilibrium properties of metric traits it is not always necessary to have a detailed knowledge of the dynamics of gene frequencies. Instead, it will often be sufficient to have appropriate information on mean values of characters, on their pattern of variation and covariation and perhaps on higher moments of the character distribution. To this aim it would be useful to have models and techniques that are less complicated to handle than the corresponding multilocus systems.