| Epistasis exists when the action of a gene at a locus (location on the genome), depends on the presence or absence of genes at other loci. In experimental quantitative genetics, two loci are said to be independent or 'non-epistatic' when their contributions to a specific quantitative trait are additive or multiplicative. Several measures for the magnitude and nature of epistasis have also been developed in the literature of theoretical population genetics. Some ramifications of these definitions are discussed, particularly the absence of these measures is shown in the general case to be equivalent to the lack of additivity or multiplicativity across loci.; The absence of epistasis usually leads to linkage equilibrium in large populations. However linkage equilibrium doesn't require genetic independence and models with special symmetries can be constructed such that they exhibit linkage equilibrium in the presence of epistasis. The equilibrium structure of a new model which encompasses several classic models is discussed in detail.; Next, the long range evolution of epistasis in large populations is addressed by the construction of a third modifier locus which induces epistasis between two loci. In this framework, the magnitude of the epistasis between two loci becomes an evolving trait, the value of which is determined by the specific allelic content of the modifier locus. The third quarter of the thesis is devoted to a special model in which the epistasis increases for small recombination rates but decreases when the recombination rate crosses a certain threshold.; Finally, in the last quarter of the thesis, some generalizations to multiple alleles/loci are discussed. |
