The proposed research is a mathematical investigation into two broad areas of evolutionary theory: molecular evolution and the evolution of quantitative traits. The primary goal of the work on molecular evolution is to understand why there is so much variation in the genetic material, DNA, between species and between individuals within a species. One theory regards most of this variation as meaningless, having no functional consequences whatsoever. The theory that we are investigating argues that most of this variation does have biological consequences. Our approach to the problem involves a comparison of the predictions of each theory to the patterns observed in actual DNA sequences. This work is of potential value for our understanding of genetic variation susceptibility be viewed as due to many small mutations in DNA or to a few large ones? Our work is relevant to the former possibility. The primary goal of the work on quantitative genetics is to understand the genetic basis of variation in measurable traits, such as size or weight, both within and between species. The great conceptual problem in this work is to formalize the combined effects of many genes to interact with one another (through dominance and epistasis) in a way that adds biological relevance that was missing from previous models. Once the theory is in place, it will be used to investigate several problems of evolutionary interest. This work will be very important for agriculture, where practitioners require better theories of the genetic basis of traits, such as milk yield in cattle, that are of economic importance.
