Modeling evolution of quantitative traits with finite locus effects in structured populations

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Recent advances in quantitative genetics show that there is a distribution of locus effects on quantitative traits, with some loci (henceforth called QTLs) explaining a large proportion of the genotypic trait variance and others having minor but detectable effects on phenotype. For QTL results to be incorporated into existing theory, a crucial task is to develop models of quantitative trait variation that allow for a finite number of loci with finite effects. In this project, such models are developed and analyzed. Our theoretical work focuses on diffusion models, i.e. models in which both time and allele frequencies are continuous. The models developed are compared with previously-derived models, with the results of simulations, and with experimental data, with the aim of identifying models useful for predicting quantitative trait evolution in natural and agricultural populations. The results of the analysis and simulations are used to create statistical tests for the action of selection on quantitative traits in populations. Quantitative traits are among the most conspicuous features of organisms, features that we immediately recognize. Examples abound, including the height of humans, the number of ears on a corn plant or the weight of piglets in a litter. The study of quantitative traits and their genetic basis is fundamental to our understanding of evolutionary biology as well as to applied genetics such as animal and plant breeding. Using recently developed technology, it is now possible to identify regions of the genome that contribute to quantitative traits. Such "QTL mapping" studies have revealed discrepancies between the data and classical theories intended to explain the contribution of individual genes to such traits. This project aims to extend our theoretical understanding of quantitative traits, and to use the theory developed to create practical statistical methods for analyzing quantitative trait data. This grant is made under the Joint DMS/NIGMS Initiative to Support Research Grants in the Area of Mathematical Biology. This is a joint competition sponsored by the Division of Mathematical Sciences (DMS) at the National Science Foundation and the National Institute of General Medical Sciences (NIGMS) at the National Institutes of Health.