The overall aim of this project is to understand better the role of selection in the genetics and evolution of natural populations through a study of the static and dynamic behavior of multilocus population genetic models, both in single populations and in models incorporating many sub-populations. The specific aim during this project period will be to examine the determination of processes, such as the relationship of phenotype to genotype, by the observation of patterns, such and response to selection Knowledge of the relationship between genotype and phenotype is important both in pure and applied genetics. Studies of dynamics, especially understanding the dynamics and causes of disequilibrium, such as found in the HLA complex, is also important for our understanding of human genetics. The models used for single populations will be standard multilocus ones. However, both the goals of the analysis and the techniques used will be quite different. The influence of epistasis and pleiotropy on predictions from population genetic models and on the maintenance of genetic variability in natural populations will be studied. Using techniques based on optimal control for finding minimum time solutions, the role of selection will be studied by specifying observable quantities such as the dynamics of mean, variances or covariances of characters under selection, and then trying to deduce information about the unobservable ones, such as the map from genotype to phenotype. The information about unobservable quantities will range from limits to behavior to estimates, depending on the input information provided. This will naturally lead to statistical questions concerning the detection of epistasis and or pleiotropy through the dynamics of gross observable characteristics such as means and variances. A similar approach based on optimal control theory will also be used to understand the evolution of genetic modifiers. A second specific aim will be to study the dynamics of genetic modifiers when selection is allowed to vary. Finally, the effects of spatial variation as well as temporal variation. on response to selection will be studied. Ways in which information about historical processes can be inferred by present day observations of hybrid zones and more generally spatial patterns of allele frequencies will be investigated.