With the aim of understanding the mechanisms of evolution of genes and populations and of maintenance of genetic variability within and between species, two mutually related research projects are proposed. (1) Statistical methods for phlyogenetic inference. Phylogenetic analysis of DNA sequences has become an important tool for studying population genetics and evolution. In the proposed research, a new algorithm for the minimum evolution method of phylogenetic inference will be developed to speed up the necessary computation. In the new algorithm, the principle f the neighbor-joining method will be used to identify many potential minimum evolution trees, and a tree with the minimum sum of all branch lengths will be chosen as the minimum evolution tree. We will also introduce simplified methods of testing the reliability of each interior branch of the tree obtained. A new protein maximum likelihood method of phylogenetic inference will be explored in view of the fact that protein trees are often more reliable than DNA tress when divergent sequences are considered. Maximum likelihood algorithms for inferring the nucleotide and amino acid sequences of ancestral organisms will also be developed to study adaptive evolution. An investigation will be conducted to find the most efficient genetic distance measures that are appropriate for constructing phylogenetic trees from recently discovered microsattelite DNA or STR loci. (2) Diversity and evolution of immune system genes. One of the most important genetic systems in vertebrates is the immune system that defends host individuals from foreign parasites. There are three multigene families involved; immunoglobulin, MHC, and T-cell receptor gene families. However, the evolutionary mechanisms of generation and maintenance of genetic diversity of these multigene families are poorly understood. This problem will therefore by studied by conducting phylogenetic analysis of DNA or protein sequences from diverse groups of vertebrates. Efforts will first be made to produce systematic classifications of immunoglobulin light-chain variable region (V) genes and T-cell receptor variable region (V) genes. The evolutionary pattern of these genes will then be studied by analyzing DNA or protein sequences of the genes from various groups of organisms. Special attention will be given to the unusual pattern of evolution of the avian-immunoglobulin system, where one or two functional V genes with a large number of V pseudogenes exist. A theoretical study will also be conducted on the general mechanism of maintenance of the immunoglobulin. MHC, and T-cell receptor gene diversity and their evolution.