9520832 NEI DNA sequences are molecular fossils from which one can learn the history of genes and organisms as well as the mechanism of evolution. For this reason, a large number of investigators are generating DNA sequences for many genes from various organisms from bacteria to humans. However, as the amount of DNA sequence data increases, it becomes difficult to extract the evolutionary significance from these data without use of proper statistical and computational methods. Current statistical and computational methods are inadequate to handle large-scale data and to solve newly arising evolutionary questions. It is also important to study patterns of nucleotide substitution and other types of DNA changes to provide a solid biological basis for any statistical and computational method. Furthermore, evolution of some genetic systems such as reproductive isolation between species still remains mysterious, and it is important to study these problems at the DNA level. The first project refines statistical methods for estimating the number of nucleotide or amino acid substitutions (evolutionary distance) between different sequences. These statistical methods are important not only for estimating evolutionary times of different organisms but also for constructing phylogenetic trees. The second project is concerned with the understanding of the mechanism of positive Darwinian selection observed in a number of gamete-recognition genes in mammals, abalone, and sea urchin and their possible roles in the evolution of reproductive isolation between different species. This study will contribute to the understanding of speciation mechanisms at the DNA level.