Estimation of evolutionary distances under stationary and nonstationary models of nucleotide substitution

Estimation of evolutionary distances has always been a major issue in the study of molecular evolution because evolutionary distances are required for estimating the rate of evolution in a gene, the divergence dates between genes or organisms, and the relationships among genes or organisms. Other closely related issues are the estimation of the pattern of nucleotide substitution, the estimation of the degree of rate variation among sites in a DNA sequence, and statistical testing of the molecular clock hypothesis. Mathematical treatments of these problems are considerably simplified by the assumption of a stationary process in which the nucleotide compositions of the sequences under study have remained approximately constant over time, and there now exist fairly extensive studies of stationary models of nucleotide substitution, although some problems remain to be solved. Nonstationary models are much more complex, but significant progress has been recently made by the development of the paralinear and LogDet distances. This paper reviews recent studies on the above issues and reports results on correcting the estimation bias of evolutionary distances, the estimation of the pattern of nucleotide substitution, and the estimation of rate variation among the sites in a sequence.

Extraordinary divergence and positive Darwinian selection in a fusagenic protein coating the acrosomal process of abalone spermatozoa.

During fertilization in marine invertebrates, fusion between sperm and egg cell membranes occurs at the tip of the sperm acrosomal process. In abalone sperm the acrosomal process is coated with an 18-kDa protein. In situ, this protein has no effect on the egg vitelline envelope, but in vitro it is a potent fusagen of liposomes. Thus, the 18-kDa protein may mediate membrane fusion between the gametes, a step in gamete recognition known to restrict heterospecific fertilization in other species. The cDNA and deduced amino acid sequences of the 18-kDa protein were determined for five species of California abalone. The deduced amino acid sequences exhibit extraordinary divergence; the percent identity varies from 27% to 87%. Analysis of nucleotide substitution shows extremely high frequencies of amino acid-altering substitution compared to silent substitution, demonstrating that positive Darwinian selection promotes the divergence of this protein. However, amino acid replacement is conservative with respect to size and polarity of residue. The data support the developing idea that in free-spawning marine invertebrates, the proteins mediating fertilization may be subjected to intense, and as yet unknown, selective forces. The extraordinary divergence of fertilization proteins may be related to the establishment of barriers to heterospecific fertilization.