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.

进化距离估计始终是分子进化（molecular evolution）研究领域的核心课题——基因进化速率、基因或生物类群间的分化时间，以及基因与生物类群间的演化关系的推断，均需以进化距离的估计为基础。与之密切相关的其他研究课题包括核苷酸替换（nucleotide substitution）模式估计、DNA序列各位点间进化速率变异程度的推断，以及分子钟假说（molecular clock hypothesis）的统计学检验。通过假定研究序列的核苷酸组成随时间近似保持恒定的平稳过程（stationary process），上述问题的数学处理可得到大幅简化；目前针对核苷酸替换平稳模型已有较为广泛的研究，但仍有部分问题有待解决。非平稳模型则复杂得多，但近年来随着平行线性距离（paralinear distance）与LogDet距离（LogDet distance）的提出，相关研究已取得显著进展。本文综述了上述课题的最新研究进展，并报告了进化距离估计偏差校正、核苷酸替换模式推断，以及序列各位点间进化速率变异程度估计的相关研究结果。