Polanski A, Kimmel M, Chakraborty R
Human Genetics Center, School of Public Health, University of Texas at Houston, Post Office Box 20334, Houston, TX 77225, USA.
Proc Natl Acad Sci U S A. 1998 May 12;95(10):5456-61. doi: 10.1073/pnas.95.10.5456.
Distribution of pairwise differences of nucleotides from data on a sample of DNA sequences from a given segment of the genome has been used in the past to draw inferences about the past history of population size changes. However, all earlier methods assume a given model of population size changes (such as sudden expansion), parameters of which (e.g., time and amplitude of expansion) are fitted to the observed distributions of nucleotide differences among pairwise comparisons of all DNA sequences in the sample. Our theory indicates that for any time-dependent population size, N(tau) (in which time tau is counted backward from present), a time-dependent coalescence process yields the distribution, p(tau), of the time of coalescence between two DNA sequences randomly drawn from the population. Prediction of p(tau) and N(tau) requires the use of a reverse Laplace transform known to be unstable. Nevertheless, simulated data obtained from three models of monotone population change (stepwise, exponential, and logistic) indicate that the pattern of a past population size change leaves its signature on the pattern of DNA polymorphism. Application of the theory to the published mtDNA sequences indicates that the current mtDNA sequence variation is not inconsistent with a logistic growth of the human population.
过去，基因组特定片段的DNA序列样本数据中核苷酸两两差异的分布已被用于推断种群大小变化的历史。然而，所有早期方法都假定了种群大小变化的特定模型（如突然扩张），并将其参数（如扩张时间和幅度）拟合到样本中所有DNA序列两两比较时观察到的核苷酸差异分布上。我们的理论表明，对于任何随时间变化的种群大小N(τ)（其中时间τ从当前开始倒推计数），一个随时间变化的合并过程会产生从种群中随机抽取的两个DNA序列之间合并时间的分布p(τ)。预测p(τ)和N(τ)需要使用已知不稳定的逆拉普拉斯变换。尽管如此，从三种单调种群变化模型（逐步、指数和逻辑斯蒂）获得的模拟数据表明，过去种群大小变化的模式会在DNA多态性模式上留下印记。将该理论应用于已发表的线粒体DNA序列表明，当前线粒体DNA序列变异与人类种群的逻辑斯蒂增长并不矛盾。
