School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia.
Syst Biol. 2011 Jan;60(1):74-86. doi: 10.1093/sysbio/syq076. Epub 2010 Nov 16.
The general Markov model (GMM) of nucleotide substitution does not assume the evolutionary process to be stationary, reversible, or homogeneous. The GMM can be simplified by assuming the evolutionary process to be stationary. A stationary GMM is appropriate for analyses of phylogenetic data sets that are compositionally homogeneous; a data set is considered to be compositionally homogeneous if a statistical test does not detect significant differences in the marginal distributions of the sequences. Though the general time-reversible (GTR) model assumes stationarity, it also assumes reversibility and homogeneity. We propose two new stationary and nonhomogeneous models--one constrains the GMM to be reversible, whereas the other does not. The two models, coupled with the GTR model, comprise a set of nested models that can be used to test the assumptions of reversibility and homogeneity for stationary processes. The two models are extended to incorporate invariable sites and used to analyze a seven-taxon hominoid data set that displays compositional homogeneity. We show that within the class of stationary models, a nonhomogeneous model fits the hominoid data better than the GTR model. We note that if one considers a wider set of models that are not constrained to be stationary, then an even better fit can be obtained for the hominoid data. However, the methods for reducing model complexity from an extremely large set of nonstationary models are yet to be developed.
核苷酸替代的通用马尔可夫模型（GMM）不假设进化过程是静止的、可逆的或均匀的。通过假设进化过程是静止的，可以简化 GMM。静止的 GMM 适用于成分均匀的系统发育数据集的分析；如果统计检验未检测到序列的边缘分布有显著差异，则认为数据集成分均匀。虽然一般时间可逆（GTR）模型假设静止，但它也假设可逆性和均匀性。我们提出了两个新的静止且不均匀的模型——一个将 GMM 约束为可逆，另一个则没有。这两个模型与 GTR 模型相结合，构成了一组嵌套模型，可用于检验静止过程的可逆性和均匀性假设。这两个模型被扩展以纳入不变位点，并用于分析显示成分均匀性的七分类人科数据集。我们表明，在静止模型类别中，非均匀模型比 GTR 模型更适合人科数据。我们注意到，如果考虑一组更广泛的不受静止约束的模型，那么人科数据的拟合效果会更好。然而，从极多的非静止模型中降低模型复杂度的方法仍有待开发。
