Hendy M D, Penny D, Steel M A
Department of Mathematics, Massey University, Palmerston North, New Zealand.
Proc Natl Acad Sci U S A. 1994 Apr 12;91(8):3339-43. doi: 10.1073/pnas.91.8.3339.
Discrete Fourier transformations have recently been developed to model the evolution of two-state characters (the Cavender/Farris model). We report here the extension of these transformations to provide invertible relationships between a phylogenetic tree T (with three probability parameters of nucleotide substitution on each edge corresponding to Kimura's 3ST model) and the expected frequencies of the nucleotide patterns in the sequences. We refer to these relationships as spectral analysis. In either model with independent and identically distributed site substitutions, spectral analysis allows a global correction for all multiple substitutions (second- and higher-order interactions), independent of any particular tree. From these corrected data we use a least-squares selection procedure, the closest tree algorithm, to infer an evolutionary tree. Other selection criteria such as parsimony or compatibility analysis could also be used; each of these criteria will be statistically consistent for these models. The closest tree algorithm selects a unique best-fit phylogenetic tree together with independent edge length parameters for each edge. The method is illustrated with an analysis of some primate hemoglobin sequences.
离散傅里叶变换最近已被开发出来用于模拟二态性状的进化（卡文德/法里斯模型）。我们在此报告这些变换的扩展，以提供系统发育树T（每条边上有对应木村三参数模型的三个核苷酸替换概率参数）与序列中核苷酸模式的预期频率之间的可逆关系。我们将这些关系称为频谱分析。在具有独立同分布位点替换的任何一种模型中，频谱分析都允许对所有多重替换（二阶及更高阶相互作用）进行全局校正，而与任何特定的树无关。从这些校正后的数据中，我们使用最小二乘选择程序，即最接近树算法，来推断进化树。也可以使用其他选择标准，如简约法或相容性分析；对于这些模型，这些标准中的每一个在统计上都是一致的。最接近树算法会选择一棵唯一的最佳拟合系统发育树以及每条边的独立边长参数。通过对一些灵长类动物血红蛋白序列的分析来说明该方法。
