Felsenstein J
Department of Genetics, University of Washington, Seattle 98195.
J Theor Biol. 1991 Oct 7;152(3):357-76. doi: 10.1016/s0022-5193(05)80200-0.
An informal degrees of freedom argument is used to count the number of phylogenetic invariants in cases where we have three or four species and can assume a Jukes-Cantor model of base substitution with or without a molecular clock. A number of simple cases are treated and in each the number of invariants can be found. Two new classes of invariants are found: non-phylogenetic cubic invariants testing independence of evolutionary events in different lineages, and linear phylogenetic invariants which occur when there is a molecular clock. Most of the linear invariants found by Cavender (1989, Molec. Biol. Evol. 6, 301-316) turn out in the Jukes-Cantor case to be simple tests of symmetry of the substitution model, and not phylogenetic invariants.
在我们有三个或四个物种且可以假定存在或不存在分子钟的碱基替换的Jukes-Cantor模型的情况下，使用一种非正式的自由度论证来计算系统发育不变量的数量。处理了一些简单的情况，并且在每种情况下都可以找到不变量的数量。发现了两类新的不变量：测试不同谱系中进化事件独立性的非系统发育三次不变量，以及存在分子钟时出现的线性系统发育不变量。事实证明，在Jukes-Cantor情况下，Cavender（1989年，《分子生物学与进化》6，301 - 316）发现的大多数线性不变量是替换模型对称性的简单测试，而不是系统发育不变量。
