祖先最大似然中的收缩效应
Shrinkage Effect in Ancestral Maximum Likelihood
摘要：
祖先最大似然法（AML）是一种同时重建系统发育树和祖先序列的方法。树和祖先序列在序列进化的马尔可夫模型下最大化观察给定数据的概率，其中分支长度也被优化，但被约束为在所有序列位点的任何边缘上取相同的值。AML与遗传学中更常见的最大似然（ML）形式不同，因为ML对所有可能的祖先序列进行平均。ML一直被认为是统计上一致的，也就是说，随着序列长度的增长，它以接近1的概率收敛到正确的树上。然而，AML的统计一致性尚未正式确定，尽管在一份文献中有非正式的评论，可以追溯到20年前。在这个简短的说明中，我们证明了一个一般的结果，这意味着AML是统计不一致的。特别是，我们表明，AML可以“收缩”树中的短边，导致在一棵树，没有内部分辨率的序列长度的增长。我们的结果适用于任何数量的类群。
英文摘要：
Ancestral maximum likelihood (AML) is a method that simultaneously reconstructs a phylogenetic tree and ancestral sequences from extant data (sequences at the leaves). The tree and ancestral sequences maximize the probability of observing the given data under a Markov model of sequence evolution, in which branch lengths are also optimized but constrained to take the same value on any edge across all sequence sites. AML differs from the more usual form of maximum likelihood (ML) in phylogenetics because ML averages over all possible ancestral sequences. ML has long been known to be statistically consistent -- that is, it converges on the correct tree with probability approaching 1 as the sequence length grows. However, the statistical consistency of AML has not been formally determined, despite informal remarks in a literature that dates back 20 years. In this short note we prove a general result that implies that AML is statistically inconsistent. In particular we show that AML can `shrink' short edges in a tree, resulting in a tree that has no internal resolution as the sequence length grows. Our results apply to any number of taxa.
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