Maximum likelihood estimators are a popular method for scoring phylogenetic trees to best explain the evolutionary histories of biomolecular sequences. In 1994, Steel showed that, given an incompatible set of binary characters and a fixed tree topology, there exist multiple sets of branch lengths that are optima of the maximum average likelihood estimator. Since parsimony techniques—another popular method of scoring evolutionary trees—tend to exhibit favorable behavior on data compatible with the tree, Steel asked if the same is true for likelihood estimators, or if multiple optima can occur for compatible sequences. We show that, despite exhibiting behavior similar to parsimony, multiple local optima can occur for compatible characters for the most parsimonious likelihood estimator. We caution that thorough understanding of likelihood criteria is necessary before they are used to analyze biological data.

中文翻译：

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最简约似然对相容字符表现出多重最优解

最大似然估计是一种流行的系统发育树评分方法，可以最好地解释生物分子序列的进化历史。1994 年，Steel 表明，给定一组不兼容的二进制字符和固定的树拓扑，存在多组分支长度，它们是最大平均似然估计量的最优值。由于简约技术——另一种对进化树进行评分的流行方法——倾向于在与树兼容的数据上表现出有利的行为，Steel 询问似然估计是否也是如此，或者对于兼容序列是否可以出现多个最优值。我们表明，尽管表现出类似于简约的行为，但对于最简约的似然估计器，兼容字符可能会出现多个局部最优。