Parsimony overcomes statistical inconsistency with the addition of more data from the same gene

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Abstract
Many authors have demonstrated that the parsimony method of phylogenetic analysis can fail to estimate phylogeny accurately under certain conditions when data follow a model that stipulates homogeneity of the evolutionary process. These demonstrations further show that no matter how much data are added, parsimony will forever exhibit this statistical inconsistency if the additional data have the same distributional properties as the original data. This final component-that the additional data must follow the same distribution as the original data-is crucial to the demonstration. Recent simulations show, however, that if data evolve heterogeneously, parsimony can perform consistently. Here we show, using natural data, that parsimony can overcome inconsistency if new data from the same gene are added to an analysis already exhibiting a condition indistinguishable from inconsistency.