To exhibit that GTR could be causing model misspecification, we proceed as follows. Kolaczkowski and Thornton (2004) looked at the effect on phylogenetic accuracy when different partitions of the data have different branch lengths (heterotachy). (2010) showed the potential for phylogenetic error in these scenarios. (2000) found instances of covarion evolution where the sites that are free to vary are different in distinct lineages, and Grievink et al. (2004) have considered the effect of ignoring changing base composition across the tree. For example, Galtier (2004) considers the effect of nonindependence of sites, whereas Galtier and Gouy (1995) and Jermiin et al. The phylogenetics literature is rich with other examples of model misspecification, each with the potential to cause problems for inference. It is the purpose of this article to give examples that demonstrate why this lack of closure may pose a problem for phylogenetic analysis and thus add GTR to the growing list of factors that are known to cause model misspecification in phylogenetics. In mathematical terms, the problem is simple: matrix multiplication of two GTR substitution matrices does not return another GTR matrix. 2012) shows that GTR, along with several other commonly used models, has an undesirable mathematical property that may be a cause of concern for the thoughtful phylogeneticist. However, a recent publication ( Sumner et al.
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