Least squares estimation of molecular distance--noise abatement in phylogenetic reconstruction

Zuckerkandl and Pauling (1962, "Horizons in Biochemistry," pp. 189-225, Academic Press, New York) first noticed that the degree of sequence similarity between the proteins of different species could be used to estimate their phylogenetic relationship. Since then models have been developed to improve the accuracy of phylogenetic inferences based on amino acid or DNA sequences. Most of these models were designed to yield distance measures that are linear with time, on average. The reliability of phylogenetic reconstruction, however, depends on the variance of the distance measure in addition to its expectation. In this paper we show how the method of generalized least squares can be used to combine data types, each most informative at different points in time, into a single distance measure. This measure reconstructs phylogenies more accurately than existing non-likelihood distance measures. We illustrate the approach for a two-rate mutation model and demonstrate that its application provides more accurate phylogenetic reconstruction than do currently available analytical distance measures.