Distance measures in terms of substitution processes

Phylogenetic reconstruction from DNA or amino acid sequences relies heavily on suitable distance measures. A number of new distance measures (asynchro nous, LogDet, and paralinear distances) which possess the desired property of tree additivity under fairly general models of sequence evolution have b een proposed recently, but they are not well understood from a mechanistic point of view. We review them here in a unifying framework, which is the su bstitution process in continuous time. The emerging interpretation will als o clarify the relationship among these distance measures. We also tackle si tuations with site-to-site variation of substitution rates which is well kn own to cause non-additive distances and inconsistent branch lengths. For ho mogeneous, stationary, time-reversible models, this may be repaired provide d that the distribution of rates is known, In contrast, we will show that, for non-stationary models, different tree topologies may produce identical joint distributions of letters in pairs of sequences, given the same distri bution of rates. This precludes the existence of any tree-additive pairwise distance measure, (C) 1999 Academic Press.