Asynchronous Distance between Homologous DNA Sequences

Abstract

The distance between homologous DNA sequences of two species is proposed to be -1/4 ln[det(P)], where P is the conditional probability matrix specifying the proportions of the various nucleotides in the second sequence, corresponding to each of the four nucleotides in the first sequence. A probability model is described which supports this choice of distance. Distance measures based on a constant evolutionary rate assumption are described and compared with the proposed measure. Sampling properties of both types of distance are examined and we conclude by applying the distance measures to mitochondrial DNA sequences of the hominoids.

Using the tangle: A consistent construction of phylogenetic distance matrices for quartets

“…This property of CTMCs and their time-reversed counterparts was observed by Barry and Hartigan [1]. It can be seen that in the stationary case (19) will certainly be true.…”

“…If one assumes the standard Markov model, the edge lengths of a phylogenetic tree can be taken mathematically to be a quantity which we refer to as the stochastic distance. (For mathematical discussion of this quantity see Goodman [8] who refers to the stochastic distance as intrinsic time, and see also Barry and Hartigan [1] who gave a biological interpretation.) Under the assumptions of a general Markov model the log det formula is commonly used to obtain pairwise distances.…”

Estimation of evolutionary distances from protein spatial structures

“…Thus a variety of models to estimate distance d ij from the fraction of different residues p ij are proposed (Zuckerkandl and Pauling 1965;Dayhoff et al 1972Dayhoff et al , 1978Uzzel and Corbin, 1971;Holmquist et al 1983;Wilbur 1985;Barry and Hartigan 1987;Ota and Nei 1994;Zharkikh 1994;Tajima and Takezaki 1994;Grishin 1995). Analysis of alignments (Dayhoff et al 1978) used for estimation of relation between distance d ij and fraction of identical residues q ij ‫ס‬ 1 − p ij misses some back substitutions for the case of lower similarity between sequences.…”

A general additive distance with time-reversibility and rate variation among nucleotide sites.

“…17, the ijth element of P(2t) can be estimated by [14] 4672 Evolution: Gu and Li Pi. Cov(dl, d2) = E qi qj ICv(z, 42)) [22] i,j=l and under the SRV model 3 Cov(dl, d2) = E I a2)) + 4(.4( Var(a), [23] i,j=1…”