Indel-Based Evolutionary Distance and Mouse–Human Divergence

Evolutionary distance (ED) between two homologous DNA sequences is defined as the per nucleotide site number of mutations that have been fixed in the course of evolution of the sequences from their last common ancestor. For not-too-tightly related sequences, ED exceeds their dissimilarity (DS), the per site number of differences between the properly aligned sequences. This happens because several mutations can affect the same site. Different methods of inferring the number of such multiple hits from the observed DS often produce rather different estimates of ED (see Li 1997; Nei and Kumar 2000). For example, figures for Ks, the number of substitutions per synonymous site, range from 0.45 (Makalowski and Boguski 1998) to 0.60 (Waterston et al. 2002; Rat Genome Sequencing Project Consortium 2004), 0.65 (Cooper et al. 2004), 0.73 (Castresana 2002), and 0.74–0.80 (Smith and Eyre-Walker 2003; Table 1) for the evolutionary path between mouse and human. Table 1. Summary of Notations ED is usually estimated on the basis of single nucleotide substitutions. Then, each site serves as an independent timer, which is advantageous when only short sequences are available. However, substitution-based ED also has two substantial limitations. First, as DS at single-site timers can assume only two states (match or mismatch), it rapidly reaches saturation when ED increases. In the simplest case of equally frequent nucleotides and no selective constraint, DS approaches 0.75 and ED is almost impossible to estimate when the number of hits per timer exceeds two or three (see Li 1997; Nei and Kumar 2000). Thus, ED between even moderately distant species can be determined only for slowly evolving non-neutral sequences. The rate of evolution of sequences affected by selection depends not only on the mutation rate, but also on the population size and the mode and strength of selection. Second, even when the number of hits per neutral site is below one or two, so that recovering ED from DS may be feasible, selectively neutral sequences often cannot be used, due to their unreliable alignments. Even for placental mammals from different orders, accumulated insertions and deletions often make it impossible to establish homology of individual sites within introns and other noncoding sequences (Shabalina et al. 2001). Thus, ED can be estimated only for sites that are embedded into conservative sequences, such as synonymous coding sites. However, synonymous sites are not entirely free from selective constraint (Hellman et al. 2003). Thus, it may be preferable to estimate ED on the basis of length-difference mutations, insertions, and deletions (indels). Then, a timer is the segment of the sequence delimited by unambiguous markers, for example, an intron flanked by conservative exons. Availability of large-scale sequence data makes such long timers acceptable. If homologous timer sequences are similar enough to allow their unambiguous alignments, the indel-based ED between them must be close to their indel-based DS, the number of gaps in their alignment over its length. Recently, methods of phylogenetic reconstruction based on individually recognizable indels become available (see Sanchis et al. 2001). However, indel-based ED between more distant, unalignable timer sequences must be estimated from the differences between their lengths. Indel-based ED is less prone to saturation than substitution-based ED, due to two factors. First, lengths of two homologous segments of DNA can diverge almost without a limit. Second, as indels are less common than substitutions, even distant sequences can be compared without encountering too many hits. This study is concerned with estimating indel-based ED between unalignable timer sequences. We derive a maximal likelihood estimate of indel-based ED, test it by recovering the known ED between rat and mouse, and apply it to estimate ED between mouse and human.