MOLECULAR EVOLUTION OVER THE MUTATIONAL LANDSCAPE

A common observation in phylogenetic comparisons of the amino acid sequences of a particular protein is that the rate of evolution of the protein is nearly constant over extended periods of time. This constancy was first noticed by Zuckerkandl and Pauling (1965) and prompted them to call the amino acid substitution process a "molecular evolutionary clock. " Since 1965 a great deal of additional data has supported the basic idea of the molecular clock although detailed studies have shown the clock to be a rather erratic one. The detailed studies have been of two different sorts: broadly based statistical studies of a number of proteins over relatively few species (e.g., Langley and Fitch, 1974), or very detailed looks at a particular protein over a large number of species (e.g., Baba et al., 1981). In general, these studies support the crucial observation made by Ohta and Kimura (1971) that the variance in the evolutionary rate is higher than would be expected if the substitution process were a Poisson process. A major goal of theoretical population genetics must be to account for this elevated variance. There are formidable statistical problems associated with the estimation of the variance in the rate of substitutions of amino acids. The problem is compounted by the fact that the variance is only interesting when compared to the mean as in the ratio K = Var(N,)/E(N1), where N, is the number of substitutions in a period of time, t. Obtaining accurate estimates of ratios is difficult in the best of statistical settings. For protein evolution data where the number of substitutions on each leg must themselves be inferred by a procedure such as Fitch and Margoliash's (1967) maximum parsimony procedure, the sampling variance of the final estimate must be relatively high (and itself almost impossible to estimate). Nonetheless, a number of studies have all pointed to a value of K of around 2 to 3. Ohta and Kimura (1971) were the first to estimate K and did so using the available data on hemoglobins and cytochrome c. They reported a value in the range 1.5 to 2.5. The studies by Langley and Fitch (1974) improved on this in the sense of using more data although their procedure was not expressly designed to estimate K. They concluded K was around 2.5. Later, Gillespie and Langley (1979) re-examined the statistical procedure used in the earlier studies and through a very crude argument also claimed that K was around 2.5. In studies that examine only a single protein over a large number of species the aim has been not so much to estimate K as to look more directly for periods of relatively fast or slow evolution in the protein. These studies, such as those by Goodman et al. (1982) generally present fairly convincing evidence of variations in the rates of evolution although Kimura (1981) has called into question the ability of these studies to uncover variation in the rates of evolution. These observations are critical for an understanding of the forces responsible for amino acid substitutions. One of the most appealing theories for the evolution of proteins is the neutral allele theory first proposed by Kimura (1968a, 1968b) and King and Jukes (1969). This theory predicts that the rate of substitutions will be constant although it does not imply that K will equal one as has been commonly assumed. Rather it was shown by Gillespie and Langley (1979) that K will always be greater than one under the neutral allele theory and will actually increase with