Abstract. The neutral theory often is presented as a theory of "noise" or silent changes at an isolated "molecular level," relevant to marking the steady pace of divergence, but not to the origin of biological structure, function, or complexity. Nevertheless, precisely these issues can be addressed in neutral models, such as those elaborated here with regard to scrambled ciliate genes, gRNA-mediated RNA editing, the transition from selfsplicing to spliceosomal splicing, and the retention of duplicate genes. All of these are instances of a more general scheme of "constructive neutral evolution" that invokes biased variation, epistatic interactions, and excess capacities to account for a complex series of steps giving rise to novel structures or operations. The directional and constructive outcomes of these models are due not to neutral allele fixations per se, but to these other factors. Neutral models of this type may help to clarify the poorly understood role of nonselective factors in evolutionary innovation and directionality.

According to New Synthesis doctrine, the direction of evolution is determined by selection and not by "internal causes" that act by way of propensities of variation. This doctrine rests on the theoretical claim that because mutation rates are small in comparison to selection coefficients, mutation is powerless to overcome opposing selection. Using a simple population-genetic model, this claim is shown to depend on assuming the prior availability of variation, so that mutation may act only as a "pressure" on the frequencies of existing alleles, and not as the evolutionary process that introduces novelty. As shown here, mutational bias in the introduction of novelty can strongly influence the course of evolution, even when mutation rates are small in comparison to selection coefficients. Recognizing this mode of causation provides a distinct mechanistic basis for an "internalist" approach to determining the contribution of mutational and developmental factors to evolutionary phenomena such as homoplasy, parallelism, and directionality.

Many models of evolution calculate the rate of evolution by multiplying the rate at which new mutations originate within a population by a probability of fixation. Here we review the historical origins, contemporary applications, and evolutionary implications of these "origin-fixation" models, which are widely used in evolutionary genetics, molecular evolution, and phylogenetics. Origin-fixation models were first introduced in 1969, in association with an emerging view of "molecular" evolution. Early origin-fixation models were used to calculate an instantaneous rate of evolution across a large number of independently evolving loci; in the 1980s and 1990s, a second wave of origin-fixation models emerged to address a sequence of fixation events at a single locus. Although origin fixation models have been applied to a broad array of problems in contemporary evolutionary research, their rise in popularity has not been accompanied by an increased appreciation of their restrictive assumptions or their distinctive implications. We argue that origin-fixation models constitute a coherent theory of mutation-limited evolution that contrasts sharply with theories of evolution that rely on the presence of standing genetic variation. A major unsolved question in evolutionary biology is the degree to which these models provide an accurate approximation of evolution in natural populations.

The comparative analysis of protein sequences depends crucially on measures of amino acid similarity or distance. Many such measures exist, yet it is not known how well these measures reflect the operational exchangeability of amino acids in proteins, since most are derived by methods that confound a variety of effects, including effects of mutation. In pursuit of a pure measure of exchangeability, we present (1) a compilation of data on the effects of 9671 amino acid exchanges engineered and assayed in a set of 12 proteins; (2) a statistical procedure to combine results from diverse assays of exchange effects; (3) a matrix of "experimental exchangeability" values EX ij derived from applying this procedure to the compiled data; and (4) a set of three tests designed to evaluate the power of an exchangeability measure to (i) predict the effects of amino acid exchanges in the laboratory, (ii) account for the disease-causing potential of missense mutations in the human population, and (iii) model the probability of fixation of missense mutations in evolution. EX not only captures useful information on exchangeability while remaining free of other effects, but also outperforms all measures tested except for the best-performing alignment scoring matrix, which is comparable in performance. M EASURES of the pairwise distance (or similarity) of rate at which mutation introduces new alleles (Kimura amino acids provide the basis for scoring schemes 1983). in the alignment of sequences (Henikoff and Henikoff Although mutational effects are rarely treated as im-1993) and in other types of comparative analysis (Wen portant phenomena in their own right, they appear to et Yang et al. 1998; Atchley et al. 2001; Alexbe extremely important. For instance, each nonidentiandre and Zhulin 2003). A great many such matrices cal amino acid pair can be assigned a "genetic code disexist: an incomplete listing available from the AAIndex tance" G ij ʦ {1, 2, 3} equal to the minimum number of database (Kawashima and Kanehisa 2000) includes 83 nucleotides that must be changed to switch from amino matrices of pairwise amino acid similarity or distance acid i to amino acid j; the different categories someand 494 indices of amino acid properties. Formally retimes are referred to as "singlet," "doublet," and "triplet" lated to these are various schemes to distinguish "conexchanges. The practical importance of genetic code disservative" from "radical" amino acid changes (Hughes tance is amply demonstrated by the effectiveness of Fitch's et al. 1990; Hughes 1992;Rand et al. 2000; Zhang 2000).matrix of "mutational" distance (Fitch 1966) as a source A tacit assumption has been that the ultimate yardof match scores for protein sequence alignment (Feng stick for measuring amino acid similarity is the propenet al. 1985). Furthermore, pairs of amino acids with the sity for evolutionary change from one amino acid to ansame genetic code distance may differ in the density other. However, evolutionary transition probabilities, of minimum-length muta...

While mutational biases strongly influence neutral molecular evolution, the role of mutational biases in shaping the course of adaptation is less clear. Here we consider the frequency of transitions relative to transversions among adaptive substitutions. Because mutation rates for transitions are higher than those for transversions, if mutational biases influence the dynamics of adaptation, then transitions should be overrepresented among documented adaptive substitutions. To test this hypothesis, we assembled two sets of data on putatively adaptive amino acid replacements that have occurred in parallel during evolution, either in nature or in the laboratory. We find that the frequency of transitions in these data sets is much higher than would be predicted under a null model where mutation has no effect. Our results are qualitatively similar even if we restrict ourself to changes that have occurred, not merely twice, but three or more times. These results suggest that the course of adaptation is biased by mutation.