Adaptation at specific loci. VII. Natural selection,dispersal and the diversity of molecular-functional variation patterns among butterfly species complexes (Colias: Lepidoptera,Pieridae)

Natural genetic variants at the phosphoglucose isomerase, PGI, gene differ in spatial patterning of their polymorphism among species complexes of Colias butterflies in North America. In both lowland and alpine complexes, molecular-functional properties of the polymorphic genotypes can be used to predict genotype-specific adult flight performances and resulting large genotypic differences in adult fitness components. In the lowland species complex, there is striking uniformity of PGI polymorph frequencies at a number of sites across the American West; this fits with earlier findings of strong, similar differences in fitness components over this range. In an alpine complex, Colias meadii shows similar uniformity of PGI frequencies within habitat types, either montane steppe or alpine tundra, over several hundred kilometres in the absence of dispersal. At the same time, large shifts (10-20%) in frequency of the most common alleles occur between steppe and tundra populations, whether these are isolated or, as in some cases, are in contact and exchange many dispersing adults each generation. Data on male mating success of common C. meadii PGI genotypes in steppe and tundra show heterozygote advantage in both habitat types, with shifts in relative homozygote disadvantage between habitats which are consistent with observed frequency differences. Nonadaptive explanations for this situation are rejected, and alternative, thermal-ecology-based adaptive hypotheses are proposed for later experimental test. These findings show that strong local selection may dominate dispersal as an evolutionary agent, whether or not dispersal is present, and that selection may often be the major force promoting 'cohesion' of species over long distances. This case offers new opportunities for integrating studies of molecular structure and function with ecological aspects of natural selection in the wild, both within and among species.     

Human-chimpanzee DNA sequence variation in the four major genes of the renin angiotensin system

The renin angiotensin system (RAS) is involved in blood pressure control and water/sodium metabolism. The genes encoding the proteins of this system are candidate genes for essential hypertension. The RAS involves four main molecules: angiotensinogen, renin, angiotensin I-converting enzyme, and the angiotensin II type 1 receptor (encoded by the genes AGT, REN, DCP1, and AGTR1, respectively). We performed a molecular screening over 17,037 bp of the coding and 5' and 3' untranslated regions of these genes, from three to six common chimpanzees. We identified 44 single-nucleotide polymorphisms (SNPs) in chimpanzee samples, including 18 coding-region SNPs, 5 of which led to an amino acid replacement. We observed common and different features at various sites (synonymous, nonsynonymous, and noncoding) within and between the four chimpanzee genes: (1) the nucleotide diversity at noncoding sites was similar; (2) the nucleotide diversity at nonsynonymous sites was low, probably reflecting purifying selection, except for the AGT gene; (3) the nucleotide diversity at synonymous sites, which was dependent on the G+C content at the third position of the codon, was high, except for the AGTR1 gene. Comparison of the chimpanzee SNPs with those previously reported for humans identified 119 sites with fixed differences (including 62 coding sites, 17 of which resulted in amino acid differences between the species). Analysis of polymorphism within species and divergence between species shed light on the evolutionary constraints on these genes. In particular, comparison of the pattern of mutation at polymorphic and fixed sites between humans and chimpanzees suggested that the high G+C content of the DCP1 gene was maintained by positive selection at its silent sites. Finally, we propose 68 ancestral alleles for the human RAS genes and discuss the implications for their use in future hypertension-susceptibility association studies.     

Adaptation at Specific Loci. I. Natural Selection on Phosphoglucose Isomerase of Colias Butterflies: Biochemical and Population Aspects

Electrophoretic variants of phosphoglucose isomerase (PGI) in Colias butterflies have been studied from field and laboratory viewpoints. The transmission pattern is that of a dimeric enzyme controlled by one structural gene locus. Populations usually harbor four to six allelic mobility classes. These mobility classes are shared among species complexes, though their frequencies differ widely. Preliminary Ferguson plot analysis of the variants has been carried out. Purified preparations of Colias PGI alleles are more effective in standardizing Ferguson plots than heterologous proteins, such as ferritin. Variation of Ferguson plot parameters is not an infallible guide to electrophoretically "cryptic alleles," as one putative case proved to be due to nonallele-specific effects. S, M, and F mobility classes in two Colias semispecies show the same retardation coefficients in Ferguson plots. Adults early in the flight periods of their nonoverlapping generations show genotype frequencies in Hardy-Weinberg equilibrium, but heterozygote excess develops as the insects age. Simple directional selection and large-scale population mixing are unlikely to be causes of this, although several other selection modes remain possible. Identical-by-descent lines of the four frequent-to-common alleles in C. eurytheme have been set up in culture, and enzyme has been purified from these for study of functional properties. Major differenecs in heat stability and in various kinetic parameters are found among the ten possible genotypes. In some cases, heterosis for kinetic parameters is seen; in other cases, opposing trends in kinetic function and heat stability create potential for net heterosis in function. Possible interpretations of these results in an adaptive metabolic context are discussed, and directions for further work are stated.     

Positive selection on multiple antique allelic lineages of transferrin in the polyploid Carassius auratus

Transferrin polymorphism has been studied in the polyploid Carassius auratus by cloning and sequence analysis of cDNAs from its three subspecies C. auratus gibelio, C. auratus auratus, and C. auratus cuvieri. DNA polymorphism of extremely high extent was shown for the transferrin gene by the 248 segregation sites among coding region sequences of its alleles. The deduced amino acid sequences of the transferrin alleles showed variable theoretical physicochemical parameters, which might constitute molecular basis for their electrophoretic heterogeneity. Positive selection was inferred by the replacement/synonymous ratios larger than 1 in partial allelic lineages which was subsequently confirmed by likelihood simulation under neutral or selection models. Furthermore, the correspondent sites to these selected codons were collectively located at two planes in the crystallographic structure of rabbit transferrin, which suggested that the rapid evolution of C. auratus transferrin might correlate to its adaptation to variable environmental elements such as oxygen pressure. The minimal 26 recombination events were detected among coding sequences of C. auratus transferrin, with partial mosaic sequences and breakpoints identified by identity scanning and information site analyses. Phylogenetic analyses revealed multiple antique allelic lineages of transferrin, which was estimated to diverge fifteen to twenty MYA. All these features strongly suggested the role of balancing selection in long persistence of high transferrin polymorphism in C. auratus. Furthermore, owing to its particular evolutionary backgrounds, the silver crucian carp might possess a distinctive balancing selection mechanism.     

Selection on amino acid substitutions in Arabidopsis

Studies of nucleotide diversity have found an excess of low-frequency amino acid polymorphisms segregating in Arabidopsis thaliana, suggesting a predominance of weak purifying selection acting on amino acid polymorphism in this inbreeding species. Here, we investigate levels of diversity and divergence at synonymous and nonsynonymous sites in 6 circumpolar populations of the outbreeding Arabidopsis lyrata and compare these results with A. thaliana, to test for differences in mutation and selection parameters across genes, populations, and species. We find that A. lyrata shows an excess of low-frequency nonsynonymous polymorphisms both within populations and species wide, consistent with weak purifying selection similar to the patterns observed in A. thaliana. Furthermore, nonsynonymous polymorphisms tend to be more restricted in their population distribution in A. lyrata, consistent with purifying selection preventing their geographic spread. Highly expressed genes show a reduced ratio of amino acid to synonymous change for both polymorphism and fixed differences, suggesting a general pattern of stronger purifying selection on high-expression proteins.     

Positive selection on an acrosomal sperm protein,M7 lysin,in three species of the mussel genus Mytilus

Marine invertebrate sperm proteins are particularly interesting because they are characterized by positive selection and are likely to be involved in prezyogotic isolation and, thus, speciation. Here, we present the first survey of interspecific and intraspecific variation of a bivalve sperm protein among a group of species that regularly hybridize in nature. M7 lysin is found in sperm acrosomes of mussels and dissolves the egg vitelline coat, permitting fertilization. We sequenced multiple alleles of the mature protein-coding region of M7 lysin from allopatric populations of mussels in the Mytilus edulis species group (M. edulis, M. galloprovincialis, and M. trossulus). A significant McDonald-Kreitman test showed an excess of fixed amino acid replacing substitutions between species, consistent with positive selection. In addition, Kolmogorov-Smirnov tests showed significant heterogeneity in polymorphism to divergence ratios for both synonymous variation and combined synonymous and nonsynonymous variation within M. galloprovincialis. These results indicate that there has been adaptive evolution at M7 lysin and, furthermore, show that positive selection on sperm proteins can occur even when postzygotic reproductive isolation is incomplete.     

Bayesian analysis suggests that most amino acid replacements in Drosophila are driven by positive selection

One of the principal goals of population genetics is to understand the processes by which genetic variation within species (polymorphism) becomes converted into genetic differences between species (divergence). In this transformation, selective neutrality, near neutrality, and positive selection may each play a role, differing from one gene to the next. Synonymous nucleotide sites are often used as a uniform standard of comparison across genes on the grounds that synonymous sites are subject to relatively weak selective constraints and so may, to a first approximation, be regarded as neutral. Synonymous sites are also interdigitated with nonsynonymous sites and so are affected equally by genomic context and demographic factors. Hence a comparison of levels of polymorphism and divergence between synonymous sites and amino acid replacement sites in a gene is potentially informative about the magnitude of selective forces associated with amino acid replacements. We have analyzed 56 genes in which polymorphism data from D. simulans are compared with divergence from a reference strain of D. melanogaster. The framework of the analysis is Bayesian and assumes that the distribution of selective effects (Malthusian fitnesses) is Gaussian with a mean that differs for each gene. In such a model, the average scaled selection intensity (gamma = N(e)s) of amino acid replacements eligible to become polymorphic or fixed is -7.31, and the standard deviation of selective effects within each locus is 6.79 (assuming homoscedasticity across loci). For newly arising mutations of this type that occur in autosomal or X-linked genes, the average proportion of beneficial mutations is 19.7%. Among the amino acid polymorphisms in the sample, the expected average proportion of beneficial mutations is 47.7%, and among amino acid replacements that become fixed the average proportion of beneficial mutations is 94.3%. The average scaled selection intensity of fixed mutations is +5.1. The presence of positive selection is pervasive with the single exception of kl-5, a Y-linked fertility gene. We find no evidence that a significant fraction of fixed amino acid replacements is neutral or nearly neutral or that positive selection drives amino acid replacements at only a subset of the loci. These results are model dependent and we discuss possible modifications of the model that might allow more neutral and nearly neutral amino acid replacements to be fixed.     

Evidence for Positive Selection within the PgiC1 Locus in the Grass Festuca ovina

The dimeric metabolic enzyme phosphoglucose isomerase (PGI, EC 5.3.1.9) plays an essential role in energy production. In the grass Festuca ovina, field surveys of enzyme variation suggest that genetic variation at cytosolic PGI (PGIC) may be adaptively important. In the present study, we investigated the molecular basis of the potential adaptive significance of PGIC in F. ovina by analyzing cDNA sequence variation within the PgiC1 gene. Two, complementary, types of selection test both identified PGIC1 codon (amino acid) sites 200 and 173 as candidate targets of positive selection. Both candidate sites involve charge-changing amino acid polymorphisms. On the homology-modeled F. ovina PGIC1 3-D protein structure, the two candidate sites are located on the edge of either the inter-monomer boundary or the inter-domain cleft; examination of the homology-modeled PGIC1 structure suggests that the amino acid changes at the two candidate sites are likely to influence the inter-monomer interaction or the domain-domain packing. Biochemical studies in humans have shown that mutations at several amino acid sites that are located close to the candidate sites in F. ovina, at the inter-monomer boundary or the inter-domain cleft, can significantly change the stability and/or kinetic properties of the PGI enzyme. Molecular evolutionary studies in a wide range of other organisms suggest that PGI amino acid sites with similar locations to those of the candidate sites in F. ovina may be the targets of positive/balancing selection. Candidate sites 200 and 173 are the only sites that appear to discriminate between the two most common PGIC enzyme electromorphs in F. ovina: earlier studies suggest that these electromorphs are implicated in local adaptation to different grassland microhabitats. Our results suggest that PGIC1 sites 200 and 173 are under positive selection in F. ovina.     

Molecular evolution of the phytochrome gene family in sorghum: changing rates of synonymous and replacement evolution

The photoreceptor phytochromes, encoded by a small gene family, are responsible for controlling the expression of a number of light-responsive genes and photomorphogenic events, including agronomically important phenotypes such as flowering time and shade-avoidance behavior. The understanding and control of flowering time are particularly important goals in sorghum cultivar development for diverse environments, and naturally occurring variation in the phytochrome genes might prove useful in breeding programs. Also of interest is whether variation observed at the phytochrome loci in domesticated sorghum, or in particular races, is a result of human selection. Population genetic studies can reveal evidence of such selection in patterns of polymorphism and divergence. In this study we report a population genetic analysis of the PHY gene family in Sorghum bicolor (L.) Moench in a diverse panel including both cultivated and wild accessions. We show that the level of nucleotide variation in all gene family members is about half the average for this species, consistent with purifying selection acting on these loci. However, the rate of amino acid substitution is accelerated at PHYC compared to the other two loci. In comparisons to a closely related sorghum species, PHYC shows a pattern of intermediate frequency amino acid changes that differ from the patterns observed in comparisons across longer evolutionary distances. There is also a departure from expected patterns of polymorphism and divergence at synonymous sites in PHYC, although the data do not fit a simple model of directional or diversifying selection. Cultivated sorghum has a level of variation similar to that of wild relatives (ssp. verticilliflorum), but many polymorphisms are subspecies-specific, including several amino acid variants.     

The genomic rate of adaptive amino acid substitution in Drosophila

The proportion of amino acid substitutions driven by adaptive evolution can potentially be estimated from polymorphism and divergence data by an extension of the McDonald-Kreitman test. We have developed a maximum-likelihood method to do this and have applied our method to several data sets from three Drosophila species: D. melanogaster, D. simulans, and D. yakuba. The estimated number of adaptive substitutions per codon is not uniformly distributed among genes, but follows a leptokurtic distribution. However, the proportion of amino acid substitutions fixed by adaptive evolution seems to be remarkably constant across the genome (i.e., the proportion of amino acid substitutions that are adaptive appears to be the same in fast-evolving and slow-evolving genes; fast-evolving genes have higher numbers of both adaptive and neutral substitutions). Our estimates do not seem to be significantly biased by selection on synonymous codon use or by the assumption of independence among sites. Nevertheless, an accurate estimate is hampered by the existence of slightly deleterious mutations and variations in effective population size. The analysis of several Drosophila data sets suggests that approximately 25% +/- 20% of amino acid substitutions were driven by positive selection in the divergence between D. simulans and D. yakuba.     

Phosphoglucose isomerases of hagfish, zebrafish, gray mullet, toad, and snake, with reference to the evolution of the genes in vertebrates

Phosphoglucose isomerase (PGI) is a protein with multiple functions. To infer its structure changes and evolution in vertebrates, we cloned cDNAs encoding PGI genes from hagfish (Paramyxine yangi), gray mullet (Mugil cephalus), zebrafish (Danio rerio), toad (Bufo melanosticus), and snake (Boiga kraepelini). Only one PGI gene was cloned in each of hagfish, toad, and snake, but two PGI genes were found in zebrafish and gray mullet, respectively. The PGI of hagfish encodes 554 amino acids, in contrast to the PGIs of bonyfishes, toad, and snake which encode 553 amino acids and the PGIs of mammals which encode 558 amino acids. Among 558 aligned amino acid sites, there are 314 sites (56.27%) totally conserved. To see if diversifying selection acts on PGI amino acids of vertebrates, we calculated the pairwise ratio of nonsynonymous versus synonymous substitution per site (Ka/Ks) and the ratio of radical amino acid changes versus conservative amino acid changes per sites (dR/dC) between PGI sequences. The average pairwise ratio between nonsynonymous substitutions per nucleotide (Ka) and synonymous substitutions per nucleotide (Ks) among vertebrate PGI sequences equals 0.047 +/- 0.019. The average pairwise ratio between radical amino acid changes and conservative amino acid changes (dR/dC) among the vertebrate PGIs equal 0.938 +/- 0.158 for charge changes, 0.558 +/- 0.085 for polarity changes, and 0.465 +/- 0.0714 when both polarity and volume are considered. There is no amino acid within the vertebrate PGIs under diversifying selection as analyzed by the method of Yang et al. (2000b). The results suggest that the present vertebrate PGIs are at evolutionary stasis and are being subjected to intense purifying selection. The purifying selection is to maintain polarity and volume of the protein but not the charge groups of amino acids. Phylogenetic analysis reveals that vertebrate PGIs can be classified into three major groups: the mammalian, amphibian-reptilian, and teleostean PGIs. The gene tree suggests that the gene duplication event of PGI in bonyfishes occurred before diversification of Acanthopterygii but after the split of bonyfishes and tetrapods. The evolution of multiple functions of PGI is discussed.     

Partial protection from cyclical selection generates a high level of polymorphism at multiple non‐neutral sites

Temporally varying selection is known to maintain genetic polymorphism under certain restricted conditions. However, if part of a population can escape from selective pressure, a condition called the “storage effect” is produced, which greatly promotes balanced polymorphism. We investigate whether seasonally fluctuating selection can maintain polymorphism at multiple loci, if cyclically fluctuating selection is not acting on a subpopulation called a “refuge.” A phenotype with a seasonally oscillating optimum is determined by alleles at multiple sites, across which the effects of mutations on phenotype are distributed randomly. This model resulted in long‐term polymorphism at multiple sites, during which allele frequencies oscillate heavily, greatly increasing the level of nonneutral polymorphism. The level of polymorphism at linked neutral sites was either higher or lower than expected for unlinked neutral loci. Overall, these results suggest that for a protein‐coding sequence, the nonsynonymous‐to‐synonymous ratio of polymorphism may exceed one. In addition, under randomly perturbed environmental oscillation, different sets of sites may take turns harboring long‐term polymorphism, thus making trans‐species polymorphism (which has been predicted as a classical signature of balancing selection) less likely.     

Evidence for the adaptive evolution of the carbon fixation gene rbcL during diversification in temperature tolerance of a clade of hot spring cyanobacteria

Determining the molecular basis of enzyme adaptation is central to understanding the evolution of environmental tolerance but is complicated by the fact that not all amino acid differences between ecologically divergent taxa are adaptive. Analysing patterns of nucleotide sequence evolution can potentially guide the investigation of protein adaptation by identifying candidate codon sites on which diversifying selection has been operating. Here, I test whether there is evidence for molecular adaptation of the carbon fixation gene rbcL for a clade of hot spring cyanobacteria in the genus Synechococcus that has diverged in thermotolerance. Amino acid replacements during Synechococcus radiation have resulted in an increase in the number of hydrophobic residues in the RbcLs of more thermotolerant strains. A similar increase in hydrophobicity has been observed for many thermostable proteins. Maximum likelihood models which allow for heterogeneity among codon sites in the ratio of nonsynonymous to synonymous nucleotide substitutions estimated a class of amino acid sites as a target of positive selection. Depending on the model, a single amino acid site that interacts with a flexible element involved in the opening and closing of the active site was estimated with either low or moderate support to be a member of this class. Site-directed mutagenesis approaches are being explored in order to directly test its adaptive significance.     

Adaptation at Specific Loci. V. Metabolically Adjacent Enzyme Loci May Have Very Distinct Experiences of Selective Pressures

The polymorphic phosphoglucomutase (PGM) and glucose-6-phosphate dehydrogenase (G6PD) loci have been studied in parallel to experimental work on the phosphoglucose isomerase (PGI) polymorphism in Colias butterflies. PGI, PGM and G6PD are also autosomal in Colias. PGM and G6PD are loosely linked (and represent the first identified autosomal linkage group in Colias); they assort independently from PGI. Recombination occurs in both sexes. Neither PGM nor G6PD shows large, consistent differences in flight capacity through the day among its genotypes, as PGI does. PGM shows some change of allele frequencies, and match to Hardy-Weinberg expectation, with air temperature in middle and latter parts of the season, but not early in the season. G6PD may show some heterozygote excess over Hardy-Weinberg expectation early in the day, but more testing is needed. No evidence for differential survivorship was seen at PGM or G6PD, in contrast to PGI. At the PGM and G6PD loci, male heterozygotes are advantaged in mating with females, but without the evidence of female choice which occurs for PGI. These effects are not correlated among the three loci. There is no assortative mating at G6PD (nor at PGI). There is minor positive assortative mating of PGM heterozygotes, but it is too weak to account for the PGM-genotype-specific male mating advantage. No trends of multilocus genotype frequencies involving PGI are seen. Certain PGM-G6PD two-locus genotypes are over-represented, and others under-represented, in wild adult samples, particularly among males and uniformly among successfully mating males. Our results emphasize that enzyme loci sharing a substrate need not have common experience of the existence or strength of natural selection, and suggest initial food-resource processing and allocation as a possible context for fitness-related effects of the PGM and G6PD polymorphisms.     

Selection efficiency and effective population size in Drosophila species

A corollary of the nearly neutral theory of molecular evolution is that the efficiency of natural selection depends on effective population size. In this study, we evaluated the differences in levels of synonymous polymorphism among Drosophila species and showed that these differences can be explained by differences in effective population size. The differences can have implications for the molecular evolution of the Drosophila species, as is suggested by our results showing that the levels of codon bias and the proportion of adaptive substitutions are both higher in species with higher levels of synonymous polymorphism. Moreover, species with lower synonymous polymorphism have higher levels of nonsynonymous polymorphism and larger content of repetitive sequences in their genomes, suggesting a diminished efficiency of selection in species with smaller effective population size.     

Gene conversion as a source of nucleotide diversity in Plasmodium falciparum

Examination of polymorphisms in the Plasmodium falciparum gene for falcipain 2 revealed that this gene is one of two paralogs separated by 10.8 kb in chromosome 11. We designate the annotated gene denoted chr11.gen_424 as encoding falcipain 2A and the annotated gene denoted chr11.gen_427 as encoding falcipain 2B. The paralogs are 96% identical at the nucleotide level and 93% identical at the amino acid level. The consensus sequences differ in 31/309 synonymous sites and 45/1140 nonsynonymous sites, including three amino acid replacements (V393I, A400P, and Q414E) that are near the catalytic site and that may affect substrate affinity or specificity. In six reference isolates, among 36 synonymous sites and 46 nonsynonymous sites that are polymorphic in the gene for falcipain 2A, falcipain 2B, or both, significant spatial clustering is observed. All but one of the polymorphisms appear to result from gene conversion between the paralogs. The estimated rate of gene conversion between the paralogs may be as many as 1,400 to 1,700 times greater than the rate of mutation. Owing to gene conversion, one of the falcipain 2A alleles is more similar to the falcipain 2B alleles than it is to other falcipain 2A alleles. Divergence among the synonymous sites suggests that the paralogous genes last shared a common ancestor 15.2 MYA, with a range of 8.8 to 20.6 MYA. During this period, the paralogs have acquired 0.10 synonymous substitutions per synonymous site in the coding region. The 5' and 3' flanking regions differ in 47.7% and 39.8% of the nucleotide sites, respectively. Hence synonymous sites and flanking regions are not conserved in sequence in spite of their high AT content and T skew.     

Adaptive evolution of a key gene affecting queen and worker traits in the honey bee, Apis mellifera

The vitellogenin egg yolk precursor protein represents a well-studied case of social pleiotropy in the model organism Apis mellifera. Vitellogenin is associated with fecundity in queens and plays a major role in controlling division of labour in workers, thereby affecting both individual and colony-level fitness. We studied the molecular evolution of vitellogenin and seven other genes sequenced in a large population panel of Apis mellifera and several closely related species to investigate the role of social pleiotropy on adaptive protein evolution. We found a significant excess of nonsynonymous fixed differences between A. mellifera, A. cerana and A. florea relative to synonymous sites indicating high rates of adaptive evolution at vitellogenin. Indeed, 88% of amino acid changes were fixed by selection in some portions of the gene. Further, vitellogenin exhibited hallmark signatures of selective sweeps in A. mellifera, including a significant skew in the allele frequency spectrum, extreme levels of genetic differentiation and linkage disequilibrium. Finally, replacement polymorphisms in vitellogenin were significantly enriched in parts of the protein involved in binding lipid, establishing a link between the gene's structure, function and effects on fitness. Our case study provides unequivocal evidence of historical and ongoing bouts of adaptive evolution acting on a key socially pleiotropic gene in the honey bee.     

Population Genetics of Polymorphism and Divergence

Frequencies of mutant sites are modeled as a Poisson random field in two species that share a sufficiently recent common ancestor. The selective effect of the new alleles can be favorable, neutral, or detrimental. The model is applied to the sample configurations of nucleotides in the alcohol dehydrogenase gene (Adh) in Drosophila simulans and Drosophila yakuba. Assuming a synonymous mutation rate of 1.5 x 10(-8) per site per year and 10 generations per year, we obtain estimates for the effective population size (N(e) = 6.5 x 10(6)), the species divergence time (tdiv = 3.74 million years), and an average selection coefficient (sigma = 1.53 x 10(-6) per generation for advantageous or mildly detrimental replacements), although it is conceivable that only two of the amino acid replacements were selected and the rest neutral. The analysis, which includes a sampling theory for the independent infinite sites model with selection, also suggests the estimate that the number of amino acids in the enzyme that are susceptible to favorable mutation is in the range 2-23 at any one time. The approach provides a theoretical basis for the use of a 2 x 2 contingency table to compare fixed differences and polymorphic sites with silent sites and amino acid replacements.