Inferring the Fitness Effects of DNA Mutations From Polymorphism and Divergence Data: Statistical Power to Detect Directional Selection Under Stationarity and Free Recombination

Corresponding author: Hiroshi Akashi, Haworth Hall, University of Kansas, Lawrence, KS 66045-2106., hakashi{at}falcon.cc.ukans.edu (E-mail)

Communicating editor: A. G. CLARK

	ABSTRACT

TOP ABSTRACT NATURAL SELECTION AND THE... CONFIGURATION TESTS BETWEEN... CONFIGURATION TESTS OF... NONNEUTRAL SILENT SITES AND... DISCUSSION APPENDIX 1 LITERATURE CITED

The fitness effects of classes of DNA mutations can be inferred from patterns of nucleotide variation. A number of studies have attributed differences in levels of polymorphism and divergence between silent and replacement mutations to the action of natural selection. Here, I investigate the statistical power to detect directional selection through contrasts of DNA variation among functional categories of mutations. A variety of statistical approaches are applied to DNA data simulated under Sawyer and Hartl's Poisson random field model. Under assumptions of free recombination and stationarity, comparisons that include both the frequency distributions of mutations segregating within populations and the numbers of mutations fixed between populations have substantial power to detect even very weak selection. Frequency distribution and divergence tests are applied to silent and replacement mutations among five alleles of each of eight Drosophila simulans genes. Putatively "preferred" silent mutations segregate at higher frequencies and are more often fixed between species than "unpreferred" silent changes, suggesting fitness differences among synonymous codons. Amino acid changes tend to be either rare polymorphisms or fixed differences, consistent with a combination of deleterious and adaptive protein evolution. In these data, a substantial fraction of both silent and replacement DNA mutations appear to affect fitness.

THE evolutionary fate of a DNA sequence mutation is governed by genetic drift, demographic processes, and natural selection acting directly on the mutation or indirectly through its effect on closely linked mutations. Distinguishing among the roles of each of these factors in patterning within- and between-species genetic variation is a central goal of population genetics (LEWONTIN 1974 ). In particular, the shape of the distribution of fitness effects of mutations remains a contentious issue (KIMURA 1983 ; GILLESPIE 1991 ; OHTA 1992 ; TAKAHATA 1996 ).

A number of approaches attempt to infer evolutionary processes by comparing patterns of DNA variation from a given genetic region to those predicted under a specified evolutionary model (i.e., WATTERSON 1978 ; STROBECK 1987 ; TAJIMA 1989 ; HUDSON et al. 1992 , HUDSON et al. 1994 ; FU and LI 1993 ; BRAVERMAN et al. 1995 ; SIMONSEN et al. 1995 ; FU 1996 , FU 1997 ; KELLY 1997 ). The most common null model assumes an infinite number of mutable sites, no natural selection, no recombination, a stationary frequency distribution of segregating mutations, and a Wright-Fisher demographic model. Rejection of the null hypothesis can be caused by a number of departures from these assumptions including changes in population size, population subdivision, genetic linkage to adaptive and deleterious mutations, and selection on the mutations themselves (STROBECK 1987 ; HUDSON et al. 1992 ; BRAVERMAN et al. 1995 ; CHARLESWORTH et al. 1995 ; SIMONSEN et al. 1995 ; FU 1996 , FU 1997 ). However, distinguishing between the contributions of demographic history and natural selection to a given departure from the null can be difficult. For example, patterns of neutral DNA sequence variation closely linked to a site that has undergone a recent adaptive substitution or "selective sweep" are similar to those in an expanding population (SIMONSEN et al. 1995 ). Alternatively, patterns of neutral DNA variation linked to a site at which a polymorphism is maintained by balancing selection can be similar to sequence variation sampled from subdivided populations (HUDSON 1990 ).

A second class of approaches compares patterns of DNA variation between two or more genetic regions (HUDSON et al. 1987 ; MCDONALD 1996 , MCDONALD 1998 ; HEY 1997 ). Such comparisons attempt to distinguish between the effects of demographic history, which should have a roughly equal impact throughout the genome, and natural selection, whose effect may be more localized. Although the statistical power of this approach to detecting particular scenarios of evolution has not been investigated, regional differences in levels of polymorphism, or in the frequency distributions of mutations, could result from either balancing selection elevating linked neutral variation or directional selection reducing neutral polymorphism. However, between-region comparisons neither identify the particular site(s) under selection nor address what fraction of segregating or fixed mutations affects fitness.

Comparisons of evolutionary patterns between categories of mutations interspersed within a genetic region attempt to identify the direct action of natural selection. If the classes of mutations (such as replacement and silent changes) are randomly interspersed within a genetic region, then population level effects and selection at linked sites are expected to have a roughly equivalent impact on mutations in the two classes (HUDSON 1993 ). Thus, differences in the frequency distributions of polymorphic mutations (SAWYER et al. 1987 ) and in the ratios of polymorphic and fixed mutations (MCDONALD and KREITMAN 1991 ; TEMPLETON 1996 ; AKASHI 1997A ) should reflect differences in the fitness effects of the mutations. A number of claims of adaptive (MCDONALD and KREITMAN 1991 ; EANES et al. 1993 ; LONG and LANGLEY 1993 ; KAROTAM et al. 1995 ; KING 1998 ), deleterious (SAWYER et al. 1987 ; BALLARD and KREITMAN 1994 ; NACHMAN et al. 1994 , NACHMAN et al. 1996 ; Rand et al. 1994 ; AKASHI 1996 ; TEMPLETON 1996 ; WISE et al. 1998 ), and balancing (WAYNE et al. 1996 ) selection on amino acid variants, mutation-selection-drift at silent sites (BALLARD and KREITMAN 1994 ; AKASHI 1995 , AKASHI 1997A ; AKASHI and SCHAEFFER 1997 ), and deleterious effects of transposable element insertions (GOLDING et al. 1986 ) rely on such comparisons.

Although a growing number of studies are inferring evolutionary processes from comparisons among interspersed mutations, the sensitivity and robustness of this approach to detecting selection have not been examined. Here, I investigate the statistical power to detect directional selection through comparisons of patterns of variation between putative fitness classes of DNA mutations. All results are obtained under Sawyer and Hartl's Poisson random field model (SAWYER and HARTL 1992 ; HARTL et al. 1994 ) under assumptions of stationarity, free recombination, and independent fitness effects (results under departures from these assumptions will be addressed in a separate study). The performance of a number of statistical tests is compared over a wide range of selection intensities and sample sizes of DNA sequences. Such tests are applied to DNA sequence data from eight Drosophila simulans genes to determine the contribution of natural selection in silent and protein evolution.

	NATURAL SELECTION AND THE EXPECTED CONFIGURATIONS OF MUTATIONS

TOP ABSTRACT NATURAL SELECTION AND THE... CONFIGURATION TESTS BETWEEN... CONFIGURATION TESTS OF... NONNEUTRAL SILENT SITES AND... DISCUSSION APPENDIX 1 LITERATURE CITED

Kimura and Ohta treat gene frequency changes within populations and the accumulation of fixed differences between populations as two facets of an underlying process of evolution under relatively constant mutation rates, effective population sizes, and (for some mutations) directional selection (KIMURA and OHTA 1971 ; KIMURA 1983 ). Positive selection increases the probability that a mutation will rise in frequency in each generation, whereas negative selection has the opposite effect. However, except for very strong selection, the time scale of the process is on the order of N_e, the effective population size, generations. Inferring the fitness effects of mutations by measuring the evolutionary trajectories (frequency changes) of individual mutations in laboratory or natural populations requires relatively strong deterministic forces (s > 0.001; DYKHUIZEN and HARTL 1983 ). In large populations, much weaker selection (s > 1/N_e) can have an important impact in long-term evolution (FISHER 1930 ; WRIGHT 1931 ; KIMURA 1962 ; OHTA 1973 ) but cannot be measured directly. For such mutations, the trajectories of the mutations, and thus their fitness effects, can be inferred by sampling two aspects of the evolutionary process. A "snapshot" of evolution can be obtained by comparing alleles from within a population; the data consist of the number of segregating sites and their frequencies in the sample. The numbers of mutations "fixed" between an outgroup and the most recent common ancestor of the population sample can be inferred by examining sequences from closely related species.

Consider an aligned set of DNA sequences from m individuals from a population and at least one sequence from an outgroup. Assume an infinite number of mutable sites in these sequences so that all mutations occur at unique sites. Assume first that ancestral and derived nucleotides can be determined at sites that vary in the sample and at sites that differ between the sample and the outgroup. At a given variable site, the nonancestral nucleotide will be found in r = 1 to m of the sequences. The distribution of nonancestral nucleotides falling into the r frequency classes will be referred to as the "configuration" of mutations [to distinguish the pattern from the "frequency distribution" of mutations that is often used to describe polymorphic mutations (r = 1 to m - 1)]. Mutations in frequency class m will be referred to as "fixed" between the sample and the outgroup. In the absence of information about the ancestral and derived nucleotides at variable sites, the configuration can be "folded-over" by pooling each pair of frequency classes r = i and r = m - i for all integers, 1 i m/2.

Figure 1 illustrates the quantitative effects of directional selection on the expected configurations of mutations. Positive directional selection skews the configuration toward a larger proportion of mutations at high frequencies within the population or fixed in the sample (Figure 1B). Negative directional selection has the opposite effect: a greater proportion of nonancestral nucleotides segregate at low frequencies (Figure 1A). However, note that under positive selection, the total expected number of variable sites in the sample increases as a function of N_es (Figure 1D), whereas under negative selection, the opposite is true (Figure 1C).

View larger version (24K): In this window In a new window Download PPT slide   Figure 1. Expected configurations of neutral and selected mutations. The expected numbers of newly arisen mutations at frequency classes r = 1 to m in a sample of sequences were calculated according to SAWYER and HARTL 1992 and HARTL et al. 1994 . Data are shown for m = 5 sequences and tdiv = 0.6. a and b show the expected proportion of variable sites in the sample at different frequencies under negative and positive selection, respectively. c and d show the proportion of mutable sites at which variants are expected to be segregating at different frequencies or fixed in the sample under negative and positive selection, respectively. Note that the scales for the y-axis differ for c and d. For m = 5, pooling classes r = 1 and r = 4, and r = 2 and r = 3 would give a folded-over distribution with three frequency classes. Superscript f denotes "fixed" difference class (r = m). In this figure, and in the following figures, the scales of unlabeled x- and y-axes are equivalent to those of graphs in the same columns and rows, respectively.

GOLDING et al. 1986 and SAWYER et al. 1987 were the first to infer differences in the average fitness effects of mutations by contrasting within- and between-species variation among functional classes of DNA changes. SAWYER et al. 1987 suggested a simple comparison of the frequency distributions of silent and replacement polymorphisms in a 2 x 2 contingency table. Their data did not include an outgroup sequence, so the analyses were confined to polymorphism data with unknown ancestral and derived states (folded configurations). They divided segregating mutations into two frequency classes, "singletons" (r = 1 and r = m - 1) and other frequency classes (1 < r < m - 1). A departure from homogeneity in these classes among silent and replacement changes was interpreted as evidence for differences in the fitness effects of the mutations.

MCDONALD and KREITMAN 1991 included between-species variation in a similar test of homogeneity among frequency classes for silent and replacement mutations. Their 2 x 2 contingency table compares the numbers of polymorphic mutations, pooled across frequency classes (1 r < m), and the numbers of fixed differences (r = m). Because directional selection has a strong impact on the fixed differences class (Figure 1), including this information is likely to increase the sensitivity of the statistical approach to detect selection. However, by pooling all polymorphic mutations into a single category, McDonald and Kreitman's test sacrifices information from the frequency distribution of segregating mutations.

TEMPLETON 1996 combined the approaches of SAWYER et al. 1987 and MCDONALD and KREITMAN 1991 by expanding the contrast to a test of homogeneity across three frequency classes. The numbers of singleton polymorphisms (r = 1 and r = m - 1), polymorphisms at intermediate frequencies (1 < r < m - 1), and fixed differences (r = m) were compared between silent and replacement mutations. The statistical test examines information from both the folded frequency distribution of segregating mutations and the numbers of fixed differences, but information for polymorphic mutations segregating at frequencies greater than one is lost by pooling such variants into a single category.

The statistical power to detect selection through these approaches could, in principle, be enhanced by including more information from the sample and by employing a statistical test that is more sensitive to deviations caused by the particular alternative hypotheses of interest (AKASHI 1997A ). Because even very weak selection affects the expected proportion of mutations in each frequency class, treating each class (1 r < m) as a distinct category may increase the sensitivity of the approach. In addition, outgroup sequences can be used to infer ancestral and derived states at variable positions so that r = i and r = m - i classes do not have to be pooled. Finally, under the Poisson random field model, directional selection has a strong effect on the means of the configurations of mutations (Figure 1). Statistical comparisons that are more sensitive to differences in the location of distributions may be more powerful for detecting fitness effects of mutations than tests of homogeneity.

	CONFIGURATION TESTS BETWEEN NEUTRAL AND SELECTED MUTATIONS

TOP ABSTRACT NATURAL SELECTION AND THE... CONFIGURATION TESTS BETWEEN... CONFIGURATION TESTS OF... NONNEUTRAL SILENT SITES AND... DISCUSSION APPENDIX 1 LITERATURE CITED

SAWYER et al. 1987 identified the fitness effects of amino acid mutations by comparing the configurations of silent and replacement mutations within coding regions in DNA. Assuming neutral evolution at silent sites, a configuration of amino acid mutations skewed toward an excess of rare polymorphisms reflects deleterious amino acid mutations, whereas an excess of common or fixed amino acid differences supports adaptive protein evolution. The analyses below investigate the statistical power to detect selection through such comparisons between neutral and selected mutations.

Sawyer and Hartl's Poisson random field model allows relatively straightforward simulation of DNA variation data under directional selection. The model assumes a Wright-Fisher population of haploid individuals, an infinite number of mutable sites, a stationary frequency distribution of segregating mutations, and independent evolution at all sites (free recombination and independent fitness effects of mutations). Under these assumptions, the numbers of mutations in each frequency class in the configuration (r = 1 to m) are independent Poisson random variables whose means can be calculated according to the equations of SAWYER and HARTL 1992 and HARTL et al. 1994 . These means are a function of five parameters: N_e, the species effective population size; u, the expected number of mutations per nucleotide site, per generation; l, the number of aligned nucleotide sites; m, the number of alleles sampled from a given population; t_div, the time of divergence between the population sampled and the outgroup (scaled to N_e generations); and s, the selective effect of mutations. Note that number of "alleles" refers to the number of chromosomes sampled from a population regardless of whether any pairs of the DNA sequences are identical or not.

In the following power tests, N_e and u were fixed and the other parameters were varied over a range of interest. N_e = 10⁶ (KREITMAN 1983 ) and u = 10^-9 (MORIYAMA 1987 ; ROWAN and HUNT 1991 ) correspond to rough estimates for these parameters in Drosophila. Statistical power was examined for m = 5, 10, 25, and 50 alleles and for l = 500, 1000, 2500, and 5000 mutable sites. Selection coefficients were varied between -100 N_es 100, and the time of divergence between the sampled alleles and the outgroup was varied between t_div = 0.6, 1.2, 2.4, and 4.8. The lower t_div value was that estimated from intron polymorphism and divergence data in D. simulans since its split with its sister species, D. melanogaster (see AKASHI and SCHAEFFER 1997 ). The upper value corresponds to ~10% expected divergence at neutral sites. For a given set of parameter values, mutations at half of the sites were neutral and the other half were selected. Simulations were also conducted for 20% neutral and 80% selected sites and for 80% neutral and 20% selected sites. In all simulations, selection coefficients were uniform for all mutations within each category.

For each set of five parameters, the expected values of the numbers of neutral and selected mutations in each frequency class in the configuration were calculated according to the equations of Table 2 of SAWYER and HARTL 1992 and Equation 2 of HARTL et al. 1994 . The algorithm of PRESS et al. 1992 (p. 293) was used to generate 1000 simulated data sets by sampling integers from Poisson distributions with these expected values as their means. All simulations were written in the C computer language and run on Macintosh and Pentium desktop computers.

A variety of statistical tests was applied to each of the simulated data sets. For polymorphism (frequency distribution) data, the tests examined were as follows: SAWYER et al. 1987 2 x 2 test of independence with frequency classes r = 1 and 1 < r < m, a 2 x (m - 1) test of independence for all the frequency classes of polymorphic mutations and a Mann-Whitney U-test (MWU) for all the frequency classes (see Table 1 for abbreviations). For unfolded distributions, ancestral and derived states were assumed to be inferred without error.

For the tests of homogeneity, the probability of the data under the null hypothesis of independence was estimated through a Monte Carlo approach. For each simulated 2 x n table, the product of each cell value and its natural logarithm was summed across all cells to give a test statistic. The test statistic was also calculated for 1000 randomized tables. In a generalization of the Fisher exact test, the joint probability of cell values was assumed to be the joint hypergeometric probabilities of the cells under homogeneity for the same marginal values as the simulated table (see Appendix 1). For each simulated table, 1000 random tables were generated from these joint hypergeometric probabilities. The fraction of these random tables with a test statistic equal to, or greater than, that observed in the sample was used as the estimate of the two-tailed probability of the observed data under the null hypothesis of homogeneity in their configurations (the procedure follows that of B. ENGELS, personal communication). In these simulations, the first column of the table is generated under the assumption of selective neutrality. Rejection of the null hypothesis indicates that the test has detected significant selective effects on the distribution of cell counts in the second column of the table.

TAJIMA'S 1989 D-test was also applied to the simulated nonneutral class of variation. This procedure compares polymorphism data to expectations under an equilibrium, neutral, no recombination model. The critical values of the test statistic were taken from TAJIMA's (1989) tables. The D-test differs from the other statistical tests described above because the test compares a single class of mutations to a null model and because the critical values that are commonly employed assume no recombination rather than free recombination. Tajima's test was included for comparison because it is often applied to data from recombining regions of DNA (i.e., TAJIMA 1989 ; MORIYAMA and POWELL 1996 ) and because its power to detect the fitness effects of mutations has not been addressed.

For the tests restricted to polymorphism data, the statistical power to detect both negative and positive selection is shown in Figure 2 and Figure 3. The power to reject the null hypothesis generally increases as a function of the absolute value of N_es, but decreases for large negative values (Figure 3). The cause of this pattern is apparent from Figure 1; although the location of the distribution of mutations continues to change as selection becomes stronger, the sample size of nonneutral polymorphisms decreases to zero. For 25 alleles of 1250 neutral and selected sites, however, the power to detect even very strong negative selection is considerable. Among tests of homogeneity, the 2 x 2 test is more sensitive to negative selection, whereas the 2 x (m - 1) test is generally more powerful for N_es > 0. This appears to reflect the lack of information in the higher frequency classes for mutations under negative selection (Figure 1). Tajima's D-test performs poorly for small numbers of alleles, but is quite sensitive to negative directional selection when the number of sampled alleles is large. Positive directional selection has a smaller impact on the frequency distribution of mutations (Figure 1) and was not detectable by the Tajima D-test under any of the parameter values examined.

View larger version (19K): In this window In a new window Download PPT slide   Figure 2. Power of polymorphism configuration tests between neutral and weakly selected mutations. The y-axis plots the proportion of tests that reject fitness equivalence, P < 0.05, among 1000 simulated data sets for each value of Nes. See Table 1 for abbreviations for tests. Because each point on the graph reflects a proportion from a random binomial sample of size n = 1000, the 95% confidence intervals for the true values are ± 2[] . The relative order of the power of these tests (and those of Figure 3 Figure 4 Figure 5 Figure 6) was similar for the simulations under unequal numbers of neutral and selected sites described in the text.

View larger version (16K): In this window In a new window Download PPT slide   Figure 3. Power of polymorphism configuration tests between neutral and deleterious mutations. Plots are equivalent to those of Figure 2 for strongly deleterious mutations.

The polymorphism tests show different sensitivities to changes in the examined numbers of alleles and numbers of sites. Increasing the number of sites has a larger impact on the power of tests of independence and fdMWU tests, whereas the Tajima test gains considerably from increasing the number of sampled alleles. For the parameter ranges considered, the fdMWU test is at least as powerful, and is often considerably more powerful, than the other polymorphism tests for detecting both positive and negative directional selection.

The expected proportion of variable sites in the fixed differences class (r = m) is very sensitive to selection (Figure 1). Thus, adding divergence data to comparisons of the configurations of mutations is likely to add substantial power to detect natural selection. Four such tests were applied to simulated data. Three different tests of independence were employed, the 2 x 2 polymorphism (1 r < m) and divergence (r = m) test of MCDONALD and KREITMAN 1991 , the 2 x 3 singleton (r = 1), intermediate frequency (1 < r < m), and divergence (r = m) test of TEMPLETON 1996 , and the 2 x m frequency distribution and divergence test for unpooled frequency classes. These tests were performed as Monte Carlo tests of homogeneity (MCH) as described above. Mann-Whitney U-tests were also applied to the m frequency classes (see Table 1 for abbreviations for tests). The equivalent tests and the fdMWU test were also performed on folded distributions (ancestral and derived states not inferred). The power of statistical tests that include divergence data is shown in Figure 4 and Figure 5.

View larger version (25K): In this window In a new window Download PPT slide   Figure 4. Power of polymorphism and divergence configuration tests between neutral and weakly selected mutations. The y-axis plots the proportion of tests that reject fitness equivalence, P < 0.05, among 1000 simulated data sets for each value of Nes. See Table 1 for abbreviations for tests. TEMPLETON 1996 also suggested a "young vs. old" mutations 2 x 2 test of independence between singletons (r = 1 and r = m - 1) and all other frequency classes (1 < r < m - 1 and r = m). The power of this test was examined but the results are not shown. This test is sensitive to strong deleterious selection, especially for small sample sizes, but has little power to detect positive selection coefficients. For some parameters, the power of this test decreases with increasing numbers of alleles.

View larger version (19K): In this window In a new window Download PPT slide   Figure 5. Power of polymorphism and divergence configuration tests between neutral and deleterious mutations. The plots are equivalent to those of Figure 4 for strongly deleterious mutations.

As expected, inclusion of the fixed difference class adds a great deal of power to detect natural selection, especially for N_es > 0. Among the tests of independence, the 2 x 2 test is relatively insensitive to deleterious evolution but is roughly equivalent to the 2 x 3 test for positive selection. The 2 x m test of homogeneity was considerably less powerful than the 2 x 3 test over almost the entire range of parameters examined. Apparently, the higher frequency cells increase the degrees of freedom in the statistical test but contribute little to the test statistic both because the expected and observed values are not sufficiently different and because the values in the cells are small (Figure 1). For a small number of sites and a large number of alleles, the fdMWU test can be more sensitive to negative selection than tests of independence that include divergence. However, the fddMWU test is either equivalent to, or more powerful than, all the other tests over all parameter values examined. The difference in power is most notable when the number of alleles is large and when selection coefficients are small. For tests that include divergence comparisons the number of sampled sites generally has a much larger impact on statistical power than increasing the number of sampled alleles (Figure 4 and Figure 5). Examining the unfolded distributions of newly arisen mutations can have a substantial effect on power when the numbers of sampled alleles is small and when selection is weak (Figure 6).

View larger version (13K): In this window In a new window Download PPT slide   Figure 6. Configuration tests between neutral and selected mutations for folded and unfolded distributions. The y-axis plots the proportion of tests that reject fitness equivalence, P < 0.05, among 1000 simulated data sets for each value of Nes. The statistical power of the fddMWU test for folded (f) and unfolded (uf) configurations of mutations is shown. For unfolded configurations, ancestral and derived states are assumed to be inferred with complete accuracy. See Table 1 for abbreviations for tests.

It is important to note, however, that the results above hold only for the given model of evolution under the parameters examined. Although these findings probably hold for parameters within the range investigated, the superior power of the MWU test over the homogeneity tests is due to the particular deviation from the null investigated here. Under uniform selection, the location of the configuration of mutations undergoes a unilateral shift as a function of selection intensity (Figure 1). However, other alternative models may show differences in the configurations of mutations that may result in smaller deviations in their means. The choice of tests, therefore, depends on the particular alternatives under consideration. If a model predicts differences in the locations of distributions, then MWU tests may provide the greatest statistical power to detect selection. In the absence of a particular alternative hypothesis, Templeton's sidMCH test is a general method to test for departures from the null hypothesis of equivalent configurations among classes of mutations. (Similar comparisons that combine the frequency distribution of polymorphic mutations and the number of fixed differences could also enhance the sensitivity of between-region comparisons of DNA variation, but the power of such tests has not been investigated.)

The evolutionary distance, t_div, between the alleles sampled from within a population and the outgroup sequence can have a large impact on the power to detect selection. Figure 7 shows the effect of times of divergence on the pdMCH and fddMWU tests. Increasing t_div increases the sample sizes of fixed differences resulting in an increase in the power of all the tests that include this information and a decrease in the differences among these tests. However, these results assume accurate counting of the numbers of substitutions (under the infinite sites model, the number of diverged sites equals the number of substitutions). In practice, the number of substitutions is inferred given the number of differences between extant sequences and an evolutionary model that determines the appropriate correction for the number of sites that have undergone multiple substitutions. At higher levels of divergence, estimation of substitution rates can be quite sensitive to the assumed model of evolution (NEI and GOJOBORI 1986 ; GOLDMAN and YANG 1994 ; RZHETSKY and NEI 1995 ; INA 1996 ; MUSE 1996 ). Accurate estimation requires knowledge of transition probabilities among different nucleotides (or codons) and of how these probabilities vary among sites and over time. In the absence of such knowledge, shorter divergence times allow more reliable inference of the numbers of evolutionary fixations at the expense of some statistical power. In addition, ancestral and derived states at variable nucleotide positions can be inferred with greater confidence when levels of evolutionary divergence among the sequences are low (COLLINS et al. 1994 ; FRUMHOFF and REEVE 1994 ; YANG et al. 1995 ; SCHLUTER et al. 1997 ; ZHANG and NEI 1997 ).

View larger version (14K): In this window In a new window Download PPT slide   Figure 7. The effect of tdiv on the power of configuration tests between neutral and selected mutations. The y-axis plots the proportion of tests that reject fitness equivalence, P < 0.05, among 1000 simulated data sets for each value of Nes. Results for the pdMCH and fddMWU tests are shown for tdiv = 0.6, 1.2, 2.4, and 4.8. See Table 1 for abbreviations for tests.

These simulation data suggest that, under the assumptions of the Sawyer-Hartl model, comparisons of the configurations of neutral and selected mutations have considerable statistical power to detect even very weak positive and negative selection. This inference of selection is dependent on two steps. A difference in the configurations of two categories of mutations suggests different distributions of their fitness effects. If one of the categories of mutations evolves neutrally, then, under a constant directional selection model, the sign of the fitness effects of the second class of mutations can be inferred from the location of its distribution relative to that for the neutral class. An excess of rare polymorphisms, relative to the neutral class, suggests negative selection coefficients, whereas too many fixed differences suggest adaptive evolution. The assumption of neutrality at silent sites in coding regions is critical to such inferences of selection in protein evolution. The following section employs simulation data to examine the statistical power to detect a particular model of selection at silent sites and compares the configurations of putative fitness classes of silent DNA mutations in D. simulans.

	CONFIGURATION TESTS OF MUTATION-SELECTION-DRIFT

TOP ABSTRACT NATURAL SELECTION AND THE... CONFIGURATION TESTS BETWEEN... CONFIGURATION TESTS OF... NONNEUTRAL SILENT SITES AND... DISCUSSION APPENDIX 1 LITERATURE CITED

Patterns of codon usage in a number of organisms are consistent with natural selection discriminating among synonymous codons to enhance the efficiency and/or the accuracy of protein synthesis (reviewed in IKEMURA 1985 ; ANDERSSON and KURLAND 1990 ; SHARP et al. 1995 ). Under "major codon preference," codon usage bias is maintained by a balance among the forces of mutation pressure, genetic drift, and natural selection favoring translationally superior major codons (SHARP and LI 1986 ; LI 1987 ; BULMER 1988 , BULMER 1991 ). The simplest evolutionary model of this scenario considers twofold redundant codons in a haploid organism (LI 1987 ; BULMER 1991 ). Mutations occur at rates v from nonmajor codons to major codons and u in the opposite direction. Major codons confer selective advantage s. This scenario is depicted below:

Consider a locus consisting of a number of such sites. The proportion of major codons at the locus is determined by u/v, the ratio of the mutation rates, and N_es, the product of effective population size and selection coefficient. If these parameters remain relatively constant, then the proportion of major codons at the locus will reach a steady state (i.e., equal numbers of forward and backward substitutions).

Major codon preference predicts two fitness classes of silent mutations, "preferred" mutations from nonmajor to major codons and "unpreferred" mutations in the opposite direction (AKASHI 1995 ). A purely mutational model of codon bias requires differences in the forward and backward mutations rates (FREESE 1962 ; SUEOKA 1962 , SUEOKA 1988 ), but does not predict differences in the evolutionary configurations of mutations in the two directions, because both are neutral.

The statistical power to detect major codon preference at silent sites can be examined under the Sawyer-Hartl model. LI 1987 and BULMER 1991 give expressions for the steady-state proportion of major codons in a given gene under assumptions of constant N_es and independent evolution among sites. This proportion is determined by four parameters: u and v, the forward and backward mutation rates; s, the selective advantage of major codons; and N_e, the species effective population size. For these simulations, per-site mutation rates were set to u = 1.2 x 10^-9 and v = 0.8 x 10^-9. The ratio of the mutation rates, = 1.5, gives an equilibrium mutational base composition of 60% A + T, the average base composition of putatively neutrally evolving introns in D. melanogaster (SHIELDS et al. 1988 ; MORIYAMA and HARTL 1993 ). This base composition is also consistent with substitution patterns in presumably "dead-on-arrival" non-LTR transposable elements in Drosophila (D. PETROV, personal communication). The proportion of sites encoding major codons was calculated from Equation 6 of BULMER 1991 given the parameters, u, v, N_e, and s. The numbers of major and nonmajor codons were determined by this proportion and the number of sites in the locus, l, and were assumed fixed (no stochastic variance) for a given set of parameter values. Per-locus mutation rates to unpreferred and preferred mutations are the product of per-site mutation rates and the numbers of major and nonmajor codons, respectively. Note that, under this model, per-locus preferred and unpreferred mutation rates are a function of the strength of selection.

Figure 8 shows the expected configurations of unpreferred and preferred mutations under major codon preference. The numbers of mutations in each frequency class in the configuration, r = 1 to m, can be determined from Sawyer and Hartl's sampling equations given m, the number of alleles examined, t_div, the time of divergence between the species sampled and the outgroup, and the five parameters discussed above. Even very weak selection can skew the configurations of the two classes of silent mutations. As selection increases the proportion of major codons in a given locus, differences in the configurations of the proportion of mutations in the frequency classes become more pronounced (Figure 8, a–c) but the expected numbers of preferred mutations decrease (Figure 8, d–f). This decrease in the per-locus preferred mutation rate will result in a loss of statistical power to detect differences between the configurations of preferred and unpreferred mutations. However, under major codon preference, observed levels of codon bias in Drosophila require selection coefficients in the range of ~0 < |N_es| < 3. The analyses below examine the statistical power to detect differences in the configurations of the two classes of silent mutations under such a parameter range.

View larger version (18K): In this window In a new window Download PPT slide   Figure 8. Expected configurations of preferred and unpreferred mutations under major codon preference. The expected numbers of newly arisen mutations at frequency classes r = 1 to m in a sample of sequences were calculated according to SAWYER and HARTL 1992 and HARTL et al. 1994 . Data are shown for m = 5 sequences and tdiv = 0.6. a, b, and c show the expected proportion of variable sites in the sample at different frequencies under Nes = ±0.5, ±1.0, and ±3.0, which correspond to major codon usages of 65, 85, and 100%, respectively. c, d, and e show the proportion of sites at which variants are expected to be segregating at different frequencies or fixed in the sample. Superscript f denotes "fixed" difference class (r = m).

DNA variation data were simulated for preferred and unpreferred mutations under the Sawyer-Hartl Poisson random field model. Assuming stationary frequency distributions and independent evolution at all sites, the numbers of sampled preferred and unpreferred mutations in each frequency class are independent Poisson random variables. Simulations were conducted for the parameters described above and l = 500, 1000, 2500, and 5000 mutable sites and m = 5, 10, 25, and 50 alleles. Selection coefficients between major and nonmajor codons were varied between 0 N_es 6, and the time of divergence between the sampled alleles and the outgroup was varied between t_div = 0.6, 1.2, 2.4, and 4.8. A total of 1000 sample configurations of preferred and unpreferred mutations were simulated for each set of parameters. The pdMCH, sidMCH, and fddMCH tests of independence, and the fdMWU and fddMWU tests were applied to each simulated data set.

Figure 9 compares the statistical power of these five methods to detect mutation-selection-drift. For all tests, the power to detect selection increases initially with N_es but falls off as major codon usage reaches 100%. Each of the statistical methods shows some power to detect weak selection. The relative power of the different tests is similar to that for the neutral vs. selected mutations tests. The frequency distribution test is generally less powerful than tests that include divergence data. Among the latter category, 2 x 3 tests of independence are considerably more powerful than both 2 x 2 and 2 x m tests. Overall, however, the fddMWU test is either indistinguishable from, or more powerful than, all the other tests over the parameter ranges considered. The gain in power is greatest when the number of sampled alleles is large. For the same total number of aligned nucleotides, increasing the number of sampled sites has a greater impact on statistical power than increasing the numbers of alleles.

View larger version (24K): In this window In a new window Download PPT slide   Figure 9. Power of polymorphism and divergence configuration tests between preferred and unpreferred mutations. The y-axis plots the proportion of tests that reject fitness equivalence, P < 0.05, among 1000 simulated data sets for each value of the proportion of major codons at mutable sites. Because the direction of the deviations in the configurations of preferred and unpreferred mutations are predicted under major codon preference, one-tailed probabilities were calculated for these tests. For Monte Carlo homogeneity tests, the proportion of randomized tables with both a higher average frequency of preferred than unpreferred codons and an equal or larger test statistic than the data was taken as the probability of a given configuration. The five tests are those from Figure 6. The analyses are similar to those shown in AKASHI 1997A (Figure 5) but the per-site mutation rates are more conservative (lower), the 2 x m test of independence is included, Monte Carlo homogeneity tests replace G-tests, and power to reject the null is plotted as a function of levels of major codon usage rather than selection intensity.

These power analyses suggest that configuration comparisons, given enough mutations, can detect natural selection near its limit of efficacy. The configurations of preferred and unpreferred synonymous codons have been compared in DNA sequence data from D. simulans (AKASHI 1997A ) and the results are reiterated in Figure 10. Major codon preference predicts frequency distributions and divergence skewed toward higher values for advantageous preferred silent mutations than for deleterious unpreferred mutations. Equivalent configurations constitute the null hypothesis in this comparison and neutrality of both classes of mutations (the purely mutational model) is a subset of this null. Figure 10 shows the configurations of preferred and unpreferred mutations pooled from five alleles from each of eight D. simulans genes found in the literature or in GenBank (Table 2). Methods to identify major codons and infer ancestral and derived states for silent mutations are given in AKASHI 1995 . Equivalent data from D. melanogaster are not shown because other lines of evidence indicate a reduction in the efficacy of selection at silent sites in this lineage (AKASHI 1995 , AKASHI 1996 ). Although only five alleles were analyzed in D. simulans, close to 2500 silent sites were examined across the eight genes in Table 2. If codon bias is maintained under mutation-selection-drift in this lineage, then frequency distribution and divergence comparisons should have a high probability of rejecting fitness equivalence between preferred and unpreferred mutations.

View larger version (25K): In this window In a new window Download PPT slide   Figure 10. The configurations of preferred, unpreferred, and replacement mutations in D. simulans. The proportions of 101 unpreferred (black), 37 preferred (gray), and 22 replacement (striped) mutations segregating at the given frequencies or fixed among five alleles of each of eight D. simulans genes are shown. Pooled data are from eight D. simulans genes from Table 2. Interestingly, 11 of the 12 amino acid "fixations" in D. simulans have occurred in the Zw gene, whereas the singleton polymorphisms are distributed more evenly among the eight genes; the distribution of selection coefficients may differ among genes. Superscript f denotes "fixed" difference class (r = m).

In D. simulans, the configurations of preferred and unpreferred mutations are similar to those expected under weak selection (Figure 8B). The 37 preferred mutations are segregating at higher frequencies and are more often fixed than the 101 unpreferred changes (Mann-Whitney U-test, z = 3.12, P = 0.0009, one-tailed). The other statistical tests were also significant at the 5% level; frequency distributions are skewed toward higher values (Mann-Whitney U-test, z = 1.71, P = 0.044), ratios of polymorphism to divergence are lower (Fisher's exact test, P = 0.007), and the ratios of singleton, intermediate frequency, and fixed differences are skewed toward higher values for preferred than for unpreferred mutations (Monte Carlo homogeneity test, P = 0.015). These patterns are both consistent with major codon preference and difficult to explain in the absence of selection (AKASHI 1997A ).

	NONNEUTRAL SILENT SITES AND TESTS OF NATURAL SELECTION IN PROTEIN EVOLUTION

TOP ABSTRACT NATURAL SELECTION AND THE... CONFIGURATION TESTS BETWEEN... CONFIGURATION TESTS OF... NONNEUTRAL SILENT SITES AND... DISCUSSION APPENDIX 1 LITERATURE CITED

SAWYER et al. 1987 and MCDONALD and KREITMAN 1991 proposed comparisons of configurations between a putatively neutrally evolving (silent) and a potentially selected (replacement) class of mutations. A number of claims of adaptive protein evolution depend on such an assumption of neutral evolution of synonymous mutations (MCDONALD and KREITMAN 1991 ; EANES et al. 1993 ; LONG and LANGLEY 1993 ; KAROTAM et al. 1995 , KING 1998 ). Configuration tests, however, support weak selection at silent sites in Drosophila (AKASHI 1995 , AKASHI 1997A ; AKASHI and SCHAEFFER 1997 ), and a number of other patterns of silent DNA evolution in Drosophila are consistent with mutation-selection-drift (SHIELDS et al. 1988 ; SHARP and LI 1989 ; KLIMAN and HEY 1993 , KLIMAN and HEY 1994 ; MORIYAMA and HARTL 1993 ; AKASHI 1994 ; MORIYAMA and POWELL 1997 ; POWELL and MORIYAMA 1997 ). Although major codon preference could, in principle, affect interpretations of comparisons between silent and replacement mutations (AKASHI 1995 ), the magnitude of such effects has not been evaluated.

Computer simulations were conducted to determine whether neutral protein evolution and selection at silent sites could mimic patterns that have been attributed to adaptive amino acid substitutions. DNA variation data were generated under a combination of the two scenarios described in the sections above. A given locus consists of two categories of mutations; half of the sites evolve under major codon preference and the other half evolve neutrally. Preferred and unpreferred mutations at major codon preference sites are pooled into a single category representing silent mutations and compared to the neutral class, representing replacement mutations. (This does not assume that all protein mutations are neutral. Amino acid positions at which mutations are strongly selected against do not contribute to variation and would not be counted in the number of mutable replacement sites in these simulations.) DNA variation data were generated as described above for the same mutational parameters, effective population size, times of divergence, and sample sizes. pdMCH tests of homogeneity and fdMWU and fddMWU tests were applied to 1000 simulated configurations of silent and replacement mutations for each set of parameters.

Figure 11 shows the fraction of statistical tests that reject equivalence of the configurations of nonneutral silent and neutral replacement mutations. Under the parameters examined, these tests show some power to reject the null when major codons reach a frequency of about 70 to 80% (N_es 1). At higher levels of major codon usage (stronger selection), the tests can be quite sensitive to mutation-selection-drift. At t_div = 0.6, the fdMWU test is more powerful than the pdMCH test, and the fddMWU test is generally most powerful. At higher levels of divergence, all tests become more sensitive to major codon preference and the pdMCH test outperforms the fdMWU test (data not shown).

View larger version (12K): In this window In a new window Download PPT slide   Figure 11. Power of polymorphism and divergence configuration tests between neutral mutations and mutations under major codon preference. The y-axis plots the proportion of tests that reject fitness equivalence, P < 0.05, among 1000 simulated data sets for each value of major codon usage. See text for simulation parameters and Table 1 for abbreviations for tests.

The impact of mutation-selection-drift on silent/replacement configuration comparisons is very sensitive to the strength of selection. If major codon preference accurately describes silent evolution, then silent/replacement comparisons may be valid in low codon bias genes. However, when selection intensity (and the proportion of major codons) is high, the majority of silent mutations are deleterious unpreferred changes (Figure 8, d–f), and the means of the configurations of silent mutations tend to be lower than those of the neutral expectation. The null model can be rejected at a high rate, and the relative locations of the configurations are consistent with neutral evolution at silent sites and adaptive amino acid substitutions. For the data examined in this study, the average codon bias across the eight D. simulans genes is ~80% major codons; comparisons of replacement mutations to pooled silent mutations are difficult to interpret.

Separate contrasts of replacement mutations to preferred and unpreferred silent changes may shed some light on mechanisms of protein evolution (AKASHI 1995 ). Under major codon preference, the configurations of preferred and unpreferred mutations reflect evolution under small positive and negative selection coefficients, respectively. Thus, configurations of replacement mutations skewed toward a larger fraction of high frequency variants and fixed differences than preferred mutations reflect adaptive protein evolution, whereas configurations skewed toward an excess of low frequency amino acid mutations relative to unpreferred silent mutations support deleterious protein evolution.

The configurations of replacement mutations as well as preferred and unpreferred silent mutations among the five alleles of eight D. simulans genes are shown in Figure 10. Surprisingly, roughly half of the variable replacement sites are singleton polymorphisms and the other half are fixed in the samples of five D. simulans alleles. Because no prediction had been made for the shape of the configuration of replacement mutations, TEMPLETON's (1996) sidMCH test was applied to the data. The configuration of replacement mutations is significantly different from that of both preferred (P = 0.028, two-tailed) and unpreferred (P < 0.001) silent changes. Although the number of replacement mutations in these data is small, this configuration does not appear to conform to the predictions for protein evolution under uniform selection coefficients (including neutral evolution).

The excesses of rare amino acid polymorphisms and fixed differences can be explained by relaxing the assumption of uniform N_es. One possibility is a combination of a large fraction of slightly deleterious amino acid changes and heterogeneity in effective population size over time. Lower effective population sizes in the past would have allowed slightly deleterious mutations to go to fixation, whereas more effective selection in larger current populations keeps deleterious polymorphisms at low frequencies. Such a nonequilibrium scenario was suggested by OHTA 1993 to explain lower ratios of polymorphism to divergence for replacement than silent evolution at the Drosophila Adh locus. However, because major codon preference is very sensitive to small changes in N_es (AKASHI 1996 ), population-level phenomena should impact silent DNA mutations as well as amino acid changes. Roughly equal numbers of preferred and unpreferred silent fixations in the D. simulans lineage (Table 2) argue against large, or prolonged, fluctuations in effective population size.

Heterogeneity in selection coefficients, either across sites or across time, could also account for the configurations of amino acid mutations in D. simulans. One possibility is that selection coefficients vary among amino acid positions; low frequency polymorphisms are deleterious mutations that rarely go to fixation, whereas fixed differences in the sample reflect occasional adaptive amino acid substitutions. In this scenario, the polymorphic and fixed mutations in the sample are not a result of a single process of evolution under constant parameters but reflect a combination of the evolutionary dynamics of multiple fitness classes of mutations.

Selection coefficients varying across time, rather than among DNA sites, could also explain the deficiency of intermediate frequency amino acid polymorphisms (HARTL and DYKHUIZEN 1985 ). Most amino acid mutations are deleterious and are unlikely to reach appreciable frequencies within populations, but occasional environmental changes cause a subset of polymorphisms to become adaptive and rapidly go to fixation. Although the configuration of amino acid mutations in D. simulans is intriguing, more rigorous inference of mechanisms of protein evolution will require DNA sequence data both for a larger number of genes in this species and equivalent data from other lineages. In addition, interpreting these data may require predictions for the configurations of amino acid mutations under more complex models of evolution than those considered here.

	DISCUSSION

TOP ABSTRACT NATURAL SELECTION AND THE... CONFIGURATION TESTS BETWEEN... CONFIGURATION TESTS OF... NONNEUTRAL SILENT SITES AND... DISCUSSION APPENDIX 1 LITERATURE CITED

Under the Sawyer-Hartl Poisson random field model, comparisons of the configurations of functional categories of DNA mutations can have considerable power to detect even very weak directional selection on classes of DNA mutations. These findings cannot be generalized beyond evolution under the parameter ranges considered and under the Sawyer-Hartl assumptions of stationarity, free recombination, and independent fitness effects of all mutations. Given these assumptions, configuration comparisons that include information from both frequency distributions of polymorphic mutations and numbers of fixed differences confer the greatest power to detect the fitness effects of mutations. The Mann-Whitney U-test, which is sensitive to differences in the locations of distributions, is a more powerful statistical approach to detect uniform selection coefficients than contingency tests of homogeneity. Accumulating DNA variation data for a large number of mutations with similar fitness effects is critical to the power of these tests. Configuration tests suggest that among eight D. simulans genes, a large fraction of both silent and replacement mutations affect fitness. Some limitations to this approach and these findings are discussed below.

Robustness of configuration comparisons:
Under the Sawyer-Hartl assumptions, the numbers of observed mutations in each frequency class for each category of mutations are independent Poisson random numbers. Under these conditions, the test statistics of both Monte Carlo homogeneity tests and Mann-Whitney U-tests will be appropriately distributed under the null hypothesis of equivalent configurations of mutations. However, independent evolution at all sites, a stationary frequency distribution of mutations, and random sampling from a panmictic population are clearly not biologically realistic assumptions for many DNA sequence studies. One of the most appealing features of configuration comparisons is its claimed robustness to these assumptions. In the special case of no recombination, each of the alleles in a sample will be related by a single genealogy. If mutations have occurred at a constant (and low) rate on this genealogy, then the numbers of mutations from each category on each branch of the genealogy will be independent Poisson random numbers, regardless of whether the particular genealogy is sampled from an equilibrium, panmictic population (SAWYER et al. 1987 ; HUDSON 1993 ). A similar argument has been made for intermediate levels of recombination. If the two classes of mutations are randomly interspersed in a genetic region (with respect to differences in evolutionary histories of subregions in the data), then configuration tests should be robust to departures from stationarity and panmixis (MCDONALD and KREITMAN 1991 ; HUDSON 1993