Genic Mutation Rates in Mammals: Local Similarity, Chromosomal Heterogeneity, and X-Versus-Autosome Disparity (original) (raw)

Abstract

The reduction of mutation rates on the mammalian X chromosome relative to autosomes is most often explained in the literature as evidence of male-driven evolution. This hypothesis attributes lowered mutation rates on the X chromosome to the fact that this chromosome spends less time in the germline of males than in the germline of females. In contrast to this majority view, two articles argued that the patterns of mutation rates across chromosomes are inconsistent with male-driven evolution. One article reported a 40% reduction in synonymous substitution rates (K s) for X-linked genes relative to autosomes in the mouse-rat lineage. The authors argued that this reduction is too dramatic to be explained by male-driven evolution and concluded that selection has systematically reduced mutation rate on the X chromosome to a level optimal for this male-hemizygous chromosome. More recently, a second article found that chromosomal mutation rates in both the human-mouse and mouse-rat lineages were so heterogeneous that the X chromosome was not an outlier. Here again, the authors argued that this is at odds with male-driven evolution and suggested that selection has modulated chromosomal mutation rates to locally optimal levels, thus extending the argument of the first mentioned article to include autosomes. Here, we reexamine these conclusions using mouse-rat and human-mouse coding-region data. We find a more modest reduction of K s on the X chromosome, but our results contradict the finding that the X chromosome is not distinct from autosomes. Multiple statistical tests show that K s rates on the X chromosome differ systematically from the autosomes in both lineages. We conclude that the moderate reduction of mutation rate on the X chromosome of both lineages is consistent with male-driven evolution; however, the large variance in mutation rates across chromosomes suggests that mutation rates are affected by additional factors besides male-driven evolution. Investigation of mutation rates by synteny reveals that synteny blocks, rather than entire chromosomes, might represent the unit of mutation rate variation.

Introduction

The past two decades have seen vigorous debate regarding both the existence and strength of male-driven evolution, defined as the hypothesis that the male germline experiences more mutational pressure than does the female germline. Earlier literature on the subject provides strong evidence supporting male-driven evolution in mammals through estimates of the mutation rates on autosomes and sex chromosomes (Miyata et al. 1987; Shimmin, Chang, and Li 1993_a_; Chang and Li 1995; Bohossian, Skaletsky, and Page 2000). More recently, Makova and Li (2002) presented convincing arguments that male-driven evolution is the primary factor behind the observed lower mutation rates on the primate X chromosome.

Although most researchers have accepted male-driven evolution in mammals as a biological reality and turned their efforts to estimating its strength in various lineages, two articles have presented arguments that call into question the existence of the phenomenon. McVean and Hurst (1997) argue against male-driven evolution using two primary observations. First, the average silent substitution rate on the rodent X chromosome (K s X) is so dramatically reduced relative to the autosomal rate (K s A) that the ratio of the two (K s X/K s A) is outside the theoretical limits of male-driven evolution (K s X/K s A as reported by McVean and Hurst [1997] produces an estimate of α, the strength of male driven evolution, that exceeds infinity). Second, the mutation rate on the Y chromosome is broadly similar to that of the autosomes, yielding an α that is inconsistent with that derived from the X chromosome.

As an alternative to male-driven evolution, McVean and Hurst (1997) invoke a model to which we refer as “modulated mutability.” They argue that, because recessive deleterious mutations in X-linked genes are hemizygous in males, their negative effect on fitness is amplified relative to similar mutations in autosomal genes; consequently, selection would favor the systematic reduction of mutation rate, specifically on the X chromosome. Their argument rests on the hypothesis that selection acts at the local level to balance the presumed metabolic costs of suppressing mutations with the fitness advantage of maintaining high genomic fidelity, a model that is biologically plausible (Kimura 1967; Leigh 1970, 1973; Kondrashov 1995; Sniegowski et al. 2000), although there is as yet little empirical evidence to support it, particularly in mammals. In contrast to the conclusions of McVean and Hurst (1997), Lercher et al. (2001) assert that K s rates are highly heterogeneous among different chromosomes but broadly similar within the same chromosome. Although they did not assess the significance of K s heterogeneity among different chromosomes, both trends were statistically significant when actual data were compared with simulated genomes. The authors argue that these trends render the mutation rates on the X chromosome indistinguishable from many of the autosomes. Although the empirical findings of Lercher, Williams, and Hurst (2001) directly contradict those of McVean and Hurst (1997), Lercher, Williams, and Hurst (2001) also argue against male-driven evolution, explaining their findings in language very similar to that of McVean and Hurst (1997). They suggest that an entire chromosome represents the main, perhaps least reducible, unit of variation in mutation rates; thus, the differential mutation rates that they observe are the result of a modulation of mutation by selection acting at the individual chromosome level.

Together, these papers have twofold significance: they call into question the applicability of male-driven evolution to the mammalian lineage, and they provide the only existing empirical evidence that mutation rates are locally modulated in mammals. Given the implications of these conclusions for comparative genomic studies, we statistically reexamined the trends in chromosomal mutation rates reported by these researchers. Specifically, we used coding-region data from the same two lineages (mouse-rat and human-mouse) to determine how well the modulated mutability and male-driven evolution models fit the data.

Materials and Methods

Data Collection

In all, we examined 1,731 autosomal genes and 70 X-linked genes in the mouse-rat lineage. In the human-mouse lineage, our sample contained 4,194 genes, with 190 genes on the X chromosome. We did not survey the Y chromosome in either lineage because of the dearth of data. To our knowledge, no previous study has examined such a large set of genes for their evolutionary rates on a chromosome-by-chromosome basis. Thus, the scale of this analysis (about 7% of the mouse genome in the mouse-rat comparison and 14% of the human genome in the human-mouse comparison) should offer more representative conclusions than previous, smaller scale studies.

We obtained orthologs from the two lineages using a two-step process. First, human-mouse orthologs were gathered from synteny maps (Homologene, NCBI) and the sequences for each gene were recovered from RefSeq. Next, mouse-rat orthologs were identified by Blast (Altschul et al. 1990). Rat orthologs to mouse genes were identified as those that were reciprocal best hits when compared with a mouse data file using nucleotide Blast, with an e-value cut off of 1 × 10−50. Coding region sequences annotated from RefSeq were used to maximize the speed and utility of the Blast search. In many cases, other supporting information was available to corroborate orthology (e.g., gene name annotation or orthology reported in databases or previous literature).

The coding sequences were aligned in frame using the Pileup and Framealign programs from the GCG package (Genetics Computer Group, Madison, Wis.). Newdiverge from the same suite was used to analyze evolutionary rates (K a and K s) according to the Li (1993) method. Gene assignments to human or mouse chromosomes were gathered from Unigene as well as from the human-mouse synteny database.

Statistics

We estimated K s and the nonsynonymous substitution rate (K a) based on the Li (1993) method and used these calculations in estimating K a/K s. This ratio is commonly employed as a measure of constraint on the evolution of a gene (Li 1993). Values for K s and K a calculated by the maximum-likelihood method (Goldman and Yang 1994; Yang 1997; Yang and Nielsen 2000) were nearly indistinguishable from those generated by the Li (1993) method. Thus, we use substitution rates calculated with the Li method for the majority of the following statistical analysis, which affords greater comparability to previous work (McVean and Hurst 1997; Sharp 1997; Fay, Wyckoff, and Wu 2001).

To assess the heterogeneity of K s rates between chromosomes, we performed pairwise Kolmogorov-Smirnov tests (Hollander and Wolfe 1973). This test evaluates the null hypothesis that two data sets are drawn from the same underlying distribution. In this regard, it is similar to the _F_-test; however, the parametric _F_-test loses statistical power when dealing with unequal sample sizes and data that are not normally distributed. The Kolmogorov-Smirnov test, in contrast, is robust under these conditions and was therefore deemed most appropriate to our data, which have these limitations. Kolmogorov-Smirnov tests were performed using the online calculator. (http://www.physics.csbsju.edu/stats/KS-test.html). This program generates a D statistic, which gauges the distance between two data sets, and a _P_-value that reflects its significance based on a critical table of D values and the degrees of freedom based on the two sample sizes.

At the subchromosomal level, we also investigated the K s rates and K a/K s ratios of genes located on different synteny blocks. Synteny blocks contain widely varying numbers of genes (the smallest synteny block had three genes, whereas the largest had 207, with an average of 20 genes per block). In addition to the issue of unequal sample sizes, K s rates and K a/K s ratios are nearly normally distributed across some blocks but depart radically from a normal distribution within others. Thus, testing the similarity of two blocks is a matter of choosing the test with the most appropriate properties without sacrificing statistical power. We used Kolmogorov-Smirnov tests (as described above) and confirmed the results of the nonparametric test by performing _F_-tests in Microsoft Excel. To complement the Kolmogorov-Smirnov and _F_-tests, which examine differences in the distributions of two data sets, we were also interested in examining the differences among synteny block means. To this end, we performed _t_-tests (technically, a special execution of _F_-tests) in Microsoft Excel to determine whether or not the mean K s rates of synteny blocks are significantly different from one another. This confirmatory statistical approach allowed us to ensure that we were not losing statistical power by using the nonparametric Kolmogorov-Smirnov test.

We tested for correlation between synonymous and nonsynonymous substitution rates in two ways. At the chromosome level, we constructed matricies of D statistics from the Kolmogorov-Smirnov tests for synonymous and nonsynonymous substitution rates. We used the Mantel test (Mantel 1967; Legendre and Legendre 1998) (Mantel PPC, available for download at http://www.bio.sdsu.edu/pub/andy/MANTEL.html) with 200 randomizations to determine whether or not these matrices were correlated. Distance matrices describing the relationships among groups can be derived from any of a number of characteristics. The Mantel test determines whether two matrices describing the same groups are correlated with one another by calculating an initial correlation coefficient for the two real matrices and comparing that value to the correlation coefficient between one real matrix and a specified number of random permutations of the other. The significance of the correlation is gauged by how consistently the real correlation coefficient exceeds that of the permutations. In testing for correlations among chromosomal K a and K s rates, the Mantel test is appropriate because, unlike a simple linear correlation, which gives a Pearson correlation coefficient, the Mantel test corrects for the problem of nonindependence among group relationships (in this case, chromosomes). We also tested for correlation between K a and K s rates estimated by maximum likelihood (Goldman and Yang 1994), using Minitab for Windows XP to generate simple linear correlations.

Lastly, we examined mutation rates in the larger context of relationships among all chromosomes or among synteny blocks using discriminant function analysis (DFA) (Tabachnick and Fidell 2001). In DFA, data points are assigned to true groups and the power of particular parameters to predict the true group to which the data point belongs is assessed. In this case, chromosomes (or synteny blocks) are the true groups for individual genes and K s is employed as the sole predictor of group affiliation. DFA generates a statistic called the squared Mahalanobis distance (_D_2). This is a measure of the distance of two groups from one another relative to a regional centroid. This centroid is derived from the characteristics of all groups. The _D_2 value is then used to calculate an F statistic using the equation given in Droessler (1981). The significance is assessed using a table of critical F values having degrees of freedom equivalent to the number of groups and number of predictors. Thus, in contrast to the Kolmogorov-Smirnov tests, which describe the relationship of two groups in isolation from all other groups, the _D_2 and F values allow us to view relationships among chromosomal or synteny-block K s rates in the context of all available groups of data.

Results

K s X and K s A Rates in Mammals Are Consistent with Male-Driven Evolution

Using a much larger set of genes, we find only a modest reduction in K s X relative to K s A. For the mouse-rat data set, K s X is 0.149, and K s A is 0.183, yielding a K s X/K s A ratio of 0.814. These results contrast strongly with those of McVean and Hurst (1997), who reported K s X, K s A, and K s X/K s A of 0.145, 0.234, and 0.62, respectively, for this lineage (fig. 1_a_).

Because McVean and Hurst (1997) invoke male-specific hemizygosity of the X chromosome (rather than male-driven evolution) to explain the reduction in K s, we also derived K s X and K s A rates from a human-mouse data set, reasoning that the large discrepancy reported by McVean and Hurst should be reproducible in other mammalian lineages if their hypothesis was correct. The values of K s X, K s A, and K s X/K s A for the human-mouse data set are 0.43, 0.50, and 0.85, respectively, which is in line with our estimates for the mouse-rat lineage (fig. 1_b_).

Using the formula α = (4*[K s A/K s _X_] − 3)/(3 − 2*[K s A/K s _X_]), we estimate α (the male-to-female ratio of germline mutation rate) to be 3.52 in the mouse-rat lineage and 2.45 in the human-mouse. Our estimates are in broad agreement with those published for the mammalian lineage by numerous authors (Shimmin, Chang, and Li 1993_a_; Chang and Li 1995; Makova and Li 2002); however, they are in stark contrast to the value of α calculated by McVean and Hurst (1997) for the mouse-rat lineage, which exceeds infinity. Thus, our results concur with the conclusion of Mural and Venter (2002) and Lercher, Williams, and Hurst (2001) that the reduction of K s X in rodents is much less dramatic than that reported by McVean and Hurst (1997), and we extend this observation to the human-mouse lineage.

McVean and Hurst (1997) also calculated the average mutation rate for the Y chromosome (K s Y). They found average K s Y to be similar to the average K s A value, rather than exceeding it as predicted by male-driven evolution. They further note a discrepancy between the α estimate generated from Y-linked genes and that generated with X-linked genes. Given the dearth of data available for the Y chromosome (McVean's and Hurst's [1997] calculations employ only three genes), the estimates of K s Y and the α derived from it are best viewed with caution. Although our analysis does not include Y-derived estimates because of the scarcity of genes, we note that a recent article found that when several pairs of X-Y homologs are compared for the human-mouse lineage, genes on the Y have, on average, K s values double that of their X-chromosome counterparts (Wyckoff, Li, and Wu 2002).

Our α estimates are reported solely for comparison with previous mammalian studies where the strength of α was calculated using coding sequence (see Chang et al. [1994], Agulnik et al. [1997], and Lawson and Hewitt [2002] for examples). Given that selection and variation in K s across the genome confound calculations of α from coding-region data, we concur with the argument of Makova and Li (2002) that meaningful estimates of the male-mutation bias are best calculated from paired noncoding region data, where selection is minimal.

Mutation Rate of the X Chromosome Is an Outlier Relative to Autosomes

As figure 1 shows, K s varies considerably from chromosome to chromosome, which is in keeping with the observations of Lercher, Williams, and Hurst (2001). To explore this phenomenon more fully, we statistically examined the differences among chromosomal rates to gauge the degree and significance of this heterogeneity. We used pairwise Kolmogorov-Smirnov tests between chromosomes to determine which chromosomes were significantly different from the others in terms of K s distributions. In the human-mouse lineage, we find that the distribution of K s rates on the human X chromosome is statistically significantly different (P < 0.05) from those on 21 of the 22 human autosomes. In the mouse-rat lineage, the mouse X chromosome is significantly different at the same level from 16 of the 19 mouse autosomes (tables 1 and 2). In both lineages, no other chromosome is so uniformly distinct from other autosomes. Thus, in keeping with theories of male-driven evolution, it is clear that the mammalian X chromosome is an outlier to the autosomes (more so than any other autosome is to the rest of the genome) and, therefore, cannot be treated as statistically identical to the autosomes.

We note, as did Lercher, Williams, and Hurst (2001) and others (Ebersberger et al. 2002), that there is striking heterogeneity of K s rates among the autosomes. For instance, 47% of pairwise chromosomal Kolmogorov-Smirnov comparisons within the human-mouse lineage are statistically significant at P < 0.05; in the mouse-rat lineage, 14% of the comparisons are statistically significant at P < 0.05. This difference between the human-mouse and the mouse-rat lineages might reflect both a shorter amount of evolutionary time and fewer genes in the latter lineage, which makes statistical inferences less likely to be significant.

According to Lercher, Williams, and Hurst (2001), the heterogeneity in chromosomal mutation rates is so great that chromosomes are individually distinct and have little relation to one another; however, our data present a more complex web of relationships among chromosomal mutation rates. Squared Mahalanobis distances (_D_2) were generated from a discriminant function analysis, with human chromosomes as the “true” groups and genic K s for the human-mouse lineage as the predictor for chromosomal localization (see Materials and Methods). Discriminant function analysis considers the relationships among chromosomes in the context of the variation present throughout the entire data set (including chromosome-to-chromosome variation). Thus, it complements our pairwise Kolmogorov-Smirnov tests, which consider the significance of the difference between chromosomes in isolation from other comparisons. Confirming the Kolmogorov-Smirnov test results, F values derived from pairwise _D_2 values demonstrate that 47% of the distances between chromosomes are significant (Droessler 1981).

Interestingly, we find that within the human-mouse lineage, several chromosomes (21 and 19) have relatively high K s rates, forming a small cluster that is significantly different from most other autosomes, even those that also have relatively high K s rates (e.g., 16 and 4). Chromosomes 15 and 14 form a cluster of relatively low K s rates, distinct from most other autosomes. This pattern of chromosomal clustering is mirrored in the mouse-rat lineage, although the separation between chromosomal clusters is weaker, and both pairwise distances and _D_2 values frequently do not achieve significance. Thus, chromosomes seem to cluster into “families” of similar synonymous substitution rates. This pattern motivated us to examine mutation rate heterogeneity further at the subchromosomal level.

Synteny Blocks May Be the Unit of Mutation Rate Variation

Given the fact that the chromosome-to-chromosome heterogeneity in K s was substantial, if not as pervasive as that reported by Lercher, Williams, and Hurst (2001), we were interested in investigating trends within the autosomes that might help to explain this genome-wide heterogeneity. We gathered information about the locations of genes on chromosomes from NCBI (Homologene). In particular, we identified groups of genes located on evolutionarily conserved pieces of chromosomes (i.e., synteny blocks) between humans and mice. These blocks contain groups of genes that remain physically linked over evolutionary time as chromosomes themselves break and reshuffle. As such, they constitute ideal biologically meaningful units for examining mutation rate heterogeneity at the subchromosomal level (Mural and Venter 2002).

The Kolmogorov-Smirnov tests show that two synteny blocks whose K s distributions are significantly different from one another are essentially as likely to be on the same chromosome as on different chromosomes. We specifically examined this in the human-mouse lineage, in which synteny blocks are clearly defined and there is high-quality curation for gene locations in both species (table 3). _F_-tests confirm both the percentage of and trend in positional relationships between significant comparisons. In addition to testing the heterogeneity of K s distributions among synteny blocks, we used _t_-tests to determine how many pairwise comparisons of mean K s rates were significant. Both the percentages and positional relationships of blocks whose mean rates were significantly different from one another mirror the results of the Kolmogorov-Smirnov and _F_-tests. In summary, pairwise tests of both the means and distributions of K s rates between synteny blocks demonstrate that considerable variation exists between blocks regardless of whether or not they are positioned on the same chromosome.

Although relatively complete and well-annotated synteny maps are available for the human-mouse lineage (NCBI's Homologene; see above), the synteny information is much less complete than that available for the mouse-rat lineage. To complement our synteny analysis for the human-mouse lineage, we performed a pilot test in mouse-rat from which we draw tentative conclusions. We hand curated the available mouse-rat positional data and identified 50 putative synteny bins. These bins each contained at least two genes that existed in conserved order between mice and rats. We performed the same statistical analysis on these synteny bins as described above for the human-mouse data. Although the percentage of significant comparisons is lower in this lineage (which is to be expected, given that the two species are more closely related), the patterning of significant comparisons mirrors that of the human-mouse lineage (data not shown). We did not employ these putative mouse-rat synteny bins in further statistical analysis because of both the uncertainty of the curated synteny blocks and the limited number of genes in the analysis.

Although our pairwise analyses in both lineages suggest that positional similarity in K s rates does not extend across entire chromosomes, an exploratory discriminant function analysis using the human-mouse lineage reveals that the mean K s rate of a synteny block might not be completely independent of the chromosome on which the block is located. Using human chromosome as the true group, we found that the mean K s rate of a synteny block correctly predicts the chromosome on which the block is located 10.2% of the time, which is 2.25 times better than by chance alone (data not shown). This effect suggests a slight, yet perhaps real, tendency for blocks with similar substitution rates to be located on the same chromosome. However, this effect is sufficiently weak as to be undetectable by the Kolmogorov-Smirnov test. It is also worth noting that the ability to predict chromosomal locations of synteny blocks based on block-specific K s is largely attributable to a few outlier chromosomes (i.e., the X chromosome, chromosome 19, and chromosome 21). It is also relevant to note that neighboring synteny blocks have quite different mutation rates, suggesting that Lercher, Williams, and Hurst's (2001) “near-neighbor” approach to local similarity may have obscured sharp differences in substitution rates that exist across synteny boundaries. Our analysis suggests that synteny blocks are more biologically relevant units at which to examine mutation rate variation than are whole chromosomes.

Measures of Constraint Suggest That Selection Acts at the Level of Syntenic Blocks

Another means of testing whether or not selection is acting to adjust mutation rates over the entire length of chromosomes, as hypothesized by Lercher, Williams, and Hurst (2001), is to examine the strength of selective constraint and positive selection at the chromosomal and subchromosomal levels. The K a/K s ratio is one such measure; a K a/K s near 1 is suggestive of neutrality, whereas most genes have K a/K s ratios much less than 1 (suggestive of functional constraint). Rarely, individual genes have a K a/K s of greater than 1 (suggestive of positive selection). The average K a/K s for a specific synteny block should be indicative of the net effect of constraint, drift, and positive selection for genes on that syntenic segment over a given period of evolutionary time. We compared the means and distributions of K a/K s between pairs of synteny blocks either within the same chromosome or between different chromosomes using the Kolmogorov-Smirnov test (see Materials and Methods). It shows that the K a/K s ratios of synteny blocks on the same chromosome are essentially just as likely to be significantly different from one another as synteny blocks on different chromosomes. This is inconsistent with the interpretation that selection acts on chromosomes as a single unit.

Correlation Between K a and K s May Explain Local Similarity in K a

Lercher, Williams, and Hurst (2001) also report that K a rates mirror the chromosomal trends noted for K s, albeit more weakly. They invoke selection to explain this local similarity, reasoning that it cannot be explained as a function of local K s similarity, because the two measures are independent when calculated by maximum likelihood. We tested this assumption in two ways.

First, we constructed two distance matrices to describe the relationships among chromosomes in the human-mouse lineage, one employing the D values from the Kolmogorov-Smirnov tests for K s and the other using those from the Kolomogorov-Smirnov tests for K a (tables 1 and 2). We then performed a Mantel test with 200 randomizations to assess the significance of the correlation between the two matrices (Mantel 1967; Legendre and Legendre 1998). This confirmed that the two matrices are significantly correlated (P < 0.005). We did not test for K a and K s matrix correlation in the mouse-rat lineage for two reasons. First, it seemed likely that the lineage for which we had more data would be more likely to reveal real underlying correlation. Second, we felt that any correlation derived from the mouse-rat lineage, which has a much smaller sample size and represents a considerably shorter evolutionary distance, may be more likely to be spurious.

We also tested the independence of K a and K s calculated by maximum likelihood using simple linear correlations and found significant correlation between K a and K s in both lineages (P < 0.01, data not shown). Thus, in contrast to the conclusions of Lercher, Williams, and Hurst (2001), as well as other studies contending that correlation between K a and K s is an artifact of the Li (1993) method (Smith and Hurst 1998), we find significant correlation between synonymous and nonsynonymous substitution rates as calculated by both methods. Consequently, we caution that there is a strong possibility that any local similarity identified in K a rates is at least in part a function of the correlation to local K s rates.

Discussion

McVean and Hurst (1997) and Lercher, Williams, and Hurst (2001) both call into question the widely adopted notion of male-driven evolution in mammals. McVean and Hurst (1997) argue that K s X was too dramatically different from K s A to be consistent with the model. Conversely, Lercher, Williams, and Hurst (2001) argue against the model based on their finding that K s X is broadly similar to autosomal K s rates. Both suggest that differences among chromosomal mutation rates could be explained by a “modulated mutability” model. That is, selection is altering the mutability of stretches of the genome, possibly extending over entire chromosomes. Lercher, Williams, and Hurst (2001) also hypothesize that selection for locally similar substitution rates might be stronger in the human-mouse lineage than in the mouse-rat lineage. We tested these findings by examining orthologous coding-region data from the two lineages examined by these authors (mouse-rat and human-mouse).

Our examination of the two lineages in tandem brings our results into much closer agreement with previous literature and provides no impetus for rejecting male-driven evolution or for invoking a modulated mutability model. In contrast to the dramatic reduction of K s X relative to K s A as reported by McVean and Hurst (1997), our larger data set yields a moderate K s X reduction and an estimate of α that is in line with those published previously. Although we find the difference between K s X and K s A to be less pronounced than did McVean and Hurst (1997), both pairwise Kolmogorov-Smirnov tests and DFA of chromosomal K s rates clearly demonstrate that mutation rates on the X chromosome are statistically distinct from autosomal rates, in contradiction of Lercher, Williams, and Hurst's (2001) conclusion that the mammalian X chromosome is not an outlier.

Although our results support the observation of considerable autosomal heterogeneity in K _s_rates (Lercher, Williams, and Hurst 2001; Ebersberger et al. 2002), discriminant function analysis suggests that simple pairwise comparisons of chromosomal rates may obscure a possible “familial” relationship among groups of autosomes in terms of mutation rate similarity. This led us to explore the question of within-chromosome heterogeneity in mutation rates. Because genes within synteny blocks share similarities in evolutionary history, physical characteristics (such as chromatin structure), and possibly coordinate expression, we hypothesized that synonymous and nonsynonymous rates might be shared among these smaller units, based in large part on these commonalities. The results from our analysis of mutation rates across synteny blocks is incompatible with the idea that there is wide-spread sharing of evolutionary rates across entire chromosomes. First, we find that synteny blocks on the same chromosome in the human-mouse lineage are essentially as likely to be significantly different in Ks rate as synteny blocks on different chromosomes. The near equality of within- chromosome and between-chromosome heterogeneity is incompatible with the idea that selection modulates the substitution rates of entire chromosomes as a unit. However, discriminant function analysis analysis using chromosomes as true groups and synteny-block-average K s as the predictor does suggest that the K s of a block bears some relationship to which chromosome it resides in.

Analysis of K a/K s within synteny blocks seems to bear out the implication that selection does not act strongly on the whole-chromosomal level. We find that, in both lineages, K a/K s ratios for synteny blocks on the same human or mouse chromosome (using human chromosome in the human-mouse lineage and mouse chromosome in the mouse-rat lineage) are just as likely to be significantly different as K a/K s ratio comparisons for synteny blocks between chromosomes when examined by pairwise Kolmogorov-Smirnov tests. This makes it difficult to invoke whole-chromosome selection as a possible explanation for chromosome-to-chromosome rate heterogeneity.

All of the available evidence suggests that male-driven evolution can explain the systematic drop in K s rates for genes on the X chromosome in mammals. This suggests that global factors (such as the number of cell divisions in the germline) account for a large proportion of mutation rate disparity between the X chromosome and autosomes witnessed in a variety of studies (Shimmin, Chang, and Li 1993_b_; Chang and Li 1995; Makova and Li 2002), and by extension, perhaps between species as well. We therefore conclude that the high degree of variability in K s rates across chromosomes must be debated separately from discussions of male-driven evolution. We also suggest that looking at evolutionarily conserved synteny blocks provides a useful biological basis for further analyzing genomic data (Mural and Venter 2002) and offers further insight into rates of substitutions across mammalian chromosomes. Given the current progress on the rat genome project and calls for sequencing of other primates, the data to test hypotheses explaining the large variance in chromosomal K s rates should soon be available. We submit that, although a possible hypothesis for this variance must include “modulated mutability” as put forth by McVean and Hurst (1997), it is too soon to conclusively argue that this phenomenon exists in mammalian taxa, given the lack of strong empirical evidence and the possibility of alternative explanations.

1

Present address: Division of Molecular Biology and Biochemistry, School of Biological Sciences, University of Missouri-Kansas City.

David Rand, Associate Editor

Fig. 1.

Synonymous substitution rate (K s) of individual mouse chromosomes in the mouse-rat comparison (a) or individual human chromosomes in the human-mouse comparison (b). The standard error of K s is given for each chromosome. The autosomal average is shown as a dashed line, and the number of genes compared for each chromosome is given in parentheses

Table 1

Kolmogorov-Smirnov Results D Statistics Human-Mouse Data.

Note.—Above diagonal, K a = total number of significant K a comparisons: 36 (14%). Below diagonal, K s = total number of significant K s comparisons: 119 (47%). Significant (_P_-value < 0.05) results in bold.

Table 1

Kolmogorov-Smirnov Results D Statistics Human-Mouse Data.

Note.—Above diagonal, K a = total number of significant K a comparisons: 36 (14%). Below diagonal, K s = total number of significant K s comparisons: 119 (47%). Significant (_P_-value < 0.05) results in bold.

Table 2

Kolmogorov-Smirnov Results D Statistics Mouse-Rat Data.

Note.—Above diagonal, K a = total number of significant K a comparisons: 21 (11%). Below diagonal, K s = total number of significant K s comparisons: 25 (14%). Significant (_P_-value < 0.05) results in bold.

Table 2

Kolmogorov-Smirnov Results D Statistics Mouse-Rat Data.

Note.—Above diagonal, K a = total number of significant K a comparisons: 21 (11%). Below diagonal, K s = total number of significant K s comparisons: 25 (14%). Significant (_P_-value < 0.05) results in bold.

Table 3

K s Comparisons by Synteny Bin (Human-Mouse).

Note.—Percentages of comparisons significant at _P_-value < 0.05.

Table 3

K s Comparisons by Synteny Bin (Human-Mouse).

Note.—Percentages of comparisons significant at _P_-value < 0.05.

We thank Julian Solway for the NIH grant for Research Training in Respiratory Biology T32 HL07605 (to G.J.W.), and we thank the Searle Scholarship, the Burroughs Wellcome Fund, the Cancer Research Foundation, and the Brain Research Foundation (grant to B.T.L.) for financial support. We thank the editor and two anonymous reviewers for their helpful comments.

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