The Rates of Molecular Evolution in Rodent and Primate Mitochondrial DNA

J Mol Evol (2001) 52:40–50 DOI: 10.1007/s002390010132

Daniel M. Weinreich*

Museum of Comparative Zoology, Harvard University, 26 Oxford Street, Cambridge, MA 02138, USA

Received: 24 September 1999 / Accepted: 18 September 2000

Abstract. A higher rate of molecular evolution in ro- tioned and is found to be entirely the consequence of a dents than in primates at synonymous sites and, to a higher mutation rate in rodents. This conclusion is con- lesser extent, at amino acid replacement sites has been sistent with a replication-dependent model of mutation in reported previously for most nuclear genes examined. mtDNA. Thus in these genes the average ratio of amino acid replacement to synonymous substitution rates in rodents is Key words: Molecular clock — Mitochondrial — lower than in primates, an observation at odds with the DNA — Mammals — Neutral theory — Mildly delete- neutral model of molecular evolution. Under Ohta’s rious theory — Maximum likelihood mildly deleterious model of molecular evolution, these observations are seen as the consequence of the com- bined effects of a shorter generation time (driving a Introduction higher mutation rate) and a larger effective population size (resulting in more effective selection against mildly The molecular clock (Zuckerkandl and Pauling 1965) deleterious mutations) in rodents. The present study re- was originally a phenomenological description of mo- ports the results of a maximum-likelihood analysis of the lecular evolution which noted that proteins (and later ratio of amino acid replacements to synonymous substi- their genes) fix substitutions at an approximately linear tutions for genes encoded in mitochondrial DNA rate with respect to time. Genes on mammalian single- (mtDNA) in these two lineages. A similar pattern is ob- copy nuclear DNA have been especially well-studied served: in rodents this ratio is significantly lower than in (Laird et al. 1969; Dickerson 1971; Easteal 1985; Wu primates, again consistent only with the mildly deleteri- and Li 1985; Li et al. 1987; Gu and Li 1992; Ohta 1993; ous model. Interestingly the lineage-specific difference is 1995; Easteal et al. 1995; Yang and Nielsen 1998) due to much more pronounced in mtDNA-encoded than in a wealth of data derived from mammalian model organ- nuclear-encoded proteins, an observation which is shown isms. The requirement to explain these observations has to run counter to expectation under Ohta’s model. Fi- contributed substantially to the development of the dom- nally, accepting certain fossil divergence dates, the inant theories of molecular evolution (Kimura 1968; lineage-specific difference in amino acid replacement-to- King and Jukes 1969; Ohta and Kimura 1971; Gillespie synonymous substitution ratio in mtDNA can be parti- 1989). In contrast, no comparison of rates of molecular evolution in the mitochondrial genomes among mammals has yet been made. Under the neutral theory (Kimura 1968) the rate of * Current address: Department of Biology, University of California at San Diego, Muir Biology Building, 9500 Gilman Drive, La Jolla, CA substitution of selectively equivalent alleles is propor- 92093-0116, USA tional to the mutation rate and independent of population Correspondence to: Daniel M. Weinreich; email: [email protected] size (King and Jukes 1969; Kimura and Ohta 1971). This 41

Table 1. GenBank accession numbers for complete mitochondrial Table 2. GenBank accession numbers for cytochrome b and cyto- sequences used chrome c oxidase subunit II sequences used

Species Accession No. Accession No.

Homo sapiens J01415 Species Cyt b CO II Pongo pygmaeus D38115 Mus musculus J01420 Rodents Rattus norvegicus X14848 Acomys wllsoni AJ010561 U18832 Apodemus sylvaticus AF160603 U18833 Cratogeomys castanops L11908 U18828 Geomys bursarius AF158693 U18829 model accords well with early measurements of amino Georychus capensis AF012243 U18837 Microtus pennsylvanicus AF119279 U62573 acid fixation rates (e.g., Dickerson 1971, Fig. 3) and an Tachyoryctes spendens AF160602 U62575 assumption of a temporally constant mutation rate. How- Primates ever, it cannot also account for estimates of nucleotide Daubentonia madagascarensis U53569 L22776 substitution rates, which were found to be inversely re- Eulemur fulvus collaris U53576 AF081041 lated to generation time (Laird et al. 1969). A constant Hapalemur griseus U53574 L22778 Hylobates syndactylus Y13303 M58007 mutation rate per organismal generation has some theo- Lemur catta U53575 L22780 retical appeal (Wu and Li 1985; Li 1993). If DNA rep- Pan paniscus D38116 D38116 lication is the primary source of mutations, then the per- Saimiri sciureus U53582 U36848 germline-cell-division mutation rate should be constant across lineages. A constant per-organismal generation divisions per organismal generation in rodents than pri- mutation rate follows if the number of germline cell di- mates (Vogel and Rathenberg 1975), replication-inde- visions per organismal generation is constant. However, pendent mutation, and more effective weak selection this reasoning leaves the chronologically constant amino against some synonymous substitutions (Akashi 1996) in acid substitution rate unexplained. rodents due to their larger N. Nor is the amino acid The mildly deleterious model (Ohta 1973) is intended substitution rate chronologically constant: putatively to account for both observations by considering weakly larger effective population size notwithstanding, mean deleterious amino acid replacement mutations with se- amino acid fixation rates are 1.7 (Ohta 1995; Yang and lection coefficients roughly in the range 0 Նs Ն−1/N, Nielsen 1998) to 1.9 (Li et al. 1987) times higher in where N is the effective population size. Such mutations rodents than other mammalian lineages. Nevertheless, in may reach fixation by genetic drift, negative selection comparisons of nuclear genes between rodents and other coefficients notwithstanding (Ohta and Kimura 1971), mammals, synonymous substitution rates appear more and under this model the rate of amino acid fixations is strongly correlated with the reciprocal of organismal inversely related to the population size. Ohta (1972, p. generation time than are amino acid replacement rates 151) cites as an “empirical fact” an inverse relationship [but see Easteal (1985) and Easteal et al. (1995) for an between generation time and effective population size alternative interpretation of these data]. (Chao and Carr 1984; but see Nei and Graur 1984). Thus Mitochondria are subcellular organelles common to under the mildly deleterious theory, organisms with most eukaryotes which possess their own genetic system shorter generation times experience a higher chronolog- (Gillham 1994). This consists of approximately 16,500 ical mutation rate. However, because they also have a bases of DNA encoding roughly 13 proteins and 22 RNA larger population size, natural selection is more effective genes in most metazoans (Wolstenholme 1992), together at eliminating mildly deleterious mutations, and the net with a distinct system of DNA replication, transcription, chronological fixation rate of amino acid replacement and translation. Mitochondria are maternally inherited, mutations will be roughly constant. and although as many as 10,000 copies of mitochondrial Owing to the redundancy of the genetic code we can DNA (mtDNA) have been reported in single cells (Gill- distinguish between two classes of mutation in protein- ham 1994), persistent mtDNA polymorphism within coding DNA sequence data: synonymous and amino acid pedigrees (heteroplasmy) has not been observed replacement. Surveys of published DNA sequences for (Hauswirth and Laipis 1982; Ivanov et al. 1996) and is nuclear-encoded genes in mammals have permitted a thought unlikely to occur on theoretical grounds (Clay- more careful examination of the neutral and mildly del- ton 1996; Jenuth et al. 1996). The absence of hetero- eterious models (Wu and Li 1985; Li et al. 1987; Ohta plasmy and their haploid maternal inheritance means that

1993; 1995; Yang and Nielsen 1998). The reality appears the mitochondrial effective population size (Nmt) is equal to be yet more complicated: the synonymous substitution to the effective population size of females (Nf) (Birky et rate is not constant in terms of organismal generation al. 1983). Thus assuming equal sex ratio and panmixia, ס time, nor is it as high in rodents as predicted by their Nmt ¼Nnuc (the diploid nuclear effective population generation time. This could be explained by one or more size). More generally, for any fixed mating structure, Nmt of the following (Wu and Li 1985): fewer germline cell may simply be regarded as a linear function of Nnuc.In 42

Fig. 1. The unrooted phylogenetic tree of Homo sapiens, Pongo pygmaeus, Mus musculus, and Rattus norvegicus. ␻ ס ( dN/dS) is the ratio of the nonsynonymous-to-synonymous substitution rates. Three evolutionary models were fit to the sequences shown in Table 1. A The value of ␻ is constrained to be constant among all branches. B ␻ ␻ Order-specific values of ( prı´mate and ␻ rodent) and a value for the common ␻ ancestor ( C.A.) are defined. C Branch-specific values of ␻ are defined.

contrast to effective population size, mtDNA mutation is possible to estimate provisionally absolute mutation rates are decoupled from nuclear mutation rates (Vawter rates in the rodent and primate lineages. Although the and Brown 1986), and within mammals mtDNA muta- precise mechanistic causes of germline mutation are un- tion rates are much higher than are nuclear rates (Brown known, analyses of rates of synonymous substitution in et al. 1979). nuclear DNA give support to a replication-dependent This paper presents an analysis of the rates of amino model (Ohta and Kimura 1971; Wu and Li 1985; Chang acid replacement and synonymous substitutions in ho- and Li 1995). Is there evidence to support a replication- mologous genes in rodent and primate mtDNA, moti- dependent model of mutation in mammalian mtDNA? vated by two questions concerned with selection and mutation, respectively. The first question pertains to the Methods relationship between mutation rates and amino acid substitution rates in mtDNA-encoded genes. For example, Sequences and Alignments. All DNA sequences were retrieved from Martin and Palumbi (1993) compared rates of substitu- GenBank (http://www.ncbi.nlm.nih.gov). Two data sets were con- tion in mtDNA-encoded genes in sharks and mammals structed: the complete mtDNA sequences from two rodents and two primates (Table 1) and the cytochrome b and cytochrome c oxidase and found that, although amino acid fixation rates dif- subunit II sequences from seven rodents and seven primates (Table 2). fered in the two lineages, those differences were entirely For the latter data set, an equal number of species from each order for accounted for by differences in mutation rate and thus which DNA sequence for both genes was available were included. that those data were consistent with the strictly neutral Homologous amino acid sequences inferred from nucleotide sequence model. In contrast, nuclear substitution rates in rodents were aligned by eye. Nucleotide alignments were made using the pro- gram mrtrans.c (W. Pearson, unpublished), which uses the amino acid and primates (outlined above) are not consistent with the sequence alignment to locate insertion/deletions. mrtrans.c was modi- neutral model and appeal to differences in population fied to accommodate the mammalian mitochondrial genetic code. size has been used to explain these data. How can we Model of Codon Substitution. d (the number of nonsynonymous best account for lineage effects in mtDNA-encoded pro- N substitutions per nonsynonymous site) and dS (the number of synony- teins in rodents and primates? mous substitutions per synonymous site) were estimated under the Second, by appeal to certain fossil divergence dates it model of codon substitution developed by Yang et al. (Goldman and 43

Fig. 2. The unrooted phylogenetic tree of seven primates and rodents, assuming a constant value of ␻ over the entire tree; second, assuming consisting of the consensus neighbor-joining tree (Saitou and Nei 1987) order-specific values of ␻; and, finally, assuming 21 independent for cytochrome b and cytochrome c oxidase subunit II. The three mod- branch-specific values. els described in Fig. 1 were fit to the sequences shown in Table 2: first,

Yang 1994; Yang and Nielsen 1998) and as implemented in the PAML Even if selection acts on synonymous substitutions, it can be shown software package (Yang 1999). This is an appropriate method to ana- that this inverse relationship between ␻ and population size is predicted lyze mtDNA-encoded genes because it is robust to transition/ so long as selection on segregating amino acid replacements is on transversion bias, codon bias, and violations of the molecular clock average stronger. model (Goldman and Yang 1994). Likelihood-ratio tests to compare the ס fit of three nested models of molecular evolution to the data were Nuclear Rates of Evolution. Lineage-specific estimates of ␻

performed as described by Yang and Nielsen (1998), in which a fixed dN/dS for rodents and primates for most of the nuclear-encoded loci phylogeny (described next) is assumed for each data set. Under model originally analyzed by Ohta (1995) were calculated here using the ס ␻ A, ( dN/dS) is assumed to be constant on all branches of the phy- maximum-likelihood estimates of dN and dS presented by Yang and logeny; under model B, distinct values of ␻ for rodent and primate Nielsen (1998, Table 2). Lineage-specific average ratios were calcu- branches are assumed; and under model C, independent values of ␻ are lated by weighting the gene-specific ratios by the gene length. fit to each branch. For the whole-mtDNA data set, rodent and primate monophyly was assumed (Fig. 1). For the cytochrome b/cytochrome c oxidase subunit II data set, the consensus of the neighbor-joining phy- Results logenies (Saitou and Nei 1987) for each gene as implemented in MEGA (Kumar et al. 1993) was constructed (Fig. 2). Theoretical Expectations for the Relative Rates of Evolution of Mitochondrial DNA and Autosomes Comparison of Rates of Evolution Among Lineages. Two ap- proaches were employed to compare rates of molecular evolution be- Charlesworth et al. (1987) considered the relative rates of ␻ tween rodents and primates. First, was compared among lineages, fixation of equivalent mutations (those having equal se- and second, absolute rate estimates were made where extrinsic (fossil) divergence estimates are available. Differences in ␻ between lineages lective effect) in sex-linked and autosomal loci in finite

may represent differences in dN or dS (or in both). Following Kimura populations by applying Kimura’s (1962) diffusion result (1977), under the neutral model we can write for a mutation’s probability of fixation. For the case of very weak selection (|Ns| Ӷ 1) the ratio of the rate of d ␮ f ␻ = N = N N selected site substitution at an autosomal locus to the rate ␮ (1) dS S fS at a mitochondrial locus is given by where ␮ and ␮ are the nonsynonymous and synonymous mutation N S 2 rates and fN and fS are the proportions of selectively neutral amino acid 1 + Ns͑1 + h͒ and synonymous mutations. For homologous genes the ratio ␮ /µ is 3 N S R ≈ (3) unlikely to vary greatly among lineages because it reflects merely the mt 1 relative frequencies of amino acid replacement and synonymous re- 1 + Ns 4 ס placement sites in the sequence. Thus so long as fS 1 (Jukes and Cantor 1969) or at least is invariant across lineages, differences among lineages in ␻ for a gene imply lineage-specific differences in f . Under assuming random mating, equal mutation rates, and Nmt ס N the mildly deleterious model (Ohta and Kimura, 1971), if we assume ¼Nnuc and adopting the several algebraic approxima- that synonymous substitutions evolve under strict neutrality, we write tions and the notation of Charlesworth et al. (1987). 0 Յh Յ1 is the selective effect on the heterozygote, and when ␮ N s <0,Rmt can be seen by inspection to be less than 1.0 dN N 1 ␻ = ϰ ϰ (2) for all values of h. Thus, independent of the strength of d ␮ f N S S S dominance, the rate of fixation of equivalent mildly del- and conclude that differences among lineages in ␻ for a gene inversely eterious mutations is less on autosomes than on mtDNA. reflect lineage-specific differences in the effective population size, N. Conversely, when s >0,Rmt is greater than 1.0 for all h 44

Table 3. Log-likelihood differences with statistical significancea between models in Fig. 1 for mtDNA-encoded loci in Table 1

2⌬l

␻b ␻b ␻ ␻b Locus Codons AvsB BvsC rodent primate rodent/ primate ATPase 6 226 44.66**** 0.36 0.007 0.119 0.059 ATPase 8 67 13.90*** 1.76 0.071 0.535 0.133 CO I 513 11.98** 1.94 0.005 0.019 0.263 CO II 227 21.04**** 0.22 0.001 0.026 0.038 CO III 260 30.72**** 0.56 0.005 0.053 0.094 Cyt b 379 28.24**** 0.48 0.012 0.032 0.375 NADH 1 318 72.76**** 2.30 0.001 0.130 0.094 NADH 2 345 18.26*** 0.99 0.002 0.111 0.018 NADH 3 115 4.57 0.09 0.024 0.094 0.255 NADH 4 459 30.76**** 1.35 0.022 0.071 0.310 NADH 41 97 3.86 1.85 0.047 0.044 1.068 NADH 5 603 32.09**** 2.47 0.005 0.098 0.051 NADH 6 172 2.29 3.14 0.050 0.065 0.769 Pooledc 3781 315.13**** 17.51 0.012 0.111 0.206

ס ␹2 ס ␹2 ס a ⌬ ␹2 2 l distributed as with df 2 because nested models each estimate two additional parameters. * 0.05[2] 5.991; ** 0.01[2] 9.210; ס ␹2 ס ␹2 *** 0.001[2] 13.816; **** 0.0001[2] 18.50. b ␻ values estimated under model B. ס ␹2 ס ␹2 ס ␹2 ס c ␹2 Codons, log-likelihood differences, and df summed: * 0.05[26] 38.885; ** 0.01[26] 45.642; *** 0.001[26] 54.052; **** 0.0001[26] 61.75. ␻ values averaged, weighted by gene length.

so that the rate of fixation of equivalent weakly advan- Whole-mtDNA Comparisons tageous mutations is greater for autosomes than for mtDNA. This result is perhaps unexpected since genetic Assuming rodent and primate monophyly, maximum covering (i.e., when h < 0.5) aids the fixation of delete- likelihood estimation for each of the 13 mtDNA-encoded rious mutations and hinders the fixation of advantageous genes from Homo, Pongo, Mus, and Rattus (Table 1) was mutations on autosomes. However, this effect is more carried out under the three models shown in Fig. 1. Un-

than offset by the fourfold increase in mitochondrial V␦x der model A all five branches in the phylogeny are as- ס ␻ (the variance in allele frequency due to Wright–Fisher sumed to evolve with a single value of ( dN/dS); sampling) as a consequence of its fourfold smaller effec- under model B rodent, primate, and common ancestor ␻ tive population size. Note also that Rmt is monotonically values of are estimated independently; and under increasing in Ns. In other words, for equivalent muta- model C ␻’s on all five branches of the phylogeny are tions at loci in the two genomes, increasing N increases assumed to be independent. Under the null hypothesis

Rmt when s > 0 and decreases Rmt when s < 0. Although that the data fit all models equally well, twice the dif- the derivation assumes very weak selection, larger ef- ference in log-likelihood values (2⌬l) between models is because each 2 ס fects in the same direction occur for |Ns| < 1 (Charles- expected to be ␹2-distributed with df

worth et al. 1987) and the monotonicity of Rmt in Ns has nested model adds two parameters. The results of this been verified by computer simulation over the range |Ns| analysis are shown in Table 3. For 10 of the 13 genes the < 5 (not shown). X-linked mutations experience genetic fit of model B was highly significantly better than of covering only in the homogametic sex. Consequently model A (P < 0.01). The remaining three showed no fixation rates for equivalent weakly deleterious (advan- significant difference in fit between models, but these tageous) mutations are also higher (lower) on mtDNA represent three of the four shortest genes and thus the than on X chromosomes. Indeed the magnitude of the statistical power is expected to be weak. Note too that, effect can be shown to be more pronounced than Eq. (3). for roughly half of the genes in Table 3, the values of 2⌬l Finally, allowing for genome-specific mutation rates between model A and model B far exceed the value of ␮ ␮ ␹2 scales Eq. (3) by the factor nuc/ mt, the ratio of the 0.0001[2]. In contrast, none of the 13 genes in Table 3 fit nuclear to mitochondrial per-chromosome mutation model C significantly better than model B. The pooled ␮ ␮ rates. If mt is greater than nuc, as it appears to be in results across loci in Table 3 give similar results. The mammals (Brown et al. 1979; Avise 1991), the relative value of 2⌬l between model A and model B summed ␹2 difference in fixation rates for mildly deleterious muta- across loci far exceeds the value of 0.0001[26], while the tions in nuclear and mitochondrial loci will be increased. P value associated with the pooled comparison between However, for advantageous mutations no general con- model B and model C is 0.89.

clusions about the value of Rmt can be made, since values For the genes in Table 3 for which model B is seen to ␮ ␮ of mt > nuc exist which can offset the effect in Eq. (3). fit the data significantly better, we next compare the 45

Table 4. Log-likelihood differences with statistical significance between models in Fig. 2 for mtDNA-encoded loci in Table 2

2⌬l

a b ␻b ␻c ␻ ␻c Locus Codons AvsB BvsC primate rodent rodent/ primate CO II 227 36.35**** 35.50** 0.042 0.010 0.238 Cyt b 329 20.1**** 47.70*** 0.049 0.023 0.469 Pooledd 556 56.36**** 83.20**** 0.046 0.018 0.375

ס ␹2 ס ␹2 ס a ⌬ ␹2 2 l (A vs B) distributed as with df 2 because model B estimates two more parameters than model A. * 0.05[2] 5.991; ** 0.01[2] 9.210; ס ␹2 ס ␹2 *** 0.001[2] 13.816; **** 0.0001[2] 18.50. ס ␹2 ס ␹2 ס b ⌬ ␹2 2 l (B vs C) distributed as with df 18 because model C estimates 18 more parameters than model B. * 0.05[18] 30.144; ** 0.01[18] ס ␹2 ס ␹2 34.805; *** 0.001[18] 42.312; **** 0.0001[18] 48.94. c ␻ values estimated under model B. These values should be regarded as order-specific means because of the significantly better fit of model C (Yang and Nielsen 1998). ␹2 ס ␹2 ס ␹2 ס ␹2 ס d ␹2 Codons, log-likelihood differences and df summed: * 0.05[4] 9.488, 0.05[36] 50.998; ** 0.01[4] 13.277, 0.01[36] 58.62; *** 0.001[4] ␻ ס ␹2 ס ␹2 ס ␹2 ס 18.467, 0.001[36] 67.985; **** 0.0001[4] 23.50, 0.0001[36] 76.50. values averaged, weighted by gene length.

maximum-likelihood estimates of the order-specific val- B has two more parameters than A. Similarly 2⌬l be- ues of ␻, also shown in Table 3. In each of these 10 tween model B and model C is expected to be ␹2- ס ␻ cases, the estimate of rodent is less than the estimate of distributed with df 18 because C has 18 more param- ␻ ␻ ␻ primate. The ratio of values ( rodent/ primate) for each eters than B. The results of this analysis are shown in gene is also shown and ranges from 0.018 to 0.375 Table 4. For both genes the fit of model B was highly among genes whose values of ␻ differ significantly be- significantly better than that of model A (P < 0.0001). ␻ tween orders. The weighted average value of rodent/ Pooling genes, the fit of model B is similarly signifi- ␻ primate across all 13 mtDNA-encoded loci is 0.206. cantly better than that of model A (P < 0.0001). Order- specific estimates of ␻ are also shown in Table 4. For ␻ both genes the estimate of rodent is again less than the Comparisons at Cytochrome b and Cytochrome c ␻ ␻ ␻ estimate of primate. The ratio of values ( rodent/ primate) Oxidase Subunit II in this data set are in the range 0.238–0.469, with a weighted average of 0.375. Holding species constant, Table 3 demonstrates that Interestingly, the fit of model C was also highly sig- ␻ significantly exceeds ␻ at 10 of 13 mtDNA- primate rodent nificantly better than that of model B (CO II, P < 0.01; encoded genes and that these values are statistically in- Cyt b, P < 0.001; pooled data, P < 0.0001) for this data distinguishable at the remaining 3 genes. It is also pos- set. This is unlikely to be the consequence of the impre- sible to make comparisons between rodent and primates cise (consensus) rodent phylogeny used because results across a range of species, holding gene identity constant. do not differ materially either when a star phylogeny This was done for both cytochrome b and cytochrome c among rodent was used or when each gene’s analysis oxidase subunit II for the seven rodents and seven pri- was carried out with the phylogeny generated by that mates shown in Table 2. Among the primates a single gene (not shown). Rather, it may be due to the larger phylogenetic topology was generated by neighbor join- number of sequences in this data set and/or to the longer ing with both genes. However, among the rodents these divergence time represented in the data set, both of two genes have previously been shown to be phyloge- which would be expected to increase the test’s power. netically inconsistent (Honeycutt et al. 1995), perhaps Whatever its cause, this result means that we must view due to different rates of nucleotide substitution (Honey- the estimates of ␻ and ␻ shown in Table 4 as cutt et al. 1995) or very rapid speciation (Engel et al. rodent primate averages across branches within each order (Yang and 1998; Conroy and Cook 1999). Assuming the consensus Nielsen 1998). However, it does not seem to undermine phylogeny (Fig. 2), maximum-likelihood estimation for the conclusion that (average) order-specific estimates of cytochrome b and cytochrome c oxidase subunit II was ␻ differ significantly or that the value of ␻ is carried out under the same three models used above. rodent roughly 40% of the value of ␻ . Under model A all branches in the phylogeny are as- primate sumed to evolve with a single value of ␻; under model B rodent, primate and common ancestor values of ␻ are Comparison at Nuclear-Encoded Genes estimated independently; and under model C ␻ on all 21 branches in the phylogeny are assumed to be indepen- The present study of mtDNA-encoded loci employs the dent. Under the null hypothesis that the data fit each maximum-likelihood method developed by Yang and model equally well, twice the difference in log-like- Nielsen (1998) and used by them to analyze Ohta’s lihood values (2⌬l) between model A and model B is (1995) data set of homologous nuclear-encoded se- -because quences from one artiodactyl, one primate, and one ro 2 ס again expected to be ␹2-distributed with df 46

␻ ␻ ␻ a Table 5. Values of artiodactyl, primate, and rodent for nuclear-encoded loci

␻ ␻ ␻ ␻ ␻ Locus Codons artiodactyl primate rodent rodent/ primate Acetylcholine receptor ␣ 456 0.042 0.088 0.045 0.504 Acetylcholine receptor ␤ 500 0.107 0.113 0.087 0.775 Acid phosphatase type 5 322 0.189 0.079 0.072 0.911 Albumin 606 0.587 0.189 0.150 0.791 Alkaline phosphatase, intestine 495 0.268 0.120 0.152 1.269 Alkaline phosphatase, liver 523 0.074 0.097 0.063 0.653 Aspartate aminotransferase Cytosolic 412 0.113 0.109 0.074 0.677 Mitochondrial 429 0.099 0.082 0.030 0.369 APT synthase ␣ 543 0.031 0.054 0.014 0.261 ATP synthase ␤ 357 0.030 0.000 0.014 ϱ ␤-1,4-Galactosyl transferase 396 0.274 0.243 0.152 0.626 Carboxypeptidase 432 0.080 0.028 0.032 1.141 Connexin 381 0.036 0.025 0.013 0.503 Corticotropin-releasing factor 182 0.269 0.099 0.159 1.605 Dopamine receptor D2 442 0.020 0.038 0.023 0.610 Fibrinogen ␣ 433 0.343 0.289 0.119 0.412 Glucose transporter 491 0.019 0.080 0.014 0.179 Growth hormone 189 0.096 0.228 0.062 0.274 Growth hormone receptor 636 0.183 1.113 0.387 0.347 Hexokinase I 915 0.128 0.108 0.036 0.335 IGF binding protein 1 258 0.178 0.355 0.126 0.355 IGF binding protein 3 287 0.073 0.957 0.100 0.104 Insulin-like growth factor 1 114 0.025 0.211 0.035 0.168 Insulin-like growth factor 2 149 0.114 0.126 0.130 1.031 Interleukin 1␣ 260 0.585 0.431 0.430 0.999 Interleukin 1␤ 263 0.481 0.626 0.315 0.503 Interleukin 2 152 1.793 0.770 0.350 0.454 Interleukin 6 205 0.698 1.910 0.659 0.345 Interleukin 7 153 0.683 1.463 0.328 0.224 Lactate dehydrogenase A 331 0.125 0.174 0.026 0.148 Lactoferrin 662 0.322 0.405 0.264 0.652 Luteinizing hormone receptor 685 0.216 0.350 0.138 0.395 Myelin proteolipid protein 148 0.117 0.273 0.000 0.000 Neuroleukin 557 0.091 0.059 0.098 1.652 Neurophysin I 162 0.097 0.078 0.061 0.781 Neurophysin II 116 0.056 0.282 0.008 0.029 Ornithine decarboxylase 460 0.081 0.062 0.122 1.963 Plasminogen activator inhibitor 386 0.125 0.141 0.120 0.850 Prolactin 197 0.280 0.327 0.440 1.344 Proopiomelanocortin 211 0.037 0.045 0.063 1.411 Protein disulfide isomerase 505 0.030 0.069 0.044 0.638 Terminal transferase 506 0.376 0.280 0.170 0.606 Thrombomodulin 341 0.198 0.222 0.081 0.364 Transforming growth factor ␤1 315 0.048 0.046 0.079 1.714 Transforming growth factor ␤2 413 0.006 0.026 0.047 1.785 Transforming growth factor ␤3 408 0.158 0.018 0.025 1.380 Transforming growth factor ␤3 receptor 843 0.135 0.286 0.143 0.499 Urokinase–plasminogen activator 403 0.317 0.398 0.353 0.887 Pooledb 18630 0.189 0.245 0.125 0.718

a Data from Yang and Nielsen (1998). b Codons summed; all other values weighted by length and averaged.

dent. Yang and Nielsen (1998) found that, at 22 of 48 were reported by Yang and Nielsen (1998) may represent nuclear loci, a model allowing lineage-specific values of effects in any of the three orders included in that study. ␻ fit the data significantly better than a model which Thus from those data we are unable to assign a statistical ␻ ␻ assumes a single value of . Estimates of artiodactyl, significance to pairwise comparisons among the values ␻ ␻ ␻ primate, and rodent, calculated for each gene using the of shown in Table 5. Nevertheless, we can perform a ס ␻ ␻ published lineage-specific values of dN and dS (Yang and sign test on the null hypothesis that Pr{ x < y} 0.5, Nielsen 1998, Table 2) are shown in Table 5. Those loci where x and y are different lineages. We observe that ס ␻ ␻ ␻ for which significant lineage-specific differences in artiodactyl exceeds primate for 20 of 48 genes [P 47 ␻ ␻ ס ⌺20 48 и 48 -j ) 0.5 0.156], artiodactyl exceeds rodent for (not shown), again much below the nuclear value re )0סj ␻ ␻ ס 33 of 48 genes (P 0.0066), and primate exceeds rodent ported for precisely these species comparisons. Thus the ␻ ␻ ס for 36 of 49 genes (P 0.00036). Thus we conclude that difference of mitochondrial and nuclear rodent/ primate ␻ across the nuclear loci rodent is less than the other two values reported in Tables 3–5 appears to represent a order-specific values of ␻ at a highly significant number genuine genome-specific contrast rather than a method- of loci, while there is no evidence of a difference in ␻ ological artifact. It is also unlikely that the observation is values between artiodactyls and primates. The average a numeric artifact. As a ratio of ratios, estimates of the ␻ ␻ ␻ ␻ value of rodent/ primate across the 48 nuclear loci in quantity rodent/ primate will be inflated by sampling vari- rodent primate Table 5 is 0.718. ance in either denominator (dS or dN ). However, higher mtDNA mutation rates (Brown et al. 1979) sug- gests that sampling variance will be higher for the mito- Discussion chondrial estimates of both quantities. This will dispro- ␻ portionately inflate the estimate of mitochondrial rodent/ ␻ In mtDNA-encoded genes the ratio of the amino acid primate, thereby making the present observation replacement rate to the synonymous substitution rate in conservative. Similarly, owing to their higher mutation rates, saturation in mitochondrial synonymous substitu- rodents is on average 20–40% of the primate ratio mt (Tables 3 and 4). These observations can be interpreted tions may bias estimates of dS downward. However, ␻ under either the neutral or the mildly deleterious model this effect should bias mitochondrial estimates of in of molecular evolution. Under the neutral model [Eq. both rodents and primates, and its effect on the mito- ␻ ␻ (1)], the higher ratio in primates implies that for mtDNA- chondrial ratio rodent/ primate is likely to be small. Algebraically we can represent this observation as encoded proteins, fa (the proportion of selectively neutral amino acid replacement mutations) is larger in primates than in rodents. However, in the absence of an a priori ␻mt ␻nuc rodent Ͻ rodent expectation for such a lineage-specific difference in ␻mt ␻nuc functional constraint at every mtDNA-encoded protein, primate primate this account is unappealing. Instead, we might favor a nonselective process to account for the correlated obser- or, equivalently, vations among genes (Lewontin and Krakauer 1973). Under the mildly deleterious model [Eq. (2)], most seg- ␻nuc ␻nuc regating amino acid replacement mutations are assumed primate Ͻ rodent. ␻mt ␻mt to be mildly deleterious and their rate of fixation is there- primate rodent fore inversely related to population size. Thus the rela- tively lower rate of amino acid substitution in all Recalling the definition of ␻ and assuming that synony- mtDNA-encoded proteins is consistent with a larger ef- mous substitutions evolve under strict neutrality, we find fective population size among rodents (Ohta 1973; Chao that and Carr 1984; but see Nei and Graur 1984). A similar interpretation can be made of the nuclear data presented ␻ nuc mt here (Table 5). nuc d N d S = и = R (4) ␻ mt nuc mt mt d N d S Comparison of Nuclear- and mtDNA-Encoded ␮ ␮ Substitution Ratios This follows because Eq. (3) must be scaled by nuc/ mt to account for genome-specific mutation rates and the ␻, the ratio of nonsynonymous-to-synonymous substitu- assumption of neutrality for synonymous mutations tions, is lower in rodents than primates in both nuclear- means that this scaling factor equals the reciprocal of mt nuc and mtDNA-encoded proteins. A single mechanism dS /d S . (Weak selection on synonymous substitutions (more effective purifying selection mediated by larger does not materially affect this reasoning, so long as the population size in rodents) appears to be a candidate to strength of selection acting on segregating synonymous explain both observations. It is interesting, however, to sites in each genome is comparable in the two lineages.) ␻ ␻ note that the average value of rodent/ primate for nuclear- Thus our empirical observation can be represented as primate rodent encoded proteins considerably exceeds that of mtDNA- Rmt < Rmt . Recall, however, that we previously encoded proteins (∼0.7 vs ∼0.3, although no followed Ohta and Kimura (1971) in assuming that s <0 и statistical test of the hypothesis of equal ratios was at- and Nprimate < Nrodent or, equivalently, that Nprimate s > и tempted). Moreover, the weighted average value of Nrodent s. Since Rmt is monotonically increasing in Ns ␻ ␻ rodent/ primate across all 13 mitochondrial proteins, com- [Eq. (3)], our theoretical expectation is therefore that primate rodent puted between Bos taurus (Anderson et al. 1982) and Rmt should exceed Rmt , whereas empirically the Mus musculus and Homo sapiens, respectively, is 0.385 inequality goes in the opposite direction. Therefore the 48 present observations appear to be at odds with the mildly begin from the premise that common selective forces are deleterious interpretation. acting on almost all genes in almost all lineages and Several assumptions made in the derivation of Eq. (3) attempt to account for data by invoking only differences warrant attention. First, the diffusion underlying Eq. (3) in mutation rate and population size. The present data assumes free recombination and therefore does not ac- suggest that we should perhaps reject this framework and count for the effect of complete linkage in mitochondrial conclude instead that gene-specific selective processes DNA (Moritz et al. 1987; but see Lunt and Hyman 1997; are acting on at least some loci encoded on different Awadalla et al. 1999; Eyre-Walker et al. 1999) on se- genomes of rodents and primates. This conclusion is lected site fixation rates (Felsenstein 1974). However, based on the comparison between genomes and extends previous analyses of nuclear data in mammals (Gillespie the comparison of estimates of Rmt between lineages seems unlikely to be compromised by this shortcoming 1989; Ohta 1995; Yang and Nielsen 1998). so long as mitochondrial recombination is absent (or at least equally rare) in both lineages. Equation (3) also assumes equal sex ratios, and if females outnumber Calibrating mtDNA Substitution Rates in Mammals with Fossils males, then Nmt >¼Nnuc, at least partially offsetting the reduction mitochondrial V␦x. But even in an hermaphro- -N , owing to the haploidy of Finally, we can attempt to partition the observed lineage½ ס ditic species N mt nuc specific differences in ␻ in mtDNA-encoded proteins mitochondria, in which case R ≈ [1 + 2⁄3Ns(1 + h)]/[1 + mt into absolute differences in either d or d by calibrating ½Ns], which is still less than 1.0 when Ns < 0 for all N S substitution rates with extrinsic species divergence time values of h. estimates. Based on paleontological data the divergence Our expression for R assumes that on average se- mt time between rat and mouse has been estimated at 12–14 lectively equivalent mutations occur in both genomes, Myr (Jaeger et al. 1986; Jacobs and Downs 1994) and the which may not be true. However, to offset the fourfold divergence time between humans and orangutans is es- reduction in mitochondrial V␦ underlying Eq. (3), we x timated to be 10–14 Myr (Pilbeam 1985; 1996). If com- would be forced to assume that the mean selection co- parisons between these two species pairs represent efficient acting against amino acid replacement muta- roughly the same amount of time, then the comparison of tions entering mitochondrially encoded loci is more than numbers of molecular substitutions (nonsynonymous or fourfold higher than that for mutations entering nuclear- synonymous) observed within lineages is a suitable encoded loci, a proposition presently with little empirical proxy for comparing the temporal rate of substitution support. [See Gillespie (1995) for a related critique of the across lineages. For all 13 mtDNA-encoded genes the mildly deleterious theory.] Equation (3) also assumes the maximum-likelihood estimate of the synonymous substi- neutrality of mitochondrial mutations within individuals. tutions per synonymous site (not shown) between Rattus The extreme transience of heteroplasmy within lineages and Mus exceed that quantity estimated between Homo ,by a sign test). In contrast 0.0001 ס Jenuth et al. 1996) supports this notion, and while re- and Pongo (P) laxation of this assumption affects the time to fixation of estimated replacement substitutions per replacement site a mitochondrial mutation within a lineage, it is unlikely (not shown) between those two rodents exceed the pri- by a 0.291 ס to affect the time to fixation within a population (Taka- mate estimate for only 5 of 13 genes (P hata 1984). sign test). Thus if we provisionally accept the paleonto- Finally, Takahata and Slatkin (1983) and Bergstrom logical data, it follows that the lineage-specific differ- and Pritchard (1998) have shown that genetic drift in ence in ␻ is driven entirely by lineage-specific differ- mtDNA during oogenesis increases the efficacy of natu- ences in dS. ral selection. This is a consequence of the fact that, al- Recently several workers have dated the rat–mouse though such drift reduces the allele frequency variance divergence at 20–29 Myr (O’h Uigin and Li 1992) to within individual eggs, it increases the allele frequency 35–40 Myr (Janke et al. 1994; Frye and Hedges 1995; variance among eggs, which, under many fitness models, Kumar and Hedges 1998). Thus perhaps the higher rate translates into an increase in fitness variance among of synonymous substitutions in the rodent pair is simply eggs. However, in the limit of oogenetic sampling of a the consequence of more elapsed time (Easteal et al. single mtDNA molecule, natural selection acting on a 1995). However, all of these studies are based on mo- mitochondrial mutation is equivalent to that acting on an lecular data and are predicated on the assumption of the asexual chromosome of equal size (Bergstrom and molecular clock. In particular, Janke et al. (1994) and ס Pritchard 1998). Thus Nmt Nf (Birky et al. 1983) pro- Frye and Hedges (1995) present analyses of mtDNA vides a ceiling rather than a floor for the effective popu- genes and, as such, represent an alternate interpretation lation size of mitochondria, and oogenetic sampling at of the data presented here. Inasmuch as substitution rate the level of mtDNA means that Eq. 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