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Contrasting Patterns of Nonneutral Evolution in Proteins Encoded in Nuclear and Mitochondrial Genomes
Daniel M. Weinreicha and David M. Randaa Department of Ecology and Evolutionary Biology, Brown University, Providence, Rhode Island 02912
Corresponding author: Daniel M. Weinreich, Department of Biology, Muir Bldg., University of California, 9500 Gilman Dr., San Diego, CA 92093., dmw{at}ucsd.edu (E-mail)
Communicating editor: A. G. CLARK
| ABSTRACT |
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We report that patterns of nonneutral DNA sequence evolution among published nuclear and mitochondrially encoded protein-coding loci differ significantly in animals. Whereas an apparent excess of amino acid polymorphism is seen in most (25/31) mitochondrial genes, this pattern is seen in fewer than half (15/36) of the nuclear data sets. This differentiation is even greater among data sets with significant departures from neutrality (14/15 vs. 1/6). Using forward simulations, we examined patterns of nonneutral evolution using parameters chosen to mimic the differences between mitochondrial and nuclear genetics (we varied recombination rate, population size, mutation rate, selective dominance, and intensity of germ line bottleneck). Patterns of evolution were correlated only with effective population size and strength of selection, and no single genetic factor explains the empirical contrast in patterns. We further report that in Arabidopsis thaliana, a highly self-fertilizing plant with effectively low recombination, five of six published nuclear data sets also exhibit an excess of amino acid polymorphism. We suggest that the contrast between nuclear and mitochondrial nonneutrality in animals stems from differences in rates of recombination in conjunction with a distribution of selective effects. If the majority of mutations segregating in populations are deleterious, high linkage may hinder the spread of the occasional beneficial mutation.
SINCE the introduction of DNA sequencing technology to population genetics (![]()
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To date, protein-coding genes on mitochondrial DNA (mtDNA) in animals have not been found to exhibit the diversity of polymorphism and divergence patterns seen in nuclear genes. On the contrary, nearly every sequencing study testing the neutrality of animal protein-coding genes in mtDNA reveals the same pattern: an excess of amino acid replacement mutations segregating within species, relative to fixed amino acid replacement mutations (![]()
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Thus the observation of a relative excess number of segregating amino acid replacement mutations in mtDNA-encoded loci is consistent with the assumption that many segregating amino acid replacement mutations are slightly deleterious. ![]()
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Here we explore two questions suggested by these observations. First, is there significantly more diversity in the patterns of polymorphism and divergence of nuclear-encoded genes than of mitochondrially encoded genes? To assess this question, we have performed a careful survey of the literature for data sets of nuclear and mitochondrial polymorphism and divergence. Second, animal mitochondrial and nuclear DNA exhibit five gross genetic differences: mtDNA apparently lacks recombination (![]()
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| MATERIALS AND METHODS |
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Published DNA sequences:
Data sets consisting of DNA sequence polymorphism and divergence for 39 nuclear loci from Drosophila spp. and 31 data sets for 7 mtDNA-encoded loci from diverse animal species were compiled from the literature. Many of the nuclear data sets are those used in ![]()
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A data set consisting of DNA sequence polymorphism and divergence for six nuclear loci from the plant Arabidopsis thaliana was similarly compiled from the literature. Gene name, protein length, sample size, fixed and polymorphic synonymous and amino acid replacement site counts, N.I., P value of the test statistic from the associated ![]()
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Computer simulations:
Computer simulations were written in "C" and compiled to run under UNIX. Simulations were parameterized in eight dimensions, shown in Table 4. Simulations follow N chromosomes, each represented by the interval (0, 1), which undergo repeated cycles (generations) of mutation, recombination, random mating and selection, and sampling. All statistics are calculated after recombination but before random mating and selection (![]()
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Mutations are of two sorts, selected and neutral, and in each generation the number of each sort in the population is determined by an independent Poisson-distributed deviate with mean Nµ/2. Chromosomes to be mutated are chosen at random and mutated "sites" are located as uniformly distributed real numbers on the interval (0, 1). Thus our simulations adhere to the infinite sites model (![]()
In any given generation, the number of recombination events is Poisson distributed with mean Nc. Pairs of "parental" chromosomes to be recombined are chosen randomly and the location of the crossover site is chosen as a uniformly distributed real number on the interval (0, 1). Each recombination event generates two novel chromosomes consisting, respectively, of all sites present on the first parental whose locations are numerically less than the crossover site together with all sites present on the second parental whose locations are numerically greater than the crossover site, and all sites present on the second parental chromosome whose locations are numerically less than the crossover site together with all sites present on the first parental whose locations are numerically greater than the crossover site.
Relative fitness is assessed for diploid genotypes. Genotype frequencies are calculated by the Hardy-Weinberg equation using allele frequencies before selection, which is equivalent to assuming random mating. Thus in these simulations N is both the census and effective population size. Under a multiplicative fitness model, the fitness of the i-jth genotype is given by
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(1) |
where s is the selection coefficient acting on selected sites, h is the degree of dominance, mi,j is the number of selected sites chromosomes i and j have in common, and ni,j is the number of selected sites appearing on exactly one of chromosomes i and j.
is the population mean fitness and is given by

Under an additive fitness model, the fitness of the i-jth genotype is given by
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(2) |
although wi,j is set to 0 if s < -1/(2mi,j + hni,j).
, mi,j, and ni,j are as above.
Finally, Wright-Fisher sampling is performed according to ![]()
Uniform deviates on (0, 1) were generated with the UNIX library random number function (drand48()), seeded with the program's unique process identifier (getpid()). Poisson and binomial deviates were generated as described in ![]()
Intralineal population bottlenecks were implemented as described in ![]()
N) and B (the size of the intralineal bottleneck, B
M) were employed as follows. In all cases, the intralineal bottleneck size (B) was set to 1 and the number of lineages was held at 1000, so that N = 1000 · M. Thus, in these simulations, N is not necessarily equal to the effective population size. The intensity of the bottleneck was parameterized by M, which assumed values of 10 (moderate intensity) and 100 (high intensity). When M is set to 1, the Bergstrom and Pritchard model degenerates to the no-bottleneck model described above.
Simulations were performed at steady-state as previously described (![]()
Since forward simulations are time intensive, these data files represented archived results, which could be reanalyzed as needed. Additionally, random chromosome samples of size n < N were drawn from archived population replicates to examine the consequence of sampling on statistics of interest. Finally, recording replicate results into data files allowed us to make our simulation reentrant, thereby permitting us to utilize QUAHOG (http://www.cs.brown.edu/software/quahog/), a UNIX-based job management facility with access to >100 ULTRASparc1 workstations within the Brown University Computer Science Department. Simulations for each point in parameter space were run until 1000 replicates had accumulated in the data file for that point, unless otherwise noted.
The correctness of the simulations was verified by comparison with expectations from analytic results (![]()
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Statistics:
Published DNA sequence data sets were tested for deviation from neutral expectation with the ![]()
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(3) |
As defined by ![]()
, and under strict neutrality the ratios in the numerator and denominator are expected to be equal (![]()
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The following statistics were tabulated from the computer simulations: the number of neutral and segregating sites in the entire population in the ith replicate (SiN,neut and SiN,sel, respectively) and the number of neutral and selected site fixation events in the ith replicate (cineut and cisel, respectively). To explore the consequences of sampling from whole populations, 10 independent random samples of x chromosomes each were drawn from each evolutionary replicate. We denote the number of neutral and selected sites segregating in the jth such sample drawn from the ith replicate as Si,jn=x,neut and Si,jn=x,sel, respectively.
N.I.N, the mean neutrality index for the entire population, was calculated as
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(4a) |
where r is the number of evolutionary replicates performed and N.I.iN, given by
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(4b) |
represents the neutrality index in the entire population in the ith simulated replicate. N.I.n=x, the mean neutrality index for a sample of x chromosomes drawn from the population, was calculated as
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(5a) |
where N.I.i,jn=x, given by
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(5b) |
represents the neutrality index in the jth subsample of size x drawn from the ith simulated replicate. Values of N.I.n=10 and N.I.n=30 were calculated. We extended our no-division-by-zero protocol to these simulated data, substituting a 1 for SiN,neut, Si,jn=x,neut, or cisel, in any case in which a zero was observed.
If one assumes that amino acid replacement mutations are selected and that synonymous mutations are neutral, then Equation 4aEquation 4b and Equation 5aEquation 5b are seen to be equal to Equation 3. Though selection is known to act on some synonymous mutations in both genomes (![]()
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Power analysis:
The statistical power of the ![]()
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| RESULTS |
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Published nuclear- and mtDNA-encoded DNA sequence analysis:
N.I. values for 39 nuclear- and 31 mtDNA-encoded loci are shown in Table 1 and Table 2. After randomly removing one of each of the three duplicate nuclear data sets (see MATERIALS AND METHODS), the mean nuclear-encoded N.I. value (±SD) is 1.21 ± 1.38 while the mtDNA-encoded mean N.I. is 4.41 ± 4.52, which differ significantly (t = 3.82, d.f. = 66, P = 0.0002). Fig 1 is a frequency histogram of N.I. values for nuclear- and mtDNA-encoded genes, and partitioning N.I. values into the classes shown in Fig 1 reveals a highly significant association with genome (G = 18.56, d.f. = 6, P = 0.005).
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Moreover, we may restrict ourselves to those data sets with significant (defined as P < 0.05) McDonald/Kreitman test results: there were 6 such nuclear-encoded loci (Acp26Aa, G6pd, jgw, per, Pgi, and z), of which 5 have N.I. values <1.0. In contrast, 15 mtDNA-encoded loci have significant test results (ATPase 6 in D. melanogaster; CO II in hominoids; Cyt b in Ambystoma spp., Brachyramphus spp., Drosophila spp., Grus spp., Melospiza melodia, Microtus spp., Pomatostomus temporalis, and Sciurus aberti; NADH 2 in Homo sapiens; NADH 3 in Mus domesticus and Pan troglodyte; NADH 5 in D. melanogaster; and restriction fragment length polymorphism (RFLP) survey in H. sapiens), only one of which has N.I. values <1.0. These two observations jointly have a P value of 0.0004 against a null hypothesis of no difference in genome-specific bias in direction of significant deviation (G = 12.37, 1 d.f.).
Published sequence analysis for nuclear DNA of A. thaliana:
N.I. values for six nuclear genes from A. thaliana are shown in Table 3. Five of the six genes have N.I. values >1.0, and the mean (±SD) N.I. value for these genes is 2.97 ± 2.02. Three of the genes exhibit significant ![]()
Diffusion approximation provides a lower bound for N.I. as a function of Ns:
By assuming selective and genetic site independence, ![]()
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(6) |
where µ is the per-chromosome mutation rate. The asterisks again denote our no-division-by-zero protocol. Thus E(u*sel) is given by the greater of Equation 5.6 of ![]()
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Simulation of N.I. as a function of Ns:
In Fig 2, we present mean simulated whole-population neutrality index values (N.I.N, Equation 4aEquation 4b) under the multiplicative (Equation 1, open circles) and additive (Equation 2, solid circles) fitness schemes, for
= -0.01
s
= 0.01 when N = 1000, µ =
= 0.0005, h = 1, Nc = 0, Tdiv = 30N = 30,000 generations, and M = B = 1. Fig 2 also shows the diffusion-derived expression (Equation 6, solid line), which is exceeded by simulated values (under both models) for all values of Ns, as expected. As previously noted (![]()
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3 million years (![]()
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6 million years (![]()
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Mean sample neutrality index values (N.I.n=x, Equation 5aEquation 5b) are also shown in Fig 2 for x = 10 (x) and 30 (+) drawn from populations under multiplicative fitness. Note first that the location of the maximum is unaffected by sampling. When s is negative, the number of segregating neutral sites in samples (Si,jn=x,neut) is again largely independent of both sample size and strength of purifying selection (not shown), as was the number of segregating neutral sites in the whole population. Thus the location of the maximum is driven by the behavior of csel, which contributes equally to Equation 4aEquation 4b and Equation 5aEquation 5b. However, the value of N.I.n=x is conservative when s is negative. Selection keeps deleterious mutations at low frequency (![]()
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4/N), thereby biasing N.I.n=10 downward (Fig 2, inset). Thus, under weak positive selection, small sample estimates of N.I. can overstate the true population deviation from the neutral expectation, although this effect is modest.
Behavior under the additive fitness model (Equation 2) does not differ qualitatively for any parameter values examined, and no further results under this model are presented.
Consequences of variation in Nc, N, µ, h, and M on values of N.I.:
As noted in the Introduction, the genetics of mtDNA- and nuclear-encoded genes exhibit five gross differences: recombination rate, effective population size, mutation rate, degree of selective dominance, and intralineal bottlenecks. These aspects were modeled in our simulations by the parameters Nc, N, µ, h, and M, respectively, which were varied independently. Mean N.I. values from these simulations are shown in Table 5. Mean N.I. is monotonic when Ns > -3 (Fig 2), and selection coefficients acting on amino acid replacement mutations in mtDNA-encoded proteins have been estimated to lie in the range -3
Ns
0 (![]()
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Three patterns seen in Fig 2 are also manifest in Table 5. First, in almost all cases, the inverse relationship between N.I. and Ns is preserved, so that weak positive selection (represented in the left column) gives N.I. values <1.0 and weak purifying selection (right column) gives N.I. values >1.0. Second, sample neutrality index values deviate from 1.0 less than whole-population values. And finally, sample size generally has only a modest effect on N.I.n=x. Several additional conclusions are apparent. Most surprising to us was the general insensitivity of N.I. to recombination. In contrast, N.I.N is very sensitive to the population size (seen when N = 10,000 and when M = 10 and 100, both of which reduce the influence of genetic drift), although this sensitivity is greatly attenuated when the neutrality index is calculated for realistically sized samples. It should also be noted that small values of N · µ cause a jump in the proportion of replicates in which zero segregating sites are observed (e.g., ![]()
2 or s < 0 and h < 0) could not be completed because under these conditions the number of segregating sites grew impractically large. Finally, computation time per generation of simulation increased with the number of chromosomes in the population, and the number of generations simulated increased with population size (since Tdiv = 30 · N). Thus, <1000 replicates were completed for large values of Nc, N, µ, and M.
Consequences of variation in Nc, N, µ, h, and M on McDonald/Kreitman power:
The ![]()
The proportion of replicates that give a significant McDonald/Kreitman test statistic while recombination rate, population size, mutation rate, dominance, and bottleneck size are independently varied is shown in Table 6, which has the same format as Table 5. The test was found to be more sensitive to negative selection than positive selection (![]()
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| DISCUSSION |
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Patterns of polymorphism and divergence in nuclear- and mtDNA-encoded proteins differ significantly:
Mitochondrially encoded proteins exhibit a consistent pattern of excess amino acid replacement mutations segregating within species, as measured by N.I. (![]()
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To be fair, we did have some a priori expectation of this pattern (e.g., ![]()
In theory, this could be a numerical artifact. Because the neutrality index (Equation 3) is a ratio of ratios, estimates of its value will be inflated by large sampling variance in either denominator (fixed amino acid replacement site or polymorphic synonymous site counts). Thus shorter genes or smaller population samples will bias the N.I. upward. And indeed, the mean gene lengths are significantly less in the mtDNA-encoded data set (mean number of amino acids ± SD encoded in nuclear data set, 381.09 ± 152.19; in mtDNA data set, 260.65 ± 156.67, t = 3.18, d.f. = 65, P = 0.0011). However, four of six mtDNA-encoded loci with N.I. values <1.0 are shorter than the sample mean, and among both data sets, N.I. is uncorrelated with gene length (not shown). Moreover, no significant difference in length exists between the 15 longest mtDNA-encoded genes and the entire nuclear data set (t = 0.167, d.f. = 47, P = 0.43) although a highly significant association between N.I. values >1.0 and genome persists (partitioning N.I. values as greater than and <1.0: G = 11.06, d.f. = 1, P = 0.0009). Similarly, no significant difference in length exists between the 18 shortest nuclear-encoded genes and the entire mitochondrial data set (t = 0.270, d.f. = 49, P = 0.39), but again a highly significant association between N.I. and genome is detected (G = 10.36, d.f. = 1, P = 0.0013). Thus the pattern in Fig 1 seems not to be driven by any bias in gene lengths. Sample sizes also differ significantly (n ± SD for nuclear data sets, 17.69 ± 14.98; for mtDNA data sets, 28.99 ± 26.91, t = 1.99, d.f. = 65, P = 0.025); however, the larger average mtDNA data set should reduce variance in those estimates and bias estimates of N.I. downward, suggesting that the reported genome-specific difference in N.I. may be conservative. Thus differences in sampling variance (either in gene length or sample size) cannot account for the pattern in Fig 1.
The McDonald/Kreitman test is insensitive to populations not at equilibrium, to recombination, and to variation in nucleotide mutation rates (![]()
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Alternatively, natural selection acting on synonymous mutations could be responsible for the pattern seen in Fig 1. For example, in D. simulans, segregating unpreferred synonymous mutations are overrepresented relative to fixations (![]()
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There are only 13 mtDNA-encoded loci in metazoans (![]()
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Genetic factors alone seem unable to account for empirical patterns in neutrality index values:
Our simulations (Fig 2) repeat the observation that N.I. is quite sensitive to Ns, the strength and direction of selection (![]()
As noted, only 17% (6 of 36) of the nuclear data sets in Table 1 show a significant deviation from neutral expectation by the ![]()
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The biological importance of the frequency distribution of s:
At present, there is little support for the hypothesis that unique selective forces acting on mitochondrially encoded OXPHOS proteins explain the pattern shown in Fig 1, although we cannot rule out this possibility. And no single genetic difference between nuclear and mtDNA genetics examined appears sufficient to explain this pattern. However, both our simulations and analytic expectations assume that s is equal for all selected mutations entering the population (we have not included deleterious mutations of large effect since such mutations contribute very little to polymorphism or divergence). This assumption of a single fixed s is clearly simplistic; indeed, it is theoretically problematic (![]()
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1.0. [It should be noted that although indirect evidence of recombination in animal mtDNA has recently accumulated (![]()
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Our hypothesis predicts that empirical neutrality index values should be inversely correlated to recombination rate, although among the nuclear genes in Table 1 for which we were able to find published estimates of recombination rate, no correlation exists. Moreover, in a cursory exploration of selective frequency distribution space we were unable to find parameter values in which this effect was observed. Recently, ![]()
in his notation) under several more sophisticated frequency distributions of s. His simulations compared N.I. under free recombination and complete linkage as a function of population size, but, like us, he was unable to find a case in which linkage carried N.I. from
1.0 to considerably larger values.
However, suggestive comparisons emerge from DNA polymorphism and divergence data recently accumulated from the plant A. thaliana (Table 3). A. thaliana is almost exclusively self-fertilizing, and its effective recombination rate is consequently very low (![]()
Another intriguing system is the Ost/O3+4 chromosomal inversion in D. subobscura. Acph-1 lies very near one of the inversion breakpoints (![]()
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Finally, several groups (![]()
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While our simulations revealed no single genetic factor to account for the marked difference in patterns of nonneutral evolution seen in nuclear- and mtDNA-encoded proteins (Fig 1), we suggest two (nonexclusive) hypotheses. Fig 2 and Table 5 demonstrate that N.I. is inversely related to Ns, so that if the selective histories of the genes in Table 1 and Table 2 are distinct, N.I. will be affected. Thus, if the fraction of mildly deleterious amino acid replacement mutations entering OXPHOS genes is larger than the corresponding fraction for nuclear loci (or equivalently if the opportunities for positive selection are greater for nuclear-encoded loci), mtDNA-encoded N.I. values will be biased upward. Additionally, we speculate that genetic linkage in mtDNA results in patterns of polymorphism and divergence that are dominated by the largest class of mutations entering the population. If the frequency distribution of selection coefficients is such that a majority of mutations that contribute to polymorphism and divergence are mildly deleterious, values of N.I. >1 may result in regions of low recombination. Both hypotheses are open to experimental attack.
| ACKNOWLEDGMENTS |
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R. Nielsen encouraged us to explore this problem by computer simulation and solved an interesting bug. Two anonymous reviewers improved this study considerably. Access to over 100 SUN workstations were kindly made available to us by the Brown University Computer Science Department. D.M.W. was supported by National Science Foundation grants 9527709 and 9707676 awarded to D.M.R.
Manuscript received June 22, 1999; Accepted for publication May 19, 2000.
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) and additive (