Copyright  2001 by the Society of America

Estimates of the Rate and Distribution of Fitness Effects of Spontaneous in

Clifford Zeyl* and J. Arjan G. M. DeVisser† *Department of Biology, Wake Forest University, Winston-Salem, North Carolina 27109 and †Laboratory of Microbiology, Wageningen University and Research Center, 6703 CT Wageningen, The Netherlands Manuscript received July 10, 2000 Accepted for publication September 19, 2000

ABSTRACT The per-genome, per-generation rate of spontaneous mutation affecting fitness (U) and the mean fitness cost per mutation (s) are important parameters in evolutionary genetics, but have been estimated for few species. We estimated U and sh (the heterozygous effect of ) for two diploid yeast strains differing only in the DNA mismatch-repair deficiency used to elevate the mutation rate in one (mutator) strain. Mutations were allowed to accumulate in 50 replicate lines of each strain, during 36 transfers of generations). Among wild-type lines, fitnesses were bimodal, with 600ف) randomly chosen single colonies one mode showing no change in mean fitness. The other mode showed a mean 29.6% fitness decline and the petite , usually caused by partial deletion of the mitochondrial genome. Excluding petites, maximum-likelihood estimates adjusted for the effect of selection were U ϭ 9.5 ϫ 10Ϫ5 and sh ϭ 0.217 for the wild type. Among the mutator lines, the best fit was obtained with 0.005 Յ U Յ 0.94 and 0.049 Ն sh Ն 0.0003. Like other recently tested model organisms, wild-type yeast have low mutation rates, with high mean fitness costs per mutation. Inactivation of mismatch repair increases the frequency of slightly deleterious mutations by approximately two orders of magnitude.

HE rate at which spontaneous mutations occur and somes that were sheltered from selection. The results Tthe frequency distribution of their effects on fitness were interpreted as indicating a relatively high Umin of -per genome per generation, with an average reduc 1ف are of interest both as basic parameters of and as important factors in the of tion of viability of 1–2% per mutation (Simmons and such diverse features as life histories, and recom- Crow 1977). However, this interpretation has been bination, , and senescence (Kondrashov challenged by reanalyses of the D. melanogaster data 1998; Lynch et al. 1999). However, estimates of these (Keightley 1996; Garcia-Dorado 1997; Caballero parameters have been reported for only a few organisms. and Keightley 1998) and by additional mutation-accu- Rates and effects of mutation can be estimated by mulation (MA) experiments on D. melanogaster (Fer- allowing spontaneous mutations to accumulate over na´ndez and Lo´pez-Fanjul 1996; Fry et al. 1999; see many generations in replicate populations founded by reviews by Garcı´a-Dorado et al. 1999; Keightley and a common ancestor. With minimal population sizes, the Eyre-Walker 1999). These more recent studies imply effectiveness of selection against deleterious mutations that U is substantially lower, and s substantially greater, is minimized and mutations are fixed by . As than the values inferred by Mukai et al. (1972). An mutations accumulate, the mean fitness of the replicate unexpectedly low U ϭ 0.0052 was also estimated for the populations is expected to decline while variance among nematode Caenorhabditis elegans (Keightley and them increases. From the per-generation changes in Caballero 1997), with a very high s ϭ 0.21. Keightley mean and variance, a lower bound for the mutation and Caballero (1997) introduced a maximum-likeli- rate per diploid genome (Umin) and an upper bound hood (ML) algorithm for estimating U and s from the for the mean fitness reduction (smax) can be estimated if fitness of MA lines. This allows s to vary among muta- it is assumed that all mutations have equal and negative tions, identifies the most likely distribution of s from a fitness effects (Bateman 1959). wide variety of gamma distributions, and yields estimates Until quite recently, the only available estimates were of U and s, rather than Umin and smax. The results of a based on experiments with Drosophila melanogaster (Mukai second C. elegans experiment (Vassilieva and Lynch 1964; Mukai et al. 1972; Ohnishi 1977) in which muta- 1999) yielded estimates of Umin ϭ 0.05 and smax ϭ 0.14. tions were allowed to accumulate on second chromo- Likewise, in two independent MA experiments on Arabi- dopsis thaliana, per-generation fitness declines were small (Schultz et al. 1999) or undetected (R. G. Shaw, D. L. Byers and E. Darmo, unpublished results). For Corresponding author: Clifford Zeyl, Department of Biology, Wake Forest University, P.O. Box 7325, Winston-Salem, NC 27109. Escherichia coli, Kibota and Lynch (1996) estimated E-mail: [email protected] Umin ϭ 0.0002 and smax ϭ 0.012, although given its smaller

Genetics 157: 53–61 ( January 2001) 54 C. Zeyl and J. A. G. M. DeVisser genome size and the occurrence of only one cell division MATERIALS AND METHODS per generation, a low per-generation mutation rate is less Founding and mutation accumulation: The surprising for E. coli than for multicellular eukaryotes. founding WT was a diploid leu2⌬ derived from strain The budding yeast Saccharomyces cerevisiae is both a Y55. The M was an otherwise identical ura3 leu2⌬ msh2::URA3 model organism of major importance in molecular ge- genotype (Chambers et al. 1996). From single colonies of netics and ideally suited to the experimental study of each founder, 50 replicate populations were founded. These 100 populations were thus initially identical, except for the evolutionary and population genetics (Zeyl 2000). A msh2 disruption in the 50 mutator populations. Each popula- genome-wide mutation rate for yeast of 0.0031 has been tion was propagated by streaking a single colony onto a new extrapolated from fluctuation tests at two loci (Drake plate of YPD agar (2% yeast extract, 2% peptone, 1% dextrose, 1991). However, it is uncertain whether this extrapola- 2% agar) every 2 days. Colony selection was randomized by picking the colony closest to the trademark on the petri plate. tion provides an accurate estimate of the rate of deleteri- At the 18th and 36th transfers, samples from an overnight ous mutation. Different loci vary greatly in mutation liquid culture of each transferred colony were frozen at Ϫ80Њ rates, as illustrated by the fact that a third locus (a in 15% glycerol. plasmid-borne nonsense suppressor with a muta- The number of generations (cell divisions) during each 48- tion rate approximately two orders of magnitude higher hr growth period was estimated by counting the cells in 10 48-hr colonies using a Coulter particle counter. This gave an -generations between transfers. The popula 16ف than the other two) was excluded as an outlier. Two of estimate of -loci may not represent a sufficient sample to tions frozen after 18 and 36 transfers would thus have under 6100ف and 600 generations, respectively. Because cell 300ف allow an accurate estimate of the genome-wide mutation gone rate. Also, it is unclear how rates of mutation detected division rates were expected to decrease as fitness declined during MA, this estimate was obtained at transfer 16, near the by fluctuation test are related to rates of mutations that midpoint of the MA process. The fitness analyses described reduce fitness. There may be many mutations that re- below were performed only on the samples frozen after 36 duce fitness but do not entirely abolish the activity of transfers. an enzyme and thus are not counted in a fluctuation test; Fluctuation tests: We wished to estimate mutation rates in conversely, mutations may eliminate enzyme activity but both WT and M strains at specific loci, to quantify the effect of mismatch repair deficiency on the rate of mutations affecting have no detectable effect on fitness in a given environ- fitness, and also to compare genome-wide mutation rates ex- ment. trapolated from fluctuation tests with those inferred from MA. Yeast can be frozen and revived, allowing samples from Luria-Delbruck fluctuation tests were performed as described each population to be cryopreserved at intervals, and for E. coli (Sniegowski et al. 1997), with culture media and plating volumes adjusted for yeast. Mutation rates were esti- then competed against their ancestors to provide pre- mated at the CAN1, URA3, and CYH2 loci, by spreading repli- cise and reproducible estimates of fitness. S. cerevisiae is cate overnight cultures on canavanine, 5-fluoroorotic acid, also highly amenable to MA, since multiple populations and cycloheximide plates, respectively. All three media are are easily propagated by the transfer of colonies estab- toxic to wild-type cells and select for mutant colonies lacking enzyme activity (Brown and Szostak 1983). Because such lished from single cells (Korona 1999). Although such mutations are presumably recessive, the fluctuation tests were extreme bottlenecking maximizes genetic drift, selec- performed on haploid versions of the two strains. The results tion against mutations still occurs during colony growth. were analyzed with a maximum-likelihood algorithm (Snie- The fraction of cells in a colony carrying a neutral muta- gowski et al. 1997). tion is approximately the product of the mutation rate Fitness assays: The relative fitness of each line after 36 transfers was estimated in replicate competitions with a geno- and the number of generations. The amount by which type congenic to the M ancestor that was genetically marked this fraction is reduced by selection against a deleterious with resistance to the antibiotic G418 (geneticin). Competi- mutation can be estimated from a simple model in tions between this marked M genotype and each ancestor have which the relative growth rates of all mutant genotypes been performed at various times for a variety of experiments and have repeatedly shown the three genotypes to have equal are reduced below that for wild-type cells by the same fitness (relative to the marked M genotype, fitness estimates Ϯ fitness cost s (Kibota and Lynch 1996). An estimate 95% confidence intervals pooled across several independent of s can thus be used to correct the inferred mutation assays are 1.000 Ϯ 0.012 for WT and 1.002 Ϯ 0.007 for M). rate for the effect of selection. Since each experimental line was descended from a single colony during the final transfer, within lines We ran MA experiments with two founding genotypes: was assumed to be negligible. a wild-type (WT) and a congenic mutator (M) strain. Because there may be many mutations with no detectable Spontaneous mutation rates can be increased by inacti- effect in a permissive environment but deleterious effects in vating any of several whose products are involved a more demanding environment (Kondrashov and Houle 1994; Elena et al. 1998), during MA the lines were grown on in mismatch repair. Our M strain carried a deletion of YPD agar (a rich, complex permissive medium) but fitness the MSH2 , greatly increasing the rates of base was assayed in a liquid defined minimal medium (SMM: 0.17% substitutions and deletions of one to two nucleotides yeast nitrogen base without amino acids, 0.5% ammonium (Marsischky et al. 1996). We estimate the rates and sulfate, and 2% dextrose), supplemented with 60 mg/liter fitness effects of spontaneous mutation in the heterozy- leucine. Liquid medium was used so that the numbers of cell divisions of each genotype could be estimated from the gous state in congenic MSH2 (WT) and msh2 (M) yeast dilution factors used in the competitions. genotypes. Before competitions were begun, all lines were acclimated Mutation Rate in Budding Yeast 55 to the assay environment as follows. Samples were taken from cantly higher in the M strain than in the isogenic WT .30ف the ultracold freezer and partially thawed, and 20-␮l aliquots strain (Table 1) by a geometric mean factor of were used to inoculate 10-ml YPD cultures in 18 ϫ 150-mm borosilicate tubes. After growth for 24 hr, 0.1 ml were trans- Our estimates for the URA3 and CAN1 loci agree well Ϫ8 Ϫ7 ferred to 9.9 ml SMM ϩ leucine and grown for 24 hr again. with published figures (2.77 ϫ 10 and 1.13 ϫ 10 , Competitions were then begun by mixing 50 ␮l of each line respectively; Drake 1991) and our estimate of the in- and 50 ␮l of the G418-resistant ancestor in 9.9 ml of fresh crease in mutation rate caused by MSH2 deletion is in SMM ϩ leucine. A 120-␮l sample of each mixture, diluted good agreement with the effect of deleting its homo- through a 10-ml tube of sterile deionized water, was spread on a YPD plate, and after 2 days’ growth the resulting 100–200 logue mutS in E. coli (deVisser et al. 1999). colonies were replica-plated to YPD plates containing G418. Fitness changes: Mean fitness declined significantly Colony counts from each plate provided estimates of the initial for both WT (mean Ϯ 95% confidence limits: 0.890 Ϯ frequencies of each competitor. After 24 hr, 0.1 ml of each 0.044) and M lines (0.791 Ϯ 0.024). Fitness distributions competition was transferred to a fresh tube of 9.9 ml SMM ϩ were clearly bimodal, especially for the WT lines (Figure leucine. After another 24 hr growth, 120-␮l samples of each competition were diluted through two 10-ml water tubes, 1), implying that there were two classes of mutation spread on YPD plates, and replica-plated as above, providing with different fitness effects. The most likely candidate estimates of the final frequencies of each genotype. Fitness for the more severe class of mutations is deletion of was quantified as the ratio of the number of cell divisions of part or all of the mitochondrial genome. This abolishes -the ability to respire and is known as the petite pheno 13ف the MA line to that of the marked ancestor during the generations of the competition (Lenski et al. 1991). Fitness assays were performed in five blocks, each block containing type due to the smaller colonies formed by such mutants one replicate of each of the 50 WT and 50 M lines. Each block (Hampsey 1997). Respiration ability was tested for all included control competitions between the two ancestors and lines by plating samples from liquid YPD cultures onto the common competitor to allow correction for any block glycerol plates (2% yeast extract, 2% peptone, 3% glyc- effect, but no block effect was detected (P ϭ 0.252). Between- erol), on which respiration is required for growth. and within-line components of variance were estimated by ANOVA. Among WT lines there was a clear correspondence be- Estimates of U and the distribution of sh: A maximum- tween fitness and respiration ability: the upper and likelihood algorithm, written and kindly provided by P. Keight- lower fitness modes correspond to 31 grande (respira- ley (Keightley 1994), was compiled by J. Muday and used to tion-competent) and 19 petite , respectively estimate the mutation rate and the distribution of fitness ef- (Figure 1). There was no overall fitness decline in WT fects for the WT and M genotypes. The program assumes a Poisson distribution of number of mutations per generation grande lines (1.003 Ϯ 0.016), while WT petite lines were and a gamma distribution of fitness effects. The gamma distri- significantly less fit than their ancestor (0.706 Ϯ 0.034). bution is determined by the values of ␣ and ␤, the scale and Among M lines, the fitness difference between shape parameters, respectively. The mean fitness cost of a grandes and petites was smaller, but average fitness was mutation s (sh in our study), is ␤/␣. The program evaluates the natural logarithm of the likelihood of the data as a func- still significantly higher for the 34 grandes (0.838 Ϯ tion of particular parameter combinations, using numerical 0.027) than for the 16 petites (0.741 Ϯ 0.034; P ϭ integration (Keightley 1994, 1998). Parameter combinations 0.000169 in a two-tailed t-test). Among all petites there were searched over a wide range of combinations of initial was no difference between M and WT lines (P ϭ 0.166), values to minimize the risk of missing a global maximum but M grandes were significantly less fit than WT grandes likelihood, and 95% confidence limits for U and sh were de- Ϫ14 fined by a twofold drop in the log likelihood relative to its (P ϭ 3.72 ϫ 10 ). maximum values. A standard measure of the effect of mutation is the per-generation increment of genetic variance, scaled by the environmental variance (V /V ). A nested ANOVA RESULTS m e was used to estimate within-line and among-line compo- Fluctuation tests: Luria-Delbruck fluctuation tests nents of variance in fitness. Within-line variance was confirmed that mutation rates at three loci were signifi- used as an estimate of Ve, and Vm was estimated as VL/

TABLE 1 Mutation rates at three loci in WT (MSH2)andM(msh2) genotypes, estimated by fluctuation tests

Genotype CAN1 CYH2 URA3 WT 3.2 ϫ 10Ϫ7 8.0 ϫ 10Ϫ10 3.3 ϫ 10Ϫ8 (2.2 ϫ 10Ϫ7–4.7 ϫ 10Ϫ7) (2.6 ϫ 10Ϫ10–2.5 ϫ 10Ϫ9) (1.4 ϫ 10Ϫ8–7.7 ϫ 10Ϫ8) M 1.7 ϫ 10Ϫ5 4.1 ϫ 10Ϫ9 4.9 ϫ 10Ϫ6 (1.4 ϫ 10Ϫ5–2.1 ϫ 10Ϫ5) (1.3 ϫ 10Ϫ9–1.3 ϫ 10Ϫ8) (3.7 ϫ 10Ϫ6–6.6 ϫ 10Ϫ6) Relative mutator strength 35.1 5.1 151.5 The 95% confidence intervals for each genotype at each locus are given in parentheses. Relative mutator strength is the ratio of estimated mutation rate in the mutator genotype to that in the wild type. 56 C. Zeyl and J. A. G. M. DeVisser

Figure 1.—Fitness distribu- tion of 50 mutation-accumula- tion lines established from (A) wild-type and (B) mismatch- repair-deficient (mutator) an- cestors. Hatched bars, respira- tion-competent (grande) lines; solid bars, petite lines. Ances- tral fitness is 1.0 by definition.

2t, where VL is the among-line variance and t is the selection bias b is then used to correct the estimate for number of generations (Lynch and Hill 1986). When U, where Ucorrected ϭ Uraw(1 ϩ b). Because the model is all lines are considered, Vm/Ve estimates for both WT deterministic, it provides an upwardly biased estimate and M are well within the usual range (Lynch and of the effect of selection, which in reality would be

Walsh 1998, p. 338), but for WT grandes alone Vm/Ve reduced by drift (Kibota and Lynch 1996). Estimates is an order of magnitude lower (Table 2). of U and sh are summarized in Table 2. U and the distribution of sh: Separate analyses were For the WT grandes, the best ML fit was obtained performed on three groups of MA lines: WT grande with U ϭ 5.5 ϫ 10Ϫ5, and with a mean s ϭ 0.217 and a lines alone, all WT lines combined, and M grande lines. relatively narrow range of s (Figure 3A). Log likelihoods We did not expect the fitness effects and frequency of were rather insensitive to ␤ and ␣ as long as their ratio mitochondrial mutations to differ among WT and M s was held near 0.22. With ␤ fixed at 60, the 95% confi- lines, a prediction supported by our inability to detect dence intervals are 3.5 ϫ 10Ϫ5–1.5 ϫ 10Ϫ4 for U and a difference in the mean fitness of WT and M petites. 0.208–0.236 for sh (Figure 3B). Correction for selection Since we are primarily interested in nuclear mutations yields a point estimate of U ϭ 9.46 ϫ 10Ϫ5. due to their relevance for evolutionary models, we did An alternative approach is to estimate U by extrapola- not analyze M petites using ML. MA and fitness estimates tion from fluctuation tests at specific loci and use that were performed on diploid yeast, so all estimates of s as a fixed value to obtain maximum-likelihood estimates are actually estimates of the mean product of s and h, of s. Drake (1991) estimated U from fluctuation tests the dominance coefficient. Mutation rate estimates were on the URA3 and CAN1 loci, after correcting for the corrected for the effect of selection during colony number of base pairs at each locus and multiplying by growth using the model of Kibota and Lynch (1996). the number of base pairs in the genome, as 3.1 ϫ 10Ϫ3. For a given number of cell divisions between single- From our fluctuation tests we obtain a per-locus geomet- colony transfers, this model calculates the amount by ric mean mutation rate in the WT ancestor of 2.0 ϫ which the probability of fixation is reduced for a delete- 10Ϫ8. Multiplying by the 6 ϫ 103 open reading frames rious mutation relative to a neutral one (Figure 2). This in the yeast nuclear genome and doubling the resulting

TABLE 2 Summary of mutation parameter estimates for wild-type grande lines (WT grande), all 50 grande and petite WT lines, mutator grande lines (M grande), and all 50 M lines

MA lines Fluctuation tests Vm/Ve Bateman-Mukai Maximum likelihood WT grande — 4.80 ϫ 10Ϫ4 — U ϭ 9.46 ϫ 10Ϫ5 sh ϭ 0.217 ≈ Ϫ4 Ϫ3 Ϫ3 Ϫ3 All WT U 2.4 ϫ 10 5.87 ϫ 10 Umin ϭ 2.92 ϫ 10 U ϭ 1.19 ϫ 10 smaxh ϭ 0.102 sh ϭ 0.303 Ϫ3 Ϫ2 M grande — 1.54 ϫ 10 Umin ϭ 2.28 ϫ 10 0.005 Յ U Յ 0.938 smaxh ϭ 0.015 0.049 Ն sh Ն 0.0003 ≈ Ϫ3 Ϫ3 Ϫ2 All M U 8.4 ϫ 10 1.47 ϫ 10 Umin ϭ 1.97 ϫ 10 — smaxh ϭ 0.018 Bateman-Mukai and ML estimates of U have been corrected for selection against deleterious mutations during colony growth using the Kibota and Lynch (1996) shown in Figure 2, except for the ML estimate for M grandes, where uncertainty in the estimate of s prohibits this correction. Mutation Rate in Budding Yeast 57

rable to the estimates for the nuclear genome because of the complications of mitochondrial genetics. Each cell contains several mitochondria, each with dozens of copies of the chromosome, which introduces the potential for selection to act on mitochondrial muta- tions both among chromosomes within mitochondria and among mitochondria within a cell. We present esti- mates of U and s with petite lines included simply as a measure of the contribution of presumed mitochon- drial mutations to relative to the contribu- tion of nuclear mutations. As expected, the best fit was obtained with a much higher U ϭ 6.6 ϫ 10Ϫ4 (95% confidence limits 4.1 ϫ 10Ϫ4–1.4 ϫ 10Ϫ3) and with mean Figure 2.—Selection bias b against deleterious mutations sh ϭ 0.303 (95% confidence limits 0.261–0.344 with ␤ during colony growth, as a function of fitness cost of mutations fixed at 18.7). Correction for selection gives U ϭ 1.19 ϫ Ϫ3 s. This function was obtained by modifying the model of 10 . The Bateman-Mukai method yields Umin ϭ 1.94 ϫ Kibota and Lynch (1996) to account for our 16 generations 10Ϫ3 and s h ϭ 0.102 for grande and petite WT lines between each transfer in place of their 25. max combined, which when corrected for selection gives Ϫ3 Umin ϭ 2.92 ϫ 10 (Table 2). haploid estimate gives U ≈ 2.4 ϫ 10Ϫ4. The higher esti- For M grande lines, the ML analysis differed in that mate obtained by Drake (1991) gives a significantly log likelihoods were highly sensitive to the value of ␤,so poorer fit to our data (log likelihood ϭ 251.87, a reduc- the results cannot be presented as a three-dimensional tion of 3.65 from the best-fit model). The log likelihood likelihood surface with ␤ held constant, as for the WT obtained using U ≈ 2.4 ϫ 10Ϫ4 is lower but not quite lines. Instead, analyses were run using a series of fixed significantly so, even if ␤ is fixed at 60.0 (a reduction values for U and searching for optimal ␣ and ␤ values of 1.98 from the best-fit model). Because there was no for a given U. An equally good fit was obtained over decline in the mean fitness of WT grande lines, the values of U from 0.005 to 0.938 (Table 2; Figure 4). Bateman-Mukai method of estimating a lower bound Lower values of U resulted in significantly lower log for the mutation rate per diploid genome (Umin) and likelihoods. With higher mutation rates, no viable mod- an upper bound for the mean fitness reduction (smax) els were found. It is possible that higher mutation rates from the per-generation changes in mean and variance could be accommodated with appropriate parameters, was not applied but with increasing U, the range of ␣ and ␤ values that The grande and petite WT lines were then combined yield best-fit models becomes increasingly narrow, even for ML analysis. For the grande lines there was no de- though the goodness of that fit remains high. Extrapola- cline in mean fitness, and the inferred mutation rate tion from the fluctuation test results as above gives U ≈ was very low. Therefore, estimates of U and s from the 8.4 ϫ 10Ϫ3 for the M ancestor, and using this value did combined WT lines should be dominated by the pre- not significantly reduce the fit of ML models (Table 3). Ϫ2 sumed mitochondrial mutations responsible for the pe- The Bateman-Mukai estimates are Umin ϭ 2.05 ϫ 10 tite phenotype. These estimates are not directly compa- and smaxh ϭ 0.015. ML analysis constrained by allowing

Figure 3.—(A) Log-likeli- hood surface of the fitness dis- tribution of 31 respiration- competent wild-type lines, as a function of the mutation rate U and the mean fitness cost per mutation s. (B) Distribution of mutation effects with ␣ϭ271 and ␤ϭ60, the parameter val- ues giving the best-fit maxi- mum-likelihood model corre- sponding to the peak in A. g(a), density function for the gamma distribution. 58 C. Zeyl and J. A. G. M. DeVisser

estimate of h is preliminary since the possibility of epista- sis between accumulated mutations was not accounted for and is incompatible with our results, since it would imply s Ͼ 1.0, or negative fitness. However, if many spontaneous mutations have no detectable effects in heterozygotes, then the mutation rates we have inferred are underestimates. As in Korona’s (1999) MA experiment, many of our lines lost the ability to respire. Mutations causing this petite phenotype are usually partial deletions of the mitochondrial chromosome, but we cannot rule out the possibility that at least some of our petite mutations Figure 4.—Distributions of mutation effects for two of the were nuclear, since mutations in several nuclear genes best-fit maximum-likelihood models for the fitness distribu- can also yield a petite phenotype (Hampsey 1997). Mei- tion of 34 respiration-competent mutator lines (see Table 2). (A) Gamma distribution with ␤ϭ6.25 and ␣ϭ213, osis and sporulation in yeast require respiration, so we corresponding to the best-fit model with U ϭ 0.01. (B) Gamma were unable to sporulate and test-cross our (diploid) distribution with ␤ϭ0.01 and ␣ϭ32.214, corresponding to petites to confirm cytoplasmic inheritance of the petite the best-fit model with U ϭ 0.94. phenotype. Similar numbers of petites arose among WT and M lines (19 and 16, respectively; P Ͼ 0.2 in a G-test), indicating that the frequencies of petites do not signifi- no variation among mutations in fitness effect (␤ ∞) → cantly differ between WT and M lines. Also, mean fitness did not reduce the likelihood of the best-fit model, did not differ between WT and M petites (see results). which after adjustment for selection gave estimates of These two observations are consistent with petites aris- Ϫ U ϭ 1.19 ϫ 10 2 and sh ϭ 0.031. By comparison, Bate- ing by a mechanism independent of the accumulation man-Mukai estimates for all M lines including petites, of nuclear mutations of small effect. Mutation rates in Ϫ2 after correction for selection, are Umin ϭ 1.97 ϫ 10 mitochondrial genomes are known to be high, probably and smaxh ϭ 0.018. because of the reactive by-products of oxidative phos- phorylation. The somatic accumulation of mitochon- drial genome rearrangements is responsible for several DISCUSSION degenerative human diseases (Wallace 1999). The in- As in recent studies of other model organisms, we tracellular population dynamics of mitochondrial ge- obtained very low estimates of U and very high estimates nomes may lead to conflicts between selection within of s for wild-type budding yeast. Since the experiment and between cells. For example, deletion mutants may was performed with asexual diploids, mutations were replicate more quickly than wild-type mitochondrial ge- fixed and assayed in the heterozygous state. Thus our nomes and therefore go to fixation within initially heter- estimates of s actually represent hs, the fitness costs of oplasmic cell lineages. By minimizing effective popula- mutations in heterozygotes. The same is true of our tion size to allow mutations to accumulate, we relaxed adjustments to inferred mutation rates to correct for the among-cell selection that presumably would other- the bias introduced by selection against deleterious mu- wise oppose this process. The MA transfer protocol may tations. In similar experiments with mutator yeast strains therefore have favored the accumulation of mitochon- isogenic to ours, Korona (1999) assayed fitness using drial deletions within cells. maximum growth rates and estimated h ϭ 0.08. This Inspection of the fitness data for the WT grande lines reveals that the ML estimates of U and s are determined by the fitness of a single MA line, which declined to TABLE 3 0.802 (see Figure 1A). Multiplying the best-fit estimate Ϫ Results of ML analysis for M grande lines U ϭ 9.5 ϫ 10 5 by 31 grande lines and 600 generations gives an expected total of 1.77 mutations, 1.02 of which U ␤␣Mean sh Log likelihood evade selection under the model of Kibota and Lynch (1996). This is concordant with the observation that 0.005 124.998 2535.826 0.049 218.32 0.0084 285.711 8244.323 0.035 219.93 the only substantial fitness decline among WT grandes 0.01 6.250 213.171 0.029 220.11 occurred in a single line, by an amount approximately 0.05 0.236 39.106 0.006 220.69 equal to the inferred mean sh ϭ 0.217. With this single 0.1 0.106 35.116 0.003 220.74 line removed from the analysis, there is no significant 0.5 0.020 32.426 0.0006 220.76 fitness variation among the remaining 30 WT grande 0.938 0.010 32.241 0.0003 220.76 lines (F29,120 ϭ 1.08, P ϭ 0.371). Although fitness esti- Each line shows the best-fit model obtained by searching mates for some of these lines are slightly above that for over values of ␤ and ␣ using a fixed value of U. the ancestor (Figure 1A), ML analysis in which a variable Mutation Rate in Budding Yeast 59 fraction of mutations was beneficial did not improve assays. Most of the mutations induced by ethyl methane- the fit to the data. The detection of only a single muta- sulfonate in C. elegans probably have fitness costs of tion limits the confidence that can be placed in a point Ͻ0.1% (i.e., s Ͻ 0.001; Davies et al. 1999). This was estimate of U, but the 95% confidence intervals obtained suggested by combining DNA sequence comparison be- from ML analysis (Table 2) indicate a nonzero mutation tween C. elegans and C. briggsae with ML analysis of fitness rate that is significantly lower than the U ϭ 0.0031 ex- data from mutagenized lines of C. elegans. Although our trapolated from fluctuation tests by Drake (1991). fitness assays would not detect individual mutations with We obtained estimates of U by three methods: (1) such small fitness effects, our results suggest that muta- extrapolating the results of fluctuation tests at three loci tions with 0.05 Ͼ s Ͼ 0.01 are infrequent in wild-type to the entire genome, (2) using the traditional Bateman- S. cerevisiae. We would otherwise expect that during 600 Mukai method to infer U from the per-generation rate generations of MA, our lines would have accumulated of fitness decline in MA lines, and (3) ML analysis of enough such mutations that a decline in mean fitness the fitness data using Keightley’s (1994) program. For would have been detected, along with relatively little the WT, our fluctuation-test estimate of U ≈ 2.4 ϫ 10Ϫ4 among-line variance in fitness. is in reasonable agreement with the U ϭ 9.5 ϫ 10Ϫ5 The results reported here illustrate both the motiva- obtained by correcting the ML estimate from WT grandes tion and the drawback to MA as a method for studying for selection. The lack of a detectable per-generation mutation load: it may prove impossible to derive inde- fitness decline precluded a Bateman-Mukai estimate. pendent point estimates of U and s, but MA experiments For the M strain, the U ϭ 8.4 ϫ 10Ϫ3 from fluctuation can reveal biologically important differences between tests is simply one of a broad range of mutation rates the fitness effects of spontaneous mutations in mis- and effects giving equally good fit to the data (Table match-repair-proficient and -deficient strains and the 3). This is because U and s are confounded, a common effects of experimentally induced insertions or dele- problem with ML analysis of MA results (Keightley tions. 1998). The fit of ML models to the M grande data is For most yeast genes, transposon insertions (Goebl significantly reduced by constraining them to the Bate- and Petes 1986; Burns et al. 1994) and targeted dele- Ϫ2 man-Mukai estimates of Umin ϭ 2.05 ϫ 10 and smaxh ϭ tions (Oliver et al. 1992) had no apparent phenotypic 0.015. However, ML analysis with all mutations having effect, even in a range of stressful environments. Fewer equal fitness effects gave estimates of U ϭ 1.19 ϫ 10Ϫ2 than a third of the genes identified by the yeast genome and sh ϭ 0.031, with no reduction in goodness of fit sequencing project have known functions, which has and in reasonable agreement with the Bateman-Mukai been interpreted to mean that mutations in many of estimates. The latter two values would represent a these genes have fitness effects only in environments roughly 100-fold increase in U due to MSH2 deletion, that have not yet been identified. However, analyses while the fluctuation tests at three loci indicate a 30- of mutagenized yeast have often identified only major, fold geometric mean increase (and a 65-fold arithmetic qualitative phenotypic effects and probably would not mean increase). detect effects as subtle as reduction of competitive fit- Despite the uncertainty in ML results for the M ness by a few percent. This was confirmed by Thatcher grande lines, the confidence intervals for s indicate a et al. (1998), who found that competitive fitness was major difference between the M (0.0003–0.049) and significantly reduced in 19 of 27 isogenic yeast strains WT (0.208–0.236) strains in the mean fitness effect of carrying transposon insertions that had shown no quali- mutations. Comparing the WT and M strains therefore tative phenotypic effects. This argues against the hypoth- illustrates not only the obvious point that mismatch esis that many yeast genes function only in specific, as repair greatly reduces mutation rates, but also that it is yet unknown, environments. Similar observations have slightly deleterious mutations that are eliminated. This come from a collection of 2026 yeast strains, in each of may be simply because in the absence of mismatch re- which a single open reading frame has been precisely pair they are the most abundant type. Gabriel et al. deleted (Winzeler et al. 1999). Only 17% of these dele- (1993) predicted this property of DNA repair systems tions were lethal in haploids, but competitions among because it is slightly deleterious mutations that cause a pool of 558 deletion mutants revealed reduced growth the greatest loss of population mean fitness, mutations rates in almost 40%. Most transposon insertions in E. with larger effects being efficiently removed by selec- coli (Elena et al. 1998) reduce fitness by Ͻ5%. For E. tion. coli, the fitness costs of mutation inferred from mutagen- A similar rarity of slightly deleterious mutations in esis are slightly greater than, but in reasonable agree- wild-type strains has also been observed in other recent ment with, s as estimated by MA (Kibota and Lynch MA experiments (Ferna´ndez and Lo´pez-Fanjul 1996; 1996). Our results suggest that this is not so for wild- Keightley and Caballero 1997; Fry et al. 1999; type yeast, although greater numbers of spontaneous Keightley and Eyre-Walker 1999; Vassilieva and mutations must be observed before it can be concluded Lynch 1999). It may be that mutations with small effects with confidence that spontaneous and experimentally accumulate but are not detected in competitive fitness induced mutations have different effects in yeast. Gene 60 C. Zeyl and J. A. G. M. DeVisser deletions and transposon insertions are major muta- 1998 Distribution of fitness effects caused by random insertion mutations in Escherichia coli. Genetica 102/103: 349–358. tions in molecular terms, so it is surprising that they Ferna´ndez, J., and C. Lo´pez-Fanjul, 1996 Spontaneous mutational seem to have smaller fitness effects than the spontane- variances and for fitness-related traits in Drosophila ous mutations that accumulated in our WT lines. Spon- melanogaster. Genetics 143: 829–837. Fry, J. D., P. D. Keightley, S. L. Heinsohn and S. V. Nuzhdin, 1999 taneous loss of an entire chromosome (aneuploidy) is New estimates of rates and effects of mildly deleterious mutation possible in asexually propagated diploid yeast and may in Drosophila melanogaster. Proc. Natl. Acad. Sci. USA 96: 574–579. have occurred in some of our lines. Gabriel, W., M. Lynch and R. Bu˝rger, 1993 Muller’s ratchet and mutational meltdowns. Evolution 47: 1744–1757. 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