Dominance and Overdominance of Mildly Deleterious Induced Mutations for Fitness Traits in Caenorhabditis elegans

Corresponding author: A. D. Peters, University of British Columbia, 6270 University Blvd., Vancouver, BC V6T 1Z4, Canada., peters{at}zoology.ubc.ca (E-mail)

Communicating editor: M. J. SIMMONS

	ABSTRACT

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

We estimated the average dominance coefficient of mildly deleterious mutations (, the proportion by which mutations in the heterozygous state reduce fitness components relative to those in the homozygous state) in the nematode Caenorhabditis elegans. From 56 worm lines that carry mutations induced by the point mutagen ethyl methanesulfonate (EMS), we selected 19 lines that are relatively high in fitness and estimated the viabilities, productivities, and relative fitnesses of heterozygotes and homozygotes compared to the ancestral wild type. There was very little effect of homozygous or heterozygous mutations on egg-to-adult viability. For productivity and relative fitness, we found that the average dominance coefficient, , was 0.1, suggesting that mildly deleterious mutations are on average partially recessive. These estimates were not significantly different from zero (complete recessivity) but were significantly different from 0.5 (additivity). In addition, there was a significant amount of variation in among lines, and analysis of average dominance coefficients of individual lines suggested that several lines showed overdominance for fitness. Further investigation of two of these lines partially confirmed this finding.

EXPERIMENTS to estimate the average dominance coefficient of new mutations () for fitness-related characters have a long and venerable history. The earliest experiments (WALLACE 1957 , WALLACE 1963 ; FALK 1961 ; MULLER and FALK 1961 ; review in LEWONTIN 1974 ) were aimed at distinguishing between the "classical" and "balance" theories of genetic variation as defined by DOBZHANSKY 1955 , that is, between the maintenance of genetic variation (and its concomitant load) by partially recessive deleterious mutations or by overdominance. More recently, the ubiquity of partially recessive deleterious mutations in several models of evolution (MULLER 1964 ; HAIGH 1978 ; KONDRASHOV 1984 , KONDRASHOV 1988 ; LANDE and SCHEMSKE 1985 ; CHARLESWORTH 1990 ; CHARLESWORTH et al. 1991 ; LYNCH et al. 1995A ; review in CHARLESWORTH and CHARLESWORTH 1998 ) has fueled efforts to quantify parameters associated with deleterious mutations, including dominance coefficients.

If natural selection is characterized primarily by the purging of recurrent deleterious mutations, then the average dominance coefficient for fitness () is expected to affect the mean fitness of populations at mutation-selection or mutation-selection-drift balance, unless mutations act multiplicatively across loci (KONDRASHOV 1982 ) or populations are completely panmictic (WHITLOCK 2002 ). Perhaps more interestingly, is expected to affect the relative fitnesses of outcrossing vs. inbreeding populations (CHARLESWORTH et al. 1991 ), as well as those of sexual vs. asexual populations (HAIGH 1978 ; KONDRASHOV 1982 ; CHARLESWORTH 1990 ). As such, the mean dominance coefficient of deleterious mutations is an important parameter in models of variation in mating systems and the evolution of sex and recombination.

Despite the recent concentration on studying the parameters of partially recessive deleterious mutations, the question of the relative importance of segregation load arising from overdominant loci vs. mutation load caused by recurrent deleterious mutation has never been completely answered. If even a small proportion of mutations impart a fitness advantage in the heterozygous state, then a large portion of the genetic load in outcrossing populations could result from balancing selection (DOBZHANSKY 1955 ). This would have consequences not only for the evolution of sexual reproduction and the nature of inbreeding depression, but also for the very mechanisms by which genetic variation is maintained in populations. Thus, the quantitative effects of the dominance coefficient of partially recessive deleterious mutations may be less important than the qualitative consequences if an appreciable fraction of mutations are in fact overdominant.

Evidence regarding the distribution of dominance coefficients has been equivocal, both from experiments intended to discriminate qualitatively between balanced and mutation loads and from those aimed at quantifying . Of the former, much classic evidence for overdominance came from heterozygote superiority in crosses involving inversion polymorphisms in Drosophila pseudoobscura (DOBZHANSKY 1954 ); these results are as easily explained by linkage among partially recessive deleterious mutations (associative overdominance) as by overdominance within loci (OHTA 1971 ). Of the latter, a few experiments based on induced or laboratory-accumulated mutations in D. melanogaster have concluded that is negative (that is, that the average new mutation is overdominant; WALLACE 1957 ; MUKAI et al. 1964 ; MUKAI 1969 ), although it is possible that these results were an artifact of the controls used. The majority of experiments yielding estimates of for fitness components in D. melanogaster and Caenorhabditis elegans have concluded that mutations fall on average between complete recessivity and additivity (0 0.5; SIMMONS and CROW 1977 ; see reviews in GARCIA-DORADO and CABALLERO 2000 ; see also VASSILIEVA et al. 2000 ).

Here we present an experiment to estimate the average dominance coefficient of ethyl methanesulfonate (EMS)-induced mutations in C. elegans. We have argued previously that the effects of the GC AT transitions induced by EMS are similar to those of spontaneous point mutations (DAVIES et al. 1999 ). This makes EMS-induced mutation lines a powerful system for testing the parameters of newly arising deleterious mutations in C. elegans.

	MATERIALS AND METHODS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

Experimental strains and culture conditions:
All worm strains were derived from the standard C. elegans lab strain N2, originally obtained from the Caenorhabditis Genetics Center (CGC). Mutation lines used were a subset of those described previously (DAVIES et al. 1999 ; KEIGHTLEY et al. 2000 ). These lines had been generated by exposing N2 worms to 50 mM EMS for 4 hr and then maintaining by selfing for >10 generations to yield mutations in the homozygous state (for a full description of methods, see DAVIES et al. 1999 ; KEIGHTLEY et al. 2000 ). After 12 generations of selfing, these lines had been frozen at -85° using standard techniques (SULSTON and HODGKIN 1988 ).

Because we were interested primarily in the dominance of mildly deleterious mutations, we chose lines that had relatively high fitness as measured in the original experiment (DAVIES et al. 1999 ; KEIGHTLEY et al. 2000 ). These lines, as well as the ancestral N2 strain, were thawed in batches and decontaminated using alkaline hypochlorite (SULSTON and HODGKIN 1988 ). A total of 33 lines were tested; 14 of these were unusable for crossing (due to either the production of inviable males or the failure to produce a 50:50 sex ratio when crossed). Thus, a total of 19 mutant lines were assayed, split into four blocks; N2 (wild-type) worms were thawed separately three times during the experiment and assayed contemporaneously with each block. Mutant lines were thawed in batches and were maintained for up to eight generations (including initial production of males, as described below) before being crossed and assayed.

Except where specifically noted, worms were maintained at 20° on 3.5-cm MYOB agar plates seeded with Escherichia coli strain OP50, using standard techniques (SULSTON and HODGKIN 1988 ). To generate males for crossing, several dozen individuals of each line were heat-shocked at 25.5° (HODGKIN 1988 ). The resulting male progeny were then returned to 20° and crossed to hermaphrodites from the same line in a ratio of 4–6 males:1 hermaphrodite; in most cases, such crosses yield a 50:50 sex ratio among the offspring. Lines were then maintained at 20° for three to eight generations, as both pure hermaphrodite and mixed-sex families; mixed-sex families were produced every generation by crossing males from the previous generation to hermaphrodites from pure-hermaphrodite families in a ratio of 4–6 males:1 hermaphrodite. Pure-hermaphrodite families were maintained by transferring single individuals every generation.

Experimental crosses and life-history assays:
We assayed egg-to-adult viability and productivity of four classes of hermaphrodite: homozygous wild type (N2), homozygous mutant, M-heterozygotes (heterozygotes in which the hermaphrodite parent was a mutant), and P-heterozygotes (heterozygotes in which the male parent was a mutant). A total of 1606 worms were assayed for productivity, composed of an average of 33 worms per homozygous mutant line, 14 per M-heterozygote, 18 per P-heterozygote, and 360 wild types. These yielded a total offspring count of 318,310. To remove any inherent differences between offspring produced by self-fertilization and those produced by crossing, all assayed individuals were produced by crossing. To ensure that individuals chosen for assay were the result of crossing (rather than selfing), we placed four to six young (larval stage L4 to young adult) males on a plate with a single late (L4) larval stage hermaphrodite. Pilot experiments suggested that, although offspring produced in the first day after such a cross is set up tend to have hermaphrodite-biased sex ratios, offspring produced on the second and third days show sex ratios that do not differ significantly from 50:50 (data not shown). This suggests that eggs laid on the second or third day of a cross are very unlikely to be the result of self-fertilization, although we also subsequently checked for this in each cross. Thus, on the third day after setting up the crosses, we moved each hermaphrodite to a fresh plate for 6 hr to lay eggs. These eggs, and the worms that developed from them, were used for viability and productivity assays.

Egg-to-adult viability was assayed by counting the number of eggs laid by an adult hermaphrodite in a 6-hr period and then counting the number of larval and adult offspring 3 days later. Eggs laid along the edge of a plate are difficult to see, and egg counts on plates with large numbers of such eggs are likely to be substantial underestimates. To minimize such occurrences, we placed an enclosure (a double-walled screw-top microcentrifuge tube cap) over the parent worm during the egg-lay period, forcing her to lay all eggs in the central part of the plate. The enclosure and parental worm were both removed after 6 hr. Plates on which the worm had escaped from the enclosure were excluded from viability analysis but used in the productivity analysis described below.

Three days following the egg lay, larval worms on each egg-lay plate were counted. At this stage, offspring on the egg-lay plates were sexed, and plates that deviated from a 50:50 sex ratio were excluded from both viability and productivity analyses. Hermaphrodite offspring were removed from the egg-lay plate and placed on a fresh plate for productivity assays. These worms were allowed to lay eggs for 3 days and were moved to new plates every 24 hr during this period. Eggs on these plates were allowed to hatch and grow to an advanced (L4) larval stage, at which point they were counted, to give individual daily productivities for days 1–3. Although C. elegans normally produces offspring over a period of 5 days, the majority of offspring are produced over the first 3 days. These plates were repeatedly checked for males over the following 2 days; if more than two male offspring were laid by a hermaphrodite, it was assumed that the parent had undergone cross-fertilization and she was excluded from the analysis (the normal rate of male production due to spontaneous X-chromosome nondisjunction is 1/1000; HODGKIN 1988 ). A number (6–20) of extra worms of every genotype were maintained in parallel with the primary set of plates, and worms that produced an excess of male offspring or were accidentally killed were replaced from this stock.

Daily productivities were included in the calculation of two fitness components: productivity (the unweighted sum of daily productivities over all 3 days) and relative fitness, w. This quantity is proportional to the expected fitness of a population with a stable age structure and is calculated as (CHARLESWORTH 1994 ), where l_xm_x is the product of survivorship to and productivity at day x. Since the fitness of the wild type is by definition one in this case, r_C was calculated by setting mean fitness for wild-type worms at and solving using l_xm_x across all the wild types within a given assay. The calculated value of r_C was then substituted into the above formula for the calculation of individual estimates of w. Note that this calculation requires only one estimate of r per assay, using the mean l_xm_x table across all the wild-type worms within the assay; this value (r_C) is then used to weight productivity by a negative exponential function over time. Since r is never calculated for individual worms, this measure (w) is defined for worms with l_xm_x = 0.

Analysis:
Viability was assayed as the ratio of the number of adult worms to the number of eggs counted on an egg-lay plate. This trait was analyzed using a generalized linear mixed model via the GLIMMIX macro of SAS 6.12 (LITTELL et al. 1996 ), assuming binomial error structure and a logit link function. This package requires that the numerator be less than or equal to the denominator (i.e., in our case, it requires the assumption that the egg count on each plate was perfect). Due to the uncertainty in counting eggs on the nonuniform agar substrate, there were several cases in which the number of worms exceeded our estimate of the number of eggs. In cases where the worm count exceeded the egg count by one (53 of 273 total plates), we set the egg count equal to the worm count (and therefore the ratio to 1); in cases where the worm count was greater than the egg count by more than one (25 of 273 plates), we discarded the data. Fixed factors in the analysis were "zygosity" (i.e., heterozygous vs. homozygous) and maternity (nested within zygosity; i.e., M- vs. P-heterozygotes); random factors were reference genotype (i.e., the line from which the mutant parent derived, or N2, the wild type), reference genotype x zygosity, and assay. For comparison, and in an attempt to quantify the bias introduced by correcting for egg undercounts, we also calculated the ratio of worms to eggs for each genotype directly from estimates of the two values, without any correction; standard errors on these estimates were calculated by the delta method (LYNCH and WALSH 1998 ).

Productivity-related traits (productivity and w) were analyzed by a general linear mixed model using SAS Proc Mixed (LITTELL et al. 1996 ; SAS INSTITUTE 1997). The same effects were fitted for this analysis as for the viability analysis above, with the addition of two random effects: family (offspring from the same cross—that is, a single mother and four to six fathers—are coded as being from the same family; this effect is nested within assay, reference genotype, zygosity, and maternity) and counter (nested within assay). Significance of random effects was tested by Z-statistics, under the assumption that residuals are normally distributed.

Average dominance coefficients () were estimated primarily as the proportional reduction in trait value Z among heterozygotes relative to that among homozygotes, where the numerator and denominator are least-squares estimates of differences in trait values, derived from the mixed-model analysis described above. This yields an estimate weighted by the homozygous effect s () (GARCIA-DORADO and CABALLERO 2000 ). For comparison, we also estimated as the regression of the trait value in heterozygote lines to that in homozygote lines, where and ² are genetic covariances and variances, respectively (CABALLERO et al. 1997 ); estimates from this approach are weighted by the square of the homozygous effect (). Arguably, the former approach is more appropriate, since genetic variance at mutation-selection balance is proportional to sh (MUKAI et al. 1974 ); furthermore, the regression approach is likely to be more susceptible to bias (CABALLERO et al. 1997 ).

Reassay of selected lines:
Three lines (E11, E13, and E25) showed significant evidence of overdominance in the first assay (see RESULTS); these lines were tested again with a modification of the methods described above. Two separate samples of wild-type (N2) worms, as well as one sample each of lines E11, E13, and E25, were thawed, and males were generated again using the methods described above. Four to six families each of males and hermaphrodites of each mutant line plus N2 were maintained separately for three or more generations prior to crossing. Fifteen to 20 homozygote crosses and 7–10 each of M- and P-heterozygote crosses were set up for each mutant line to yield 80–82 homozygotes and 39–41 of each type of heterozygote. Despite repeated attempts, line E25 did not outcross on any of the reassay plates, so data were obtained only for lines E11 and E13. These worms, plus 50 worms from each N2 sample, were assayed for productivity and relative fitness as described above.

Productivity and relative fitness data were analyzed by SAS Proc Mixed, with maternal and paternal treatments (mutant or wild type) and their interaction as fixed effects, and maternal and paternal line (nested within maternal or paternal treatment) and their interaction, maternal and paternal family (nested within maternal or paternal line), sibship, and counter as random effects. The two homozygous N2 (control) replicates differed significantly from each other (see RESULTS), so individual comparisons between heterozygotes and controls were made between crosses involving the same N2 replicate, and more general comparisons involving N2 were made using the replicate (rather than the individual) as the unit of replication.

	RESULTS

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

Mutational effects on viability:
The mean viability of wild-type (N2) worms was 93.6% (SE 1.1); that of heterozygotes was 93.0% (SE 1.2); and that of homozygote mutants was 93.4% (SE 1.4). None of the factors included in the generalized linear mixed model significantly affected viability on average. Contrasts involving individual genotypes (Fig 1) reveal three genotypes that show significantly lower viability than the wild type: E5 heterozygotes (P = 0.02) and homozygotes (P = 0.001), and E24 homozygotes (P = 0.003). In addition, the E14 homozygote showed significantly lower viability than the E14 heterozygote (P = 0.04), suggesting that the suite of mutations carried by line E14 is on average partially recessive (although neither the heterozygote nor the homozygote showed a significant difference in viability compared to the wild type). A Bonferroni correction for multiple comparisons (28 comparisons) renders all but the E5 homozygote vs. wild-type difference (P = 0.028) nonsignificant. Direct calculation of worm-to-egg ratios for every genotype gave qualitatively similar results (all point estimates close to one, none significantly different from any other), although the inclusion of plates on which the eggs were undercounted yielded very high standard errors for these estimates.

View larger version (85K): In this window In a new window Download PPT slide   Figure 1. Estimates of heterozygote (darkly shaded bars) and homozygote (lightly shaded bars) viabilities ±SE by line, compared to wild type (solid line) ±SE (lightly shaded field). Asterisks above axis labels correspond to the significance of the dominance effect (het - hom); asterisks above individual bars correspond to the significance of the difference between the value of the given genotype and the wild type. *P < 0.05; **0.001 < P < 0.01.

Overall, these results suggest that mutations, whether in the heterozygous or homozygous state, have very little effect on viability on average. This is particularly important in the context of the present experiment, since differences in viability among heterozygotes, mutant homozygotes, and wild-type individuals in the F₂ progeny would make interpretation of the productivity-based results (below) difficult. More generally, it suggests that viability under benign conditions is a relatively small target for deleterious mutation in worms. This is partially consistent with the results of VASSILIEVA et al. 2000 , who inferred that a related trait, "survival to maturity," is subject to low mutation rates (0.003/genome/generation), but that the average effect of each mutation is quite high (39%). Direct comparisons between these results should be made with care, however, since they measure viability over slightly different time frames: here, viability is a measure of survivorship from egg to late larval stages (L3 and later) and does not score offspring production at all; survival to maturity measures survivorship from an early larval stage (L1) to adulthood and requires the production of viable offspring (VASSILIEVA et al. 2000 ).

Dominance for w and productivity:
For both productivity and w, heterozygotes performed significantly better than mutant homozygotes, and the magnitude of this difference varies significantly among lines; i.e., both zygosity (F_1,18 = 16.7, P < 0.001 for productivity; F_1,18 = 18.0, P < 0.001 for w) and the reference genotype x zygosity interaction (Z = 2.1, P < 0.05 for productivity; Z = 2.0, P < 0.05 for w) were highly significant. More specifically, contrasts show that, on average, trait estimates for heterozygotes are not significantly different from those for wild-type worms, whereas homozygote estimates are significantly lower than those for both wild-type and heterozygote worms (Table 1). In addition, heterozygote trait values are on average significantly greater than the mean of homozygote and wild-type trait values (Table 1). Thus, on average, deleterious mutations are significantly recessive in two senses: (1) heterozygotes are significantly more fit than homozygous mutants, but not significantly different from wild type, and (2) the effect of mutations in the heterozygous state is significantly smaller than would be predicted under additivity.

Our principal method of estimation of the dominance coefficient is to calculate the proportional change in mean trait value in heterozygotes vs. homozygotes (₁). Using this approach, we estimate for both productivity and w (Table 1); these estimates are not significantly different from zero, although they are significantly different from additivity. Estimates based on the regression approach yield somewhat lower estimates of for both traits.

Looking beyond the averages, it appears that the suites of mutations represented in each individual mutant line range from overdominant (heterozygote trait value is significantly higher than that of wild type), to recessive (homozygote trait value is significantly lower than that of both heterozygote and wild type; heterozygote and wild type do not differ significantly) and partially recessive (heterozygote and homozygote both significantly lower than wild type and significantly different from each other), to dominant (heterozygote and homozygote both significantly lower than wild type but not significantly different from each other; Fig 2 and Fig 3). To determine whether this variation in dominance is significantly different from zero, we performed a bootstrap analysis of the variance in h₁ for relative fitness (w) by resampling estimates of h₁ at the line level 10,000 times. The point estimate of variance in h₁ for w was 1.89; the bootstrap 95% confidence interval was (0.347–3.71), suggesting that the variance in dominance for fitness is significantly greater than zero.

View larger version (112K): In this window In a new window Download PPT slide   Figure 2. Estimates of heterozygote (darkly shaded bars) and homozygote (lightly shaded bars) productivity (A) and relative fitness (B) ±SE by line, compared to wild type (solid line) ±SE (lightly shaded field). Asterisks above axis labels correspond to the significance of the dominance effect (het - hom); asterisks above individual bars correspond to the significance of the difference between the value of the given genotype and the wild type. *P < 0.05; **P < 0.01; ***P < 0.001.

View larger version (16K): In this window In a new window Download PPT slide   Figure 3. Line estimates of heterozygous (hs) vs. homozygous (s) selection coefficients (±SE). Dashed line represents complete dominance; solid line represents additivity. Shaded boxes represent estimates from original assays; solid triangles represent pooled estimates of lines E11 and E13 from original experiment and reassay; dotted lines connect the two estimates of the same line.

One striking manifestation of this variation in dominance is the apparent existence of overdominance for some lines. This is particularly notable for relative fitness (w), where heterozygote trait values appear to be distributed symmetrically around the wild-type trait value: 10 of 19 lines have point estimates in the overdominant range, 3 of which (E11, E13, and E25) are significant (Fig 2B). To determine whether these three overdominant lines would be expected by chance alone, we calculated the probability of getting three or more false positives in the overdominant portion of the distribution, given a per-test type I error rate of 0.05. P values should be uniformly distributed between zero and one under the null hypothesis. Since we were interested in the tail of the distribution in which heterozygote fitness was greater than wild-type fitness, we excluded the 7 lines in which heterozygote fitness was significantly less fit than the wild type in a one-tailed test. The remaining 12 P values should be uniformly distributed between 0 and 0.95, and the per-test probability of getting P < 0.05 is 0.05/0.95. The probability of getting x false positives is a binomially distributed random variable with (n, p) = (12, 0.05/0.95); under such a distribution, P(x 3) = 0.022, suggesting that there are in fact significantly more overdominant lines than would be expected by chance.

The family effect was highly significant for both productivity (Z = 5.2, P < 0.001) and w (Z = 7.6, P < 0.001), suggesting that there is substantial variation among sets of parents (composed of a single hermaphrodite mother and four to six fathers) within genotypes for productivity-based traits. A large proportion of this effect is likely due to variation in the ages of maternal worms. We have observed that eggs laid by older worms tend to be more developmentally advanced than those laid by younger worms; thus, even genetically identical hermaphrodites whose ages have been synchronized by a timed egg lay may be developmentally out of synchrony if their mothers were of different ages. If this effect carries across generations, then we may not have fully accounted for it statistically with the single-generation family effect we have fitted in our analyses.

Verification of overdominance:
To test the hypothesis that the lines E11 and E13 carry overdominant mutations, we reassayed these lines. The two replicates of N2 used as controls for this reassay differed significantly from each other in productivity (T₃₀ = 2.3; P = 0.03), although not in w (T₈ = 1.8; P = 0.1). This difference may have arisen from a persistent age-variation effect such as that hypothesized above or from some other persistent environmental effect, such as mild bacterial contamination (although no evidence of such contamination was observed in these lines). It is unlikely to be due to accumulated genetic differences between the replicates, because both sets of lines were frozen at the time the mutation lines were mutagenized. We dealt statistically with the difference between N2's by treating replicate, not individual, as the unit of statistical replication among N2 worms.

The deviation from additivity, as measured by the maternal treatment x paternal treatment interaction, was significant for productivity (F_1,7 = 8.6, P = 0.02), but not for relative fitness (F_1,4 = 3.9; P = 0.1), from the reassay. A more detailed analysis shows that the significant interaction effect in productivity is due largely to the fact that heterozygotes of lines E11 and E13 have significantly higher productivity than do wild-type worms and marginally significantly higher productivity than do homozygotes of those lines (Table 2). Homozygote mutants are not significantly different in productivity from wild-type worms. Although these contrasts are not significant for relative fitness, the trends are in the same direction as those for productivity (Table 2).

Thus, the results from our reassay are consistent with the hypothesis that at least 2 of the 19 lines originally assayed display overdominance for at least one fitness-related trait, productivity. Although overdominance for relative fitness is not significant in the reassayed lines alone, pooling the data from the original assay and the reassay yields heterozygote relative fitnesses that are consistently greater than those of wild type and homozygote fitnesses that are either less than or no different from those of wild type (Fig 3). Although this is not a formally significant result, the trend is toward overdominance.

	DISCUSSION

TOP ABSTRACT MATERIALS AND METHODS RESULTS DISCUSSION LITERATURE CITED

Our estimates of are broadly consistent with previous results from Drosophila and C. elegans, which suggest that mildly deleterious mutations are partially recessive on average. In a series of mutation-accumulation experiments on D. melanogaster, Mukai and coworkers made use of balancer chromosomes to protect wild-type chromosomes from selection for 30–60 generations (MUKAI et al. 1964 , MUKAI et al. 1965 , MUKAI et al. 1972 ; MUKAI and YAMAZAKI 1968 ). For estimates of dominance, chromosomes with >60% normal viability ("quasinormals") were selected, and the viabilities of these chromosomes were assayed in the homozygous and heterozygous states, alongside controls that were homozygous for wild-type or wild-type-like second chromosomes. Similar experiments were carried out by OHNISHI 1977 (see reviews in SIMMONS and CROW 1977 ; GARCIA-DORADO and CABALLERO 2000 ) and HOULE et al. 1997 .

Estimates of in Mukai's experiments depended on the genetic background in which fitness was estimated, whether the heterozygotes were in coupling or repulsion, and the method of calculation. Coupling heterozygotes were formed by crossing mutation-accumulation (MA) chromosomes with "wild-type" chromosomes, which were either chromosomes from a healthy MA line (presumed to be close in fitness to the original chromosome; MUKAI et al. 1964 ; MUKAI 1969 ) or separately collected chromosomes from the same or unrelated populations (MUKAI et al. 1965 ). Repulsion heterozygotes were formed by crossing two MA chromosomes (MUKAI and YAMAZAKI 1968 ). In all cases, viabilities were compared to a control on the basis of high-viability MA chromosomes. Coupling heterozygotes formed by pairing with the "original" chromosome consistently yielded estimates of overdominance for both ₁ and ₂ ( to -0.09; MUKAI et al. 1964 ; MUKAI 1969 ), whereas those formed by pairing with nonisogenic chromosomes yielded estimates that were nearly additive (; MUKAI et al. 1965 ) or nearly recessive (; SIMMONS and CROW 1977 ), depending on the method of calculation. Repulsion heterozygotes yielded estimates that were consistently nearly additive by either method of calculation (; MUKAI and YAMAZAKI 1968 ). Ohnishi's coupling and repulsion estimates of ₁ are both consistent with Mukai's repulsion results (; OHNISHI 1977 ); however, estimates of ₂ from these experiments are much lower (; GARCIA-DORADO and CABALLERO 2000 ). In a recent MA experiment in D. melanogaster, HOULE et al. 1997 estimated the mean dominance coefficient across five life-history traits (not including viability) as (although neither the overall mean nor any individual mean was significantly different from zero); due to the unavailability of appropriate controls (HOULE et al. 1994 ), an estimate of ₁ could not be calculated. It should also be noted that HOULE et al. 1994 included nonquasinormal chromosomes in their analysis, which might lead to a lower estimate of (OHNISHI 1977 ; GARCIA-DORADO and CABALLERO 2000 ).

Recently, VASSILIEVA et al. 2000 estimated ₂ for six life-history characters in lines of C. elegans that had undergone 214 generations of mutation accumulation. Across all traits, the average dominance coefficient was , although the estimates from the different traits fall into two groups: the first (survival to maturity and longevity) are not significantly different from zero (), while the rest (productivity, intrinsic rate of increase, rate of convergence, and generation rate) are not significantly different from additive (). Their estimate for productivity () differed substantially from ours (), although the variance on both of these estimates is substantial (SE = 0.18 and 0.12, respectively). This difference cannot be explained solely by the different methods of calculation: our estimate of is even lower than our estimate of ₁. The difference is also unlikely to be explained by the fact that the present experiment preferentially used fitter lines, while VASSILIEVA et al. 2000 used lines chosen nearly at random; if anything, high-fitness lines are expected to be biased toward higher values of (GARCIA-DORADO and CABALLERO 2000 ). Even the average number and effects of mutations are similar between our EMS lines and the MA lines of Vassilieva et al.: for productivity, we have estimated that these EMS lines carry 1.5 detectable mutations on average, with an average effect of 23% (KEIGHTLEY et al. 2000 ), while VASSILIEVA et al. 2000 estimate that their 214-generation lines carry 1.6 mutations per haploid (0.015/diploid/generation x 214 generations/2) with an average homozygous effect of 22%.

One important difference between our experiment and that of VASSILIEVA et al. 2000 may lie in the profile of mutation types. Our lines carry EMS-induced mutations whereas those of VASSILIEVA et al. 2000 carry spontaneous mutations. Although we have argued that the mutational effects of G/C A/T transitions, which are the primary form of mutations induced by EMS, should be similar to those of substitution mutations as a whole (DAVIES et al. 1999 ), it is also likely that the proportion of insertion/deletion mutations induced by EMS differs from the spontaneous rate. This might be particularly important in light of recent findings that transposable element insertions show a trend toward higher dominance coefficient on average than the average of all other types of spontaneous mutation in Drosophila (FRY and NUZHDIN 2003 ). Although there is reason to think that this elevated dominance is due to specific properties of transposable elements and not to insertions in general (FRY and NUZHDIN 2003 ), and transposable elements are not known to be active in the strains of C. elegans used in our experiment or that of VASSILIEVA et al. 2000 , the possibility that other types of insertions have similarly elevated dominance coefficients cannot be discounted. Certainly the general point that different types of mutations might have systematic differences in dominance is an important one. Thus, if EMS-induced mutations have a different spectrum of mutation types than do spontaneous mutations, EMS-induced mutations may not give a fully representative view of dominance. It is worth noting, however, that even among experiments focusing on EMS-induced mutations the variation in estimates of has been substantial: MUKAI 1970 , OHNISHI 1977 , and TEMIN 1978 estimate as 0.03, 0.47, and 0.18, respectively, for mildly detrimental EMS-induced mutations in Drosophila; it therefore seems unlikely that all variation among estimates arises from biases in the mutation profile under EMS.

Another consideration is the possible effect of beneficial mutations on our estimates of dominance. Consider a single line homozygous for a beneficial mutation at one locus and a detrimental mutation at another. If the beneficial mutation increases the trait value by some proportion t and the detrimental mutation decreases the trait value by some proportion s, then the total trait value (assuming no epistasis) is (1 + t)(1 - s). If both mutations have dominance coefficient h, the total trait value in a heterozygote is (1 + ht)(1 - hs), and the apparent dominance coefficient will be = (1 - (1 + ht)(1 - hs))/(1 - (1 + t)(1 - s)) = h(t - s + hst)/(t - s + st). Since t - s + hst < t - s + st for all 0 h < 1, the apparent dominance coefficient will be smaller than the actual dominance coefficient h. Thus, the existence of beneficial mutations may artificially decrease estimates of . In the extreme, this could lead to the spurious appearance of overdominance. This is in fact an example of associative overdominance: crosses between a parent with a mix of beneficial and detrimental mutations and a wild-type parent are equivalent to crosses between two individuals with different sets of detrimental mutations. However, such biases are likely to be important only if a large proportion of mutations are beneficial; we consider this to be unlikely.

In one sense, despite these caveats, our results fit nicely into two emerging patterns: that mildly deleterious mutations are partially recessive on average, but that there is substantial variation in the degree of dominance. Both of these patterns may have implications for evolutionary processes that are driven by deleterious mutations. If is low, then the average strength of selection acting on newly arising mutations in diploid populations may be weak, even if the selection coefficient against homozygotes is not. This affects, for example, the rate of accumulation of deleterious mutations via Muller's ratchet in newly arising asexual populations (HAIGH 1978 ; GORDO and CHARLESWORTH 2000 ), although it has very little effect on the probability of fixation in sexual populations (WHITLOCK and BURGER 2003 ). Low values of h may also imply extremely high values of inbreeding depression, although the magnitude of this effect depends on the genomic mutation rate U, the homozygous selection coefficient s, and the number of loci undergoing recurrent deleterious mutation (Fig 4). This has implications for the evolution of mating systems as well as for conservation biology. If inbreeding depression due to partially recessive deleterious mutations is severe, then there can be disruptive selection for selfing vs. outcrossing populations. Modifiers that increase selfing are associated with a decrease in fitness in the short term, but become associated with high-fitness genotypes after selfing lineages have been purged of their inbreeding load (LANDE and SCHEMSKE 1985 ), although over the longer term such lineages may also suffer the effects of Muller's ratchet (LYNCH et al. 1995B ). Similarly, the decrease in genetic variation triggered by population bottlenecks causes increased inbreeding, which may in turn cause a further decrease in variation as the inbreeding load is purged from the population (HEDRICK and KALINOWSKI 2000 ).

View larger version (17K): In this window In a new window Download PPT slide   Figure 4. Inbreeding depression () in a population switching from random mating (f = 0) to f = 0.25, as a function of the dominance coefficient h, genomic deleterious mutation rate U, and the number of loci n contributing to inbreeding load. Thin lines, n = 5000 loci; boldface lines, n = 50,000 loci. Dotted lines, U = 0.5; short dashed lines, U = 0.75; long dashed lines, U = 1.0; solid lines, U = 1.25. Loci were assumed to be at mutation-selection balance and interact multiplicatively, with homozygous selection coefficient against deleterious mutations s = 0.01. Inbreeding depression was calculated as = 1 - (WI/WO)n, where WO is the mean fitness at a single locus at mutation-selection balance under random mating, and WI is the mean fitness at that locus after inbreeding.

The inference of substantial variability in dominance coefficients also has implications for evolutionary processes. For example, models invoking deleterious mutations often depend on the assumption that each mutation is partially recessive; however, if h varies, any given mutation may be additive (h = 0.5), partially dominant (h > 0.5), or even overdominant (h < 0) even if the overall estimate of is partially recessive. Mutations with h > 0.5 do not contribute to inbreeding depression (Fig 4), while those with h < 0 may be maintained as polymorphisms by selection and contribute disproportionately.

Indeed, our results show hints of this pattern, with the majority of point estimates falling in the partially dominant and overdominant ranges, and very few in the partially recessive range (Fig 3). Although it would be a mistake to draw broad conclusions from those lines with h > 0.5, the repeated trend of h < 0 in some lines suggests that the hypothesis of overdominance is worthy of further study. During the 1950s and 1960s, a series of experiments on induced and accumulated mutations in D. melanogaster yielded a set of contradictory conclusions: several experiments found evidence of overdominance; but the detection of overdominance depended on the genetic background or disappeared altogether in replicated experiments (WALLACE 1957 , WALLACE 1963 ; FALK 1961 ; MUKAI et al. 1964 , MUKAI et al. 1965 , MUKAI et al. 1966 , MUKAI et al. 1972 ; MUKAI and YAMAZAKI 1968 ; MUKAI 1969 ; review in LEWONTIN 1974 ). In addition, the controls used in these experiments might have had the opportunity to accumulate mutations of their own, leading to the possibility that the patterns observed were due to associative overdominance. Although these objections offer alternative explanations for the patterns seen, they do not directly falsify overdominance per se. More recent estimates of for new mutations have failed to provide evidence for overdominance; but, importantly, they were not designed to look for it. Experiments designed and analyzed under the assumption that all mutations are partially recessive might not be expected to yield evidence of overdominance: the effects of small numbers of overdominant alleles might be swamped out by those of partially recessive alleles in lineages carrying more than a few mutations; similarly, if is estimated across multiple lines, the presence of overdominance in individual lines may be obscured. For example, K. SZAFRANIEC and R. KORONA (Fig 4 in unpublished results) report a surprising number (9/38) of mutation pairs in Saccharomyces cerevisiae that repeatably increase fitness in the heterozygous state (i.e., both the average fitness of individuals carrying one of the two mutations and the fitness of individuals carrying both mutations are greater than that of the ancestral wild type), although any tests of the significance of this result would be post hoc.

If even a small proportion of loci exhibit overdominance, then the implications for biological processes are wide ranging indeed. Half a century ago, a central debate in population genetics focused on the relative importance of "balanced" vs. "classical" loads because of the fundamentally different mechanisms they implied for the maintenance of variation in populations (DOBZHANSKY 1955 ). Today, the assumption that variation and loads are due to partially recessive deleterious mutations drives models of many evolutionary processes (review in CHARLESWORTH and CHARLESWORTH 1998 ). While the importance of these models is not diminished, because it is clear that most deleterious mutations are in fact partially recessive, the possibility of overdominance may restrict their generality. For example, even if sexual populations are able to purge themselves of deleterious mutations more efficiently than asexual populations (KONDRASHOV 1984 ; CHARLESWORTH 1990 ), asexuals that can fix heterozygosity at overdominant loci may still enjoy a fitness advantage over sexuals, depending on the proportion of loci that are overdominant.

Variation in dominance contributes to variation in the effect of newly arising mutations. When combined with our earlier conclusion that a large fraction of deleterious mutations have vanishingly small (but still deleterious) effects under laboratory conditions in C. elegans (DAVIES et al. 1999 ), the present result suggests that many newly arising deleterious mutations may have very small effects indeed. In addition, the variation in h we see across lines implies that there is substantial variation in the expected effect of new deleterious mutations. We have suggested previously that the existence of very weak selection against newly arising mutations might change the predictions of deterministic models of mutations and sex (PETERS and KEIGHTLEY 2000 ). Furthermore, variation in mutation effect has been shown to affect the circumstances under which stochastic processes (Muller's ratchet) are expected to operate (BUTCHER 1995 ). Our result reinforces the conclusion that newly arising mutations tend to be weak, but that there is great variability among effects, at least when expressed under benign conditions. If some of that variation includes overdominant mutations, then the implications for evolution are far reaching indeed.

	ACKNOWLEDGMENTS

We thank S. P. Otto, D. Promislow, and M. Pineda-Krch for extensive discussion; M. Lynch and M. Simmons for extensive comments on an earlier version of the manuscript; and J. Elrick for technical assistance. This work was funded by the Biosciences and Biotechnology Research Council (United Kingdom) and the Natural Science and Engineering Research Council (Canada).

Manuscript received November 29, 2002; Accepted for publication June 17, 2003.

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