King''s Formula for the Mutation Load with Epistasis

A formula by J. L. King gives the equilibrium mutation load as L = 2 sigma ui(1 - qi)/z - x) in which ui is the mutation rate to deleterious alleles at the ith locus, qi is the frequency of mutant alleles at this locus, x is the mean number of such mutant genes per individual before selection, z is the mean number in individuals eliminated by selection, and the summation is over all relevant loci. We show that this rule is inaccurate for intense selection and that a correct formula is L = 2 sigma ui(1 - qi) w/(z - x) = 2U w/(z - x) = 2U/(z - x + 2U) in which U is the mean number of new mutations per haploid genome in the population and w is the mean relative fitness before selection. If w/(z - x) less than 1/2, the mutation load is less than the Haldane value (U less than or equal to L less than or equal to 2U) and can be considerably less. In a diploid asexual population, however, with independent occurrence of mutations, L = 1 - e-2U regardless of the mode of selection.     

POLYGENIC MUTATION IN DROSOPHILA MELANOGASTER: ESTIMATES FROM DIVERGENCE AMONG INBRED STRAINS

A highly inbred line of Drosophila melanogaster was subdivided into 25 replicate sublines, which were independently maintained for 100 generations with 10 pairs of unselected flies per generation. The polygenic mutation rate (V_M) for two quantitative traits, abdominal and sternopleural bristle number, was estimated from divergence among sublines at 10 generation intervals from generations 30-100, and from response of each line to divergent selection after more than 65 generations of mutation accumulation. Estimates of V_M averaged over males and females both from divergence among lines and from response to selection within lines were 3.3 × 10^-3 V_E for abdominal bristles and 1.5 × 10^-3 V_E for sternopleural bristles, where V_E is the environmental variance. The actual rate of production of mutations affecting these traits may be considerably higher if the traits are under stabilizing selection, and if mutations affecting bristle number have deleterious effects on fitness. There was a substantial component of variance for sex × mutant effect interaction and the sublines evolved highly significant mutational variation in sex dimorphism of abdominal bristle number. Pleiotropic effects on sex dimorphism may be a general property of mutations at loci determining bristle number.     

Mutant alleles of small effect are primarily responsible for the loss of fitness with slow inbreeding in Drosophila melanogaster.

Multilocus simulation is used to identify genetic models that can account for the observed rates of inbreeding and fitness decline in laboratory populations of Drosophila melanogaster. The experimental populations were maintained under crowded conditions for approximately 200 generations at a harmonic mean population size of Nh approximately 65-70. With a simulated population size of N = 50, and a mean selective disadvantage of homozygotes at individual loci approximately 1-2% or less, it is demonstrated that the mean effective population size over a 200-generation period may be considerably greater than N, with a ratio matching the experimental estimate of Ne/Nh approximately 1.4. The buildup of associative overdominance at electrophoretic marker loci is largely responsible for the stability of gene frequencies and the observed reduction in the rate of inbreeding, with apparent selection coefficients in favor of the heterozygote at neutral marker loci increasing rapidly over the first N generations of inbreeding to values approximately 5-10%. The observed decline in fitness under competitive conditions in populations of size approximately 50 in D. melanogaster therefore primarily results from mutant alleles with mean effects on fitness as homozygotes of sm < or = 0.02. Models with deleterious recessive mutants at the background loci require that the mean selection coefficient against heterozygotes is at most hsm approximately 0.002, with a minimum mutation rate for a single Drosophila autosome 100 cM in length estimated to be in the range 0.05-0.25, assuming an exponential distribution of s. A typical chromosome would be expected to carry at least 100-200 such mutant alleles contributing to the decline in competitive fitness with slow inbreeding.     

Somatic mutations at microsatellite loci in western Redcedar (Thuja plicata: Cupressaceae)

A per-generation somatic mutation rate for microsatellites was estimated in western redcedar (Thuja plicata, Donn ex D. Don.: Cupressaceae). A total of 80 trees representative of the average size and age of reproductive trees were sampled in four natural populations in southwestern British Columbia. Samples of bulked haploid megagametophytes were collected from two or three positions on each tree, assuming that the collections were far enough apart that the same mutant sector was not sampled twice. All samples were genotyped at eight microsatellite loci. A single mutation corresponding to a stepwise increase in one dinucleotide repeat was detected. The estimated mutation rate for microsatellites was 6.3 x 10(-4) mutations per locus per generation (or 3.1 x 10(-4) per allele per generation), with a 95% confidence interval of 3.0 x 10(-5) to 4.0 x 10(-3) mutations per locus. Somatic mutations can contribute to a greater mutational load in trees, as compared to shorter lived plants, and genotypic mosaics within an individual have important implications for plant defense strategies and plant evolution.     

Estimation of mutation rate from rare protein variants.

A method for estimating the mutation rate for protein loci from the number of rare alleles in the population is presented. It seems to have a number of advantages compared with Kimura and Ohta's method. Applying this method to Neel's data from American Indians in South America and to Nozawa's data from Japanese macaques, the mutation rate for electrophoretically detectable alleles is estimated to be (2 approximately 3) x 10(-6) per locus per generation. This estimate may not include many severely or substantially deleterious mutations.     

Small fitness effects and weak genetic interactions between deleterious mutations in heterozygous loci of the yeast Saccharomyces cerevisiae

Rare, random mutations were induced in budding yeast by ethyl methanesulfonate (EMS). Clones known to bear a single non-neutral mutation were used to obtain mutant heterozygotes and mutant homozygotes that were later compared with wild-type homozygotes. The average homozygous effect of mutation was an approximately 2% decrease in the growth rate. In heterozygotes, the harmful effect of these relatively mild mutations was reduced approximately fivefold. In a test of epistasis, two heterozygous mutant loci were paired at random. Fitness of the double mutants was best explained by multiplicative action of effects at single loci, with little evidence for epistasis and essentially excluding synergism. In other experiments, the same mutations in haploid and heterozygous diploid clones were compared. Regardless of the haploid phenotypes, mildly deleterious or lethal, fitness of the heterozygotes was decreased by less than half a per cent on average. In general, the results presented here suggest that most mutations tend to exhibit small and weakly interacting effects in heterozygous loci regardless of how harmful they are in haploids or homozygotes.     

Cyclical dynamics under constant selection against mutations in haploid and diploid populations with facultative selfing

We have found that constant selection against mutations can cause cyclical dynamics in a population with facultative selfing. When this happens, the distribution of the number of deleterious mutations per genotype fluctuates with the period approximately 1/sHe generations, where sHe is the coefficient of selection against a heterozygous mutation. The amplitude of oscillations of the mean population fitness often exceeds an order of magnitude. Cyclical dynamics can occur under intermediate selfing rates if selection against heterozygous mutations is weak and selection against homozygous mutations is much stronger. Cycling is possible without epistasis or with diminishing-returns epistasis, but not with synergistic epistasis. Under multiplicative selection, cycling might happen if the haploid mutation rate exceeds 1.9 in the case of selfing of haploids, and if this diploid mutation rate exceeds 4.5 in the case of selfing of diploids. We propose a heuristic explanation for cycling under facultative selfing and discuss its possible relevance.     

Valine-Resistance, a Potential Marker in Plant Cell Genetics. II. Optimization of Uv Mutagenesis and Selection of Valine-Resistant Colonies Derived from Tobacco Mesophyll Protoplasts

The induction and selection of valine-resistant mutants from haploid tobacco (Nicotiana tabacum L.) mesophyll protoplast-derived cells have been studied. Using cells from an original mutant plant obtained previously, we performed reconstruction experiments in order to determine the best conditions for the recovery of resistant cells among a population of sensitive cells. Optimal selective conditions were shown to depend on various factors including cell density, time of addition of valine and seasonal variations affecting the mother plants.-Using cell densities of approximately 10( 4) cells/ml, we defined efficient selective conditions: more than 25% of the putative mutant clones selected from UV-mutagenized protoplasts were reproducibly confirmed to be valine resistant. Further characterization of some regenerated mutant plants indicated that valine-resistance was associated with an uptake deficiency, as in the case of the original mutant plant of the Val(r)-2 line used for reconstruction experiments. Spontaneous mutation rates for valine-resistance were below accurately detectable levels, i.e., less than 10(-6) per cell per generation. Induced mutation frequency varied nonlinearily with UV dose from 10(-5) to 5 x 10(-4) resistant clones per surviving colony. Two independent loci (vr2 and vr3) were previously shown to be involved in valine-resistance due to amino acid uptake deficiency. Haploid tobacco plants were produced through anther culture from an F(1) double-heterozygous plant obtained from a cross between the original mutant plant and a wild-type plant. Study of the level of resistance to valine of protoplast-derived cells allowed the classification of these haploid plants in four types: sensitive, resistant and two intermediary resistant types believed to result from the presence of a mutant allele at only one of the two loci involved. The frequencies of UV-induced mutations in cells derived from haploid plants of one of the intermediary types were compared to those observed in wild-type cells. The results are considered in light of the amphidiploid structure of the tobacco genome.     

Spontaneous and Ethyl Methanesulfonate-Induced Mutations Controlling Viability in DROSOPHILA MELANOGASTER. II. Homozygous Effect of Polygenic Mutations

Polygenic mutations affecting viability were accumulated on the second chromosome of Drosophila melanogaster by treating flies with EMS in successive generations. The treated chromosomes were later made homozygous and tested for their effects on viability by comparison of the frequency of such homozygotes with that of other genotypes in the same culture. The treated wild-type chromosomes were kept heterozygous in Pm/+ males by mating individual males in successive generations to Cy/Pm females. The number of generations of accumulation was 1 to 30 generations, depending on the concentration of EMS. A similar experiment for spontaneous polygenic mutations was also conducted by accumulating mutations for 40 generations. The lower limit of the spontaneous mutation rate of viability polygenes is estimated to be 0.06 per second chromosome per generation, which is about 12 times as high as the spontaneous recessive lethal mutation rate, 0.005. EMS-induced polygenic mutations increase linearly with the number of treated generations and with the concentration of EMS. The minimum mutation rate of viability polygenes is about 0.017 per 10(-4)m, which is only slightly larger than the lethal rate of 0.013 per 10(-4) m. The maximum estimate of the viability reduction of a single mutant is about 6 to 10 percent of the normal viability. The data are consistent with a constant average effect per mutant at all concentrations, but this is about three times as high as that for spontaneous mutants. It is obvious that one can obtain only a lower limit for the mutation rate, since some mutants may have effects so near to zero that they cannot be detected. The possibility of measuring something other than the lower limit is discussed. The ratio of the load due to detrimental mutants to that caused by lethals, the D/L ratio, is about 0.2 to 0.3 for EMS-induced mutants, as compared to about 0.5 for spontaneous mutants. This is to be expected if EMS treatment produces a large fraction of small deletions and other chromosome rearrangements which are more likely to be lethal.     

Deleterious Mutations as an Evolutionary Factor. II. Facultative Apomixis and Selfing

A population with u deleterious mutations per genome per generation is considered in which only those individuals that carry less than a critical number k of mutations are viable. Besides a large number of loci subject to mutation and selection, the genome contains one or two special loci responsible for the mode of reproduction. Amphimixis vs. apomixis and amphimixis vs. selfing are considered separately. In the first case, the genome degradation rate v (= u/square root k) is found to play the decisive role, as in the case of recombination. When v greater than 1.25, obligate amphimixis is established. If v decreases below this value, the alleles with first low and then larger penetrance are fixed, until alleles conferring obligate asexual reproduction become advantageous. The proportion of resources allocated to produce seeds also increases with decrease of v. These results are unlikely to depend on the genetic basis of the mode of reproduction. The result of competition between outcrossing and selfing depends on both u and k, as well as on whether the mutations are recessive. The alleles for selfing with low penetrance are selected against if the mutations are at all recessive. The fitness of alleles with high penetrance depends primarily on u, decreasing when u increases. There may exist conditions when only the alleles providing intermediate selfing rates can be fixed in a population. In other cases a population may exist with either obligate outcrossing or selfing at a high rate. Thus, truncation selection against deleterious mutations may be a factor supporting obligate or facultative sex despite the twofold advantage of apomixis or selfing.     

Genetic Studies of Unusual Loci That Affect Body Shape of the Nematode CAENORHABDITIS ELEGANS and May Code for Cuticle Structural Proteins

In Caenorhabditis elegans, four loci (sqt-1, sqt-2, sqt-3 and rol-8) in which mutations affect body shape and cuticle morphology have unusual genetic properties. Mutant alleles of sqt-1 can interact to produce animals with a variety of mutant phenotypes: left roller, right roller, dumpy and long. At least three mutant phenotypes are specified by mutations in the sqt-3 locus. Most alleles at these loci are either dominant or cryptic dominant (i.e., are dominant only in certain genetic backgrounds). Most alleles of these loci exhibit codominance. Two putative null alleles of the sqt-1 locus produce a wild-type phenotype. Many alleles of these genes demonstrate unusual intergenic interactions that are not the result of simple epistasis: animals doubly heterozygous for mutations at two loci often display unexpected and unpredictable phenotypes. We suggest that these genetic properties might be expected of genes, such as the collagen genes, the products of which interact to form the animal's cuticle, and which are member genes of a gene family.     

Rates and fitness consequences of new mutations in humans

The human mutation rate per nucleotide site per generation (μ) can be estimated from data on mutation rates at loci causing Mendelian genetic disease, by comparing putatively neutrally evolving nucleotide sequences between humans and chimpanzees and by comparing the genome sequences of relatives. Direct estimates from genome sequencing of relatives suggest that μ is about 1.1 × 10(-8), which is about twofold lower than estimates based on the human-chimp divergence. This implies that an average of ~70 new mutations arise in the human diploid genome per generation. Most of these mutations are paternal in origin, but the male:female mutation rate ratio is currently uncertain and might vary even among individuals within a population. On the basis of a method proposed by Kondrashov and Crow, the genome-wide deleterious mutation rate (U) can be estimated from the product of the number of nucleotide sites in the genome, μ, and the mean selective constraint per site. Although the presence of many weakly selected mutations in human noncoding DNA makes this approach somewhat problematic, estimates are U ≈ 2.2 for the whole diploid genome per generation and 0.35 for mutations that change an amino acid of a protein-coding gene. A genome-wide deleterious mutation rate of 2.2 seems higher than humans could tolerate if natural selection is "hard," but could be tolerated if selection acts on relative fitness differences between individuals or if there is synergistic epistasis. I argue that in the foreseeable future, an accumulation of new deleterious mutations is unlikely to lead to a detectable decline in fitness of human populations.     

Polygenic mutation in Drosophila melanogaster: Mapping spontaneous mutations affecting sensory bristle number

Our ability to predict long-term responses to artificial and natural selection, and understand the mechanisms by which naturally occurring variation for quantitative traits is maintained, depends on detailed knowledge of the properties of spontaneous polygenic mutations, including the quantitative trait loci (QTL) at which mutations occur, mutation rates, and mutational effects. These parameters can be estimated by mapping QTL that cause divergence between mutation-accumulation lines that have been established from an inbred base population and selected for high and low trait values. Here, we have utilized quantitative complementation to deficiencies to map QTL at which spontaneous mutations affecting Drosophila abdominal and sternopleural bristle number have occurred in 11 replicate lines during 206 generations of divergent selection. Estimates of the numbers of mutations were consistent with diploid per-character mutation rates for bristle traits of 0.03. The ratio of the per-character mutation rate to total mutation rate (0.023) implies that >2% of the genome could affect just one bristle trait and that there must be extensive pleiotropy for quantitative phenotypes. The estimated mutational effects were not, however, additive and exhibited dependency on genetic background consistent with diminishing epistasis. However, these inferences must be tempered by the potential for epistatic interactions between spontaneous mutations and QTL affecting bristle number on the deficiency-bearing chromosomes, which could lead to overestimates in numbers of QTL and inaccurate inference of gene action.     

Genetic Interactions between Naturally Occurring Alleles at Quantitative Trait Loci and Mutant Alleles at Candidate Loci Affecting Bristle Number in Drosophila Melanogaster

Previously, we mapped quantitative trait loci (QTL) affecting response to short-term selection for abdominal bristle number to seven suggestive regions that contain loci involved in bristle development and/or that have adult bristle number mutant phenotypes, and are thus candidates for bristle number QTL in natural populations. To test the hypothesis that the factors contributing to selection response genetically interact with these candidate loci, high and low chromosomes from selection lines were crossed to chromosomes containing wild-type or mutant alleles at the candidate loci, and the numbers of bristles were recorded in trans heterozygotes. Quantitative failure to complement, detected as a significant selection line*cross effect by analysis of variance, can be interpreted as evidence for allelism or epistasis between the factors on selected chromosomes and the candidate loci. Mutations at some candidate loci (bb, emc, h, Dl, Hairless) showed strong interactions with selected chromosomes, whereas others interacted weakly (ASC, abd, Scr) or not at all (N, mab, E(spl)). These results support the hypothesis that some candidate loci, initially identified through mutations of large effect on bristle number, either harbor or are close members in the same genetic pathway as variants that contribute to standing variation in bristle number.     

Polymorphism and Balancing Selection at Major Histocompatibility Complex Loci

Amino acid replacements in the peptide-binding region (PBR) of the functional major histocompatibility complex (Mhc) genes appear to be driven by balancing selection. Of the various types of balancing selection, we have examined a model equivalent to overdominance that confers heterozygote advantage. As discussed by A. Robertson, overdominance selection tends to maintain alleles that have more or less the same degree of heterozygote advantage. Because of this symmetry, the model makes various testable predictions about the genealogical relationships among different alleles and provides ways of analyzing DNA sequences of Mhc alleles. In this paper, we analyze DNA sequences of 85 alleles at the HLA-A, -B, -C, -DRB1 and -DQB1 loci with respect to the number of alleles and extent of nucleotide differences at the PBR, as well as at the synonymous (presumably neutral) sites. Theory suggests that the number of alleles that differ at the sites targeted by selection (presumably the nonsynonymous sites in the PBR) should be equal to the mean number of nucleotide substitutions among pairs of alleles. We also demonstrate that the nucleotide substitution rate at the targeted sites relative to that of neutral sites may be much larger than 1. The predictions of the presented model are in surprisingly good agreement with the actual data and thus provide means for inferring certain population parameters. For overdominance selection in a finite population at equilibrium, the product of selection intensity (s) against homozygotes and the effective population size (N) is estimated to be 350-3000, being largest at the B locus and smallest at the C locus. We argue that N is of the order of 10(5) and s is several percent at most, if the mutation rate per site per generation is 10(-8).     

A Study of Spontaneous Mutation Rates at Ten Loci Detectable by Starch Gel Electrophoresis in DROSOPHILA MELANOGASTER

Spontaneous mutation rates at ten allozyme loci on chromosomes II and III of Drosophila melanogaster were studied. Over the three and a half years study, one alpha-GPD mutation and two different IDH mutations were obtained. The alpha-GPD mutation was inherited in the Mendelian fashion, as expected. The two IDH mutations were peculiar in that the band of new types appeared only in females. In males, only the original bands were stained, and the positions where mutant alleles' bands should be present were blank. Both IDH mutant homozygotes appeared as null allele homozygotes, while in females clear-cut single bands were present.-The rates of spontaneous mutation varied greatly. Eight loci studied (MDH, ADH, EST-6, APH, EST-C, ODH, XDH, AO) did not give any germ-line mutation. The average germ-line mutation rate over all ten loci was estimated at 4.5 x 10(-6). This rate is considerably smaller than that for sex-linked recessive visible mutations (Muller, Valencia and Valencia 1950), but it is somewhat less than autosomal recessive visible mutations (Glass and Ritterhoff 1956).     

Gene and Allelic Genealogies at a Gametophytic Self-Incompatibility Locus

The properties of gene and allelic genealogies at a gametophytic self-incompatibility locus in plants have been investigated analytically and checked against extensive numerical simulations. It is found that, as with overdominant loci, there are two genealogical processes with markedly different time scales. First, functionally distinct allelic lines diverge on an extremely long time scale which is inversely related to the mutation rate to new alleles. These alleles show a genealogical structure which is similar, after an appropriate rescaling of time, to that described by the coalescent process for genes at a neutral locus. Second, gene copies sampled within the same functional allelic line show genealogical relationships similar to neutral gene genealogies but on a much shorter time scale, which is on the same order of magnitude as the harmonic mean of the number of gene copies within an allelic line. These results are discussed in relation to data showing trans-specific polymorphisms for alleles at the gametophytic self-incompatibility locus in the Solanaceae. It is shown that population sizes on the order of 4 X 10(5) and a mutation rate per locus per generation as high as 10(-6) could account for estimated allelic divergence times in this family.     

The number of mutations selected during adaptation in a laboratory population of Saccharomyces cerevisiae

There is currently limited empirical and theoretical support for the prevailing view that adaptation typically results from the fixation of many mutations, each with small phenotypic effects. Recent theoretical work suggests that, on the contrary, most of the phenotypic change during an episode of adaptation can result from the selection of a few mutations with relatively large effects. I studied the genetics of adaptation by populations of budding yeast to a culture regime of daily hundredfold dilution and transfer in a glucose-limited minimal liquid medium. A single haploid genotype isolated after 2000 generations showed a 76% fitness increase over its ancestor. This evolved haploid was crossed with its ancestor, and tetrad dissections were used to isolate a complete series of six meiotic tetrads. The Castle-Wright estimator of the number of loci at which adaptive mutations had been selected, modified to account for linkage and variation among mutations in the size of their effect, is 4.4. The estimate for a second haploid genotype, isolated from a separate population and with a fitness gain of 60%, was 2.7 loci. Backcrosses to the ancestor with the first evolved genotype support the inference that adaptation resulted primarily from two to five mutations. These backcrosses also indicated that deleterious mutations had hitchhiked with adaptive mutations in this evolved genotype.     

Population Genetics of Polymorphism and Divergence

Frequencies of mutant sites are modeled as a Poisson random field in two species that share a sufficiently recent common ancestor. The selective effect of the new alleles can be favorable, neutral, or detrimental. The model is applied to the sample configurations of nucleotides in the alcohol dehydrogenase gene (Adh) in Drosophila simulans and Drosophila yakuba. Assuming a synonymous mutation rate of 1.5 x 10(-8) per site per year and 10 generations per year, we obtain estimates for the effective population size (N(e) = 6.5 x 10(6)), the species divergence time (tdiv = 3.74 million years), and an average selection coefficient (sigma = 1.53 x 10(-6) per generation for advantageous or mildly detrimental replacements), although it is conceivable that only two of the amino acid replacements were selected and the rest neutral. The analysis, which includes a sampling theory for the independent infinite sites model with selection, also suggests the estimate that the number of amino acids in the enzyme that are susceptible to favorable mutation is in the range 2-23 at any one time. The approach provides a theoretical basis for the use of a 2 x 2 contingency table to compare fixed differences and polymorphic sites with silent sites and amino acid replacements.     

The Evolution of Recombination: Removing the Limits to Natural Selection

One of the oldest hypotheses for the advantage of recombination is that recombination allows beneficial mutations that arise in different individuals to be placed together on the same chromosome. Unless recombination occurs, one of the beneficial alleles is doomed to extinction, slowing the rate at which adaptive mutations are incorporated within a population. We model the effects of a modifier of recombination on the fixation probability of beneficial mutations when beneficial alleles are segregating at other loci. We find that modifier alleles that increase recombination do increase the fixation probability of beneficial mutants and subsequently hitchhike along as the mutants rise in frequency. The strength of selection favoring a modifier that increases recombination is proportional to λ(2)Sδr/r when linkage is tight and λ(2)S(3)δ r/N when linkage is loose, where λ is the beneficial mutation rate per genome per generation throughout a population of size N, S is the average mutant effect, r is the average recombination rate, and δr is the amount that recombination is modified. We conclude that selection for recombination will be substantial only if there is tight linkage within the genome or if many loci are subject to directional selection as during periods of rapid evolutionary change.