Bottleneck effect on genetic variance. A theoretical investigation of the role of dominance

The phenomenon that the genetic variance of fitness components increase following a bottleneck or inbreeding is supported by a growing number of experiments and is explained theoretically by either dominance or epistasis. In this article, diffusion approximations under the infinite sites model are used to quantify the effect of dominance, using data on viability in Drosophila melanogaster. The model is based on mutation parameters from mutation accumulation experiments involving balancer chromosomes (set I) or inbred lines (set II). In essence, set I assumes many mutations of small effect, whereas set II assumes fewer mutations of large effect. Compared to empirical estimates from large outbred populations, set I predicts reasonable genetic variances but too low mean viability. In contrast, set II predicts a reasonable mean viability but a low genetic variance. Both sets of parameters predict the changes in mean viability (depression), additive variance, between-line variance and heritability following bottlenecks generally compatible with empirical results, and these changes are mainly caused by lethals and deleterious mutants of large effect. This article suggests that dominance is the main cause for increased genetic variances for fitness components and fitness-related traits after bottlenecks observed in various experiments.     

Detection of deleterious genotypes in multigenerational studies. II. Theoretical and experimental dynamics with selfing and selection

A mathematical model was developed to help interpret genotype and allele frequency dynamics in selfing populations, with or without apomixis. Our analysis provided explicit time-dependent solutions for the frequencies at diallelic loci in diploid populations under any combination of fertility, viability, and gametic selection through meiotic drive. With no outcrossing, allelic variation is always maintained under gametic selection alone, but with any fertility or viability differences, variation will ordinarily be maintained if and only if the net fitness (fertility x viability) of heterozygotes exceeds that of both homozygotes by a substantial margin. Under pure selfing and Mendelian segregation, heterozygotes must have a twofold fitness advantage; the level of overdominance necessary to preserve genetic diversity declines with apomixis, and increases with segregation distortion if this occurs equally and independently in male and female gametes. A case study was made of the Arabidopsis act2-1 actin mutant over multiple generations initiated from a heterozygous plant. The observed genotypic frequency dynamics were consistent with those predicted by our model for a deleterious, incompletely recessive mutant in either fertility or viability. The theoretical framework developed here should be very useful in dissecting the form(s) and strength of selection on diploid genotypes in populations with negligible levels of outcrossing.     

Genetic diversity in Leavenworthia populations with different inbreeding levels

Levels of neutral genetic diversity within and between populations were compared between outcrossing (self-incompatible) and inbreeding populations in the annual plant genus Leavenworthia. Two taxonomically independent comparisons are possible, since self-incompatibility has been lost twice in the group of species studied. Within inbred populations of L.uniflora and L.crassa, no DNA sequence variants were seen among the alleles sampled, but high diversity was seen in alleles from populations of the outcrosser L. stylosa, and in self-incompatible L. crassa populations. Diversity between populations was seen in all species. Although total diversity values were lower in the sets of inbreeding populations, between-population values were as high or higher, than those in the outcrossing taxa. Possible reasons for these diversity patterns are discussed. As the effect of inbreeding appears to be a greater than twofold reduction in diversity, we argue that some process such as selection for advantageous mutations, or against deleterious mutations, or bottlenecks occurring predominantly in the inbreeders, appears necessary to account for the findings. If selection for advantageous mutations is responsible, it appears that it must be some form of local adaptive selection, rather than substitution of alleles that are advantageous throughout the species. This is consistent with the finding of high between-population diversity in the inbreeding taxa.     

Age-specific inbreeding depression and components of genetic variance in relation to the evolution of senescence

Two major theories of the evolution of senescence (mutation accumulation and antagonistic pleiotropy) make different predictions about the relationships between age, inbreeding effects, and the magnitude of genetic variance components of life-history components. We show that, under mutation accumulation, inbreeding decline and three major components of genetic variance are expected to increase with age in randomly mating populations. Under the simplest version of the antagonistic pleiotropy model, no changes in the severity of inbreeding decline, dominance variance, or the genetic variance of chromosomal homozygotes are expected, but additive genetic variance may increase with age. Age-specific survival rates and mating success were measured on virgin males, using lines extracted from a population of Drosophila melanogaster. For both traits, inbreeding decline and several components of genetic variance increase with age. The results are consistent with the mutation accumulation model, but can only be explained by antagonistic pleiotropy if there is a general tendency for an increase with age in the size of allelic effects on these life-history traits.     

The effect of overdominance on characterizing deleterious mutations in large natural populations

Alternatives to the mutation-accumulation approach have been developed to characterize deleterious genomic mutations. However, they all depend on the assumption that the standing genetic variation in natural populations is solely due to mutation-selection (M-S) balance and therefore that overdominance does not contribute to heterosis. Despite tremendous efforts, the extent to which this assumption is valid is unknown. With different degrees of violation of the M-S balance assumption in large equilibrium populations, we investigated the statistical properties and the robustness of these alternative methods in the presence of overdominance. We found that for dominant mutations, estimates for U (genomic mutation rate) will be biased upward and those for h (mean dominance coefficient) and s (mean selection coefficient), biased downward when additional overdominant mutations are present. However, the degree of bias is generally moderate and depends largely on the magnitude of the contribution of overdominant mutations to heterosis or genetic variation. This renders the estimates of U and s not always biased under variable mutation effects that, when working alone, cause U and s to be underestimated. The contributions to heterosis and genetic variation from overdominant mutations are monotonic but not linearly proportional to each other. Our results not only provide a basis for the correct inference of deleterious mutation parameters from natural populations, but also alleviate the biggest concern in applying the new approaches, thus paving the way for reliably estimating properties of deleterious mutations.     

Heterosis for viability, fecundity, and male fertility in Drosophila melanogaster: comparison of mutational and standing variation

If genetic variation for fitness traits in natural populations ("standing" variation) is maintained by recurrent mutation, then quantitative-genetic properties of standing variation should resemble those of newly arisen mutations. One well-known property of standing variation for fitness traits is inbreeding depression, with its converse of heterosis or hybrid vigor. We measured heterosis for three fitness traits, pre-adult viability, female fecundity, and male fertility, among a set of inbred Drosophilia melanogaster lines recently derived from the wild, and also among a set of lines that had been allowed to accumulate spontaneous mutations for over 200 generations. The inbred lines but not the mutation-accumulation (MA) lines showed heterosis for pre-adult viability. Both sets of lines showed heterosis for female fecundity, but heterosis for male fertility was weak or absent. Crosses among a subset of the MA lines showed that they were strongly differentiated for male fertility, with the differences inherited in autosomal fashion; the absence of heterosis for male fertility among the MA lines was therefore not caused by an absence of mutations affecting this trait. Crosses among the inbred lines also gave some, albeit equivocal, evidence for male fertility variation. The contrast between the results for female fecundity and those for male fertility suggests that mutations affecting different fitness traits may differ in their average dominance properties, and that such differences may be reflected in properties of standing variation. The strong differentiation among the MA lines in male fertility further suggests that mutations affecting this trait occur at a high rate.     

Genetic diversity at a single locus under viability selection and facultative apomixis: equilibrium structure and deviations from Hardy-Weinberg frequencies

We extensively analyze the maintenance of genetic variation and deviations from Hardy-Weinberg frequencies at a diallelic locus under mixed mating with apomixis and constant viability selection. Analytical proofs show that: (1) at most one polymorphic equilibrium exists, (2) polymorphism requires overdominant or underdominant selection, and (3) a simple, modified overdominance condition is sufficient to maintain genetic variation. In numerical analyses, only overdominant polymorphic equilibria are stable, and these are stable whenever they exist, which happens for approximately 78% of random fitness and mating parameters. The potential for maintaining both alleles increases with increasing apomixis or outcrossing and decreasing selfing. Simulations also indicate that equilibrium levels of heterozygosity will often be statistically indistinguishable from Hardy-Weinberg frequencies and that adults, not seeds, should usually be censused to maximize detecting deviations. Furthermore, although both censuses more often have an excess rather than a deficit of heterozygotes, analytical sign analyses of the fixation indices prove that, overall, adults are more likely to have an excess and seeds a deficit at equilibrium.     

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.     

Pre- and postsynaptic inhibitory actions of methionine-enkephalin on identified bulbospinal neurons of the rat RVL

Testing (over)dominance as the genetic cause of heterosis and estimating the (over)dominance coefficient (h) are related. Using simulations, we investigate the statistical properties of Mukai's approach, which is intended to estimate the average (h) of hi across loci by regression of outcrossed progeny on the sum of the two corresponding homozygous parents. A new approach for estimating h is also developed, utilizing data on families formed by multiple selfed genotypes from each outcrossed parent, thus not requiring constructing homozygotes. Assuming constant mutation effects, h can be estimated accurately by both approaches under dominance. When rare alleles have low frequencies at any polymorphic locus, Mukai's approach can estimate h accurately under over(under)dominance. Therefore, the (over)dominance hypothesis for heterosis can be tested by estimating h, under either dominance or overdominance at all genomic loci. However, this is invalid with more plausible mixed dominance and overdominance at different loci. Estimating the variance of hi across loci is also investigated. In self-compatible outcrossing populations with mutations of variable effects and lethals, our new approach is better than Mukai's, not only because of not requiring homozygotes but also because of the better statistical performance reflected by the smaller mean square errors of the estimates.     

The effect of mating system differences on nucleotide diversity at the phosphoglucose isomerase locus in the plant genus Leavenworthia

To test the theoretical prediction that highly inbreeding populations should have low neutral genetic diversity relative to closely related outcrossing populations, we sequenced portions of the cytosolic phosphoglucose isomerase (PgiC) gene in the plant genus Leavenworthia, which includes both self-incompatible and inbreeding taxa. On the basis of sequences of intron 12 of this gene, the expected low diversity was seen in both populations of the selfers Leavenworthia uniflora and L. torulosa and in three highly inbreeding populations of L. crassa, while high diversity was found in self-incompatible L. stylosa, and moderate diversity in L. crassa populations with partial or complete self-incompatibility. In L. stylosa, the nucleotide diversity was strongly structured into three haplotypic classes, differing by several insertion/deletion sequences, with linkage disequilibrium between sequences of the three types in intron 12, but not in the adjacent regions. Differences between the three kinds of haplotypes are larger than between sequences of this gene region from different species. The haplotype divergence suggests the presence of a balanced polymorphism at this locus, possibly predating the split between L. stylosa and its two inbreeding sister taxa, L. uniflora and L. torulosa. It is therefore difficult to distinguish between different potential causes of the much lower sequence diversity at this locus in inbreeding than outcrossing populations. Selective sweeps during the evolution of these populations are possible, or background selection, or merely loss of a balanced polymorphism maintained by overdominance in the populations that evolved high selfing rates.     

Effective size and polymorphism of linked neutral loci in populations under directional selection

The general theory of the effective size (Ne) for populations under directional selection is extended to cover linkage. Ne is a function of the association between neutral and selected genes generated by finite sampling. This association is reduced by three factors: the recombination rate, the reduction of genetic variance due to drift, and the reduction of genetic variance of the selected genes due to selection. If the genetic size of the genome (L in Morgans) is not extremely small the equation for Ne is [formula, see text] where N is the number of reproductive individuals, C 2 is the genetic variance for fitness scaled by the squared mean fitness, (1 - Z) = Vm/C2 is the rate of reduction of genetic variation per generation and Vm is the mutational input of genetic variation for fitness. The above predictive equation of Ne is valid for the infinitesimal model and for a model of detrimental mutations. The principles of the theory are also applicable to favorable mutation models if there is a continuous flux of advantageous mutations. The predictions are tested by simulation, and the connection with previous results is found and discussed. The reduction of effective size associated with a neutral mutation is progressive over generations until the asymptotic value (the above expression) is reached after a number of generations. The magnitude of the drift process is, therefore, smaller for recent neutral mutations than for old ones. This produces equilibrium values of average heterozygosity and proportion of segregating sites that cannot be formally predicted from the asymptotic Ne, but both parameters can still be predicted by following the drift along the lineage of genes. The spectrum of gene frequencies in a given generation can also be predicted by considering the overlapping of distributions corresponding to mutations that arose in different generations and with different associated effective sizes.     

Inferring the fitness effects of DNA mutations from polymorphism and divergence data: statistical power to detect directional selection under stationarity and free recombination

The fitness effects of classes of DNA mutations can be inferred from patterns of nucleotide variation. A number of studies have attributed differences in levels of polymorphism and divergence between silent and replacement mutations to the action of natural selection. Here, I investigate the statistical power to detect directional selection through contrasts of DNA variation among functional categories of mutations. A variety of statistical approaches are applied to DNA data simulated under Sawyer and Hartl's Poisson random field model. Under assumptions of free recombination and stationarity, comparisons that include both the frequency distributions of mutations segregating within populations and the numbers of mutations fixed between populations have substantial power to detect even very weak selection. Frequency distribution and divergence tests are applied to silent and replacement mutations among five alleles of each of eight Drosophila simulans genes. Putatively "preferred" silent mutations segregate at higher frequencies and are more often fixed between species than "unpreferred" silent changes, suggesting fitness differences among synonymous codons. Amino acid changes tend to be either rare polymorphisms or fixed differences, consistent with a combination of deleterious and adaptive protein evolution. In these data, a substantial fraction of both silent and replacement DNA mutations appear to affect fitness.     

Clusters of new identical mutants and the fate of underdominant mutations

Given favorable environmental and demographic conditions, premeiotic clusters of identical mutations can produce a broad distribution of the initial frequency of underdominant alleles. Because of these clusters, new underdominant mutations may not necessarily be as rare in a population as previously assumed. The fixation of underdominant mutations, especially those with low heterozygous fitness, is increased when mutations appear in a cluster due to a genetic change that occurred before germline differentiation. Most restrictions on the fixation of underdominant mutations in a single population, such as strong genetic drift, weak selection against mutant heterozygotes, isolated population structure, inbreeding, meiotic drive, and selection in favor of mutant homozygotes can be relaxed or even dropped. Instead, the fate of strong underdominant mutations is determined mainly by ecological and genetic factors that affect the cluster size distribution of new premeiotic mutations. Accumulation of reproductive isolation by the fixation of underdominant mutations becomes more feasible with clusters, and mutation is not always the weakest force during this evolutionary process. The large mean and variance of reproductive success in many multicellular species make it possible that even underdominant mutations with very low heterozygous fitness could contribute substantially to reproductive isolation.     

The mutation rate and the distribution of mutational effects of viability and fitness in Drosophila melanogaster

The empirical distributions of the average viability and fitness of mutation accumulation lines of Drosophila melanogaster were analyzed using minimum distance estimation. Data come from two different experimental designs where mutations were allowed to accumulate: 1) in copies of chromosome II protected from natural selection and recombination (viability: Mukai et al., 1972; Ohnishi, 1977; fitness: Houle et al., 1992), 2) in inbred lines derived from the same isogenic stock (viability: Fernández & López-Fanjul, 1996; fitness: this paper). Information from all data sets converged, indicating that the mutational rates were small, about 1% for viability and 3% for fitness. For both traits, the rate of mutational decline appears to be smaller than suggested by previous studies (about one-fifth of the latter), the average mutational effect was neither severe nor very slight, ranging from -0.1 to -0.3, and the distribution of mutant effects was, at most, slightly leptokurtic. Therefore, the mutational load in natural populations is one to two orders of magnitude smaller than previously thought (as based upon analyses conditional to estimates of the mutational decline of viability or fitness that appear to be biased upward). Over 95% of the mutational variance of each trait was contributed by non-slightly deleterious mutations (absolute homozygous effect larger than 0.03 or 0.1, depending on the data set considered) occurring at a rate not higher than 0.025 per haploid genome and generation. Our data suggest that most deleterious mutations affecting fitness act mainly through a single component-trait.     

Synthesis and antibacterial activity of U-100592 and U-100766, two oxazolidinone antibacterial agents for the potential treatment of multidrug-resistant gram-positive bacterial infections

The evolution of fitness in experimental clonal populations of vesicular stomatitis virus (VSV) has been compared under different genetic (fitness of initial clone) and demographic (population dynamics) regimes. In spite of the high genetic heterogeneity among replicates within experiments, there is a clear effect of population dynamics on the evolution of fitness. Those populations that went through strong periodic bottlenecks showed a decreased fitness in competition experiments with wild type. Conversely, mutant populations that were transferred under the dynamics of continuous population expansions increased their fitness when compared with the same wild type. The magnitude of the observed effect depended on the fitness of the original viral clone. Thus, high fitness clones showed a larger reduction in fitness than low fitness clones under dynamics with included periodic bottleneck. In contrast, the gain in fitness was larger the lower the initial fitness of the viral clone. The quantitative genetic analysis of the trait "fitness" in the resulting populations shows that genetic variation for the trait is positively correlated with the magnitude of the change in the same trait. The results are interpreted in terms of the operation of Muller's ratchet and genetic drift as opposed to the appearance of beneficial mutations.     

How should we explain variation in the genetic variance of traits?

Recent work has called attention to large differences among traits in the amount of standardized genetic variance they possess. There are four general factors which could play a role in causing this variation: mutation, elimination of deleterious variation, selection of favorable alleles, and balancing selection. Three factors could directly influence the mutational variability of traits: canalization, the mutational target size, and the timing of trait expression. Here I carry out simple tests of the importance of some of these factors using data from Drosophila melanogaster. I compiled information from the literature on the mutational and standing genetic variances in outbred populations, inferred the relative mutational target size of each trait, its a timing of expression, and used models of life history to calculate fitness sensitivities for each trait. Mutational variation seems to play an important role, as it is highly correlated with standing variance. The target size hypothesis was supported by a significant correlation between mutational variance and inferred target size. There was also a significant relationship between the timing of trait expression and mutational variance. These hypotheses are confounded by a correlation between timing and target size. The elimination and canalization hypotheses were not supported by these data, suggesting that they play a quantitatively less important role in determining overall variances. Additional information concerning the pleiotropic consequences of mutations would help to validate the fitness sensitivities used to test the elimination and canalization hypotheses.     

DNA polymorphism in lycopersicon and crossing-over per physical length

Surveys in Drosophila have consistently found reduced levels of DNA sequence polymorphism in genomic regions experiencing low crossing-over per physical length, while these same regions exhibit normal amounts of interspecific divergence. Here we show that for 36 loci across the genomes of eight Lycopersicon species, naturally occurring DNA polymorphism (scaled by locus-specific divergence between species) is positively correlated with the density of crossing-over per physical length. Large between-species differences in the amount of DNA sequence polymorphism reflect breeding systems: selfing species show much less within-species polymorphism than outcrossing species. The strongest association of expected heterozygosity with crossing-over is found in species with intermediate levels of average nucleotide diversity. All of these observations appear to be in qualitative agreement with the hitchhiking effects caused by the fixation of advantageous mutations and/or "background selection" against deleterious mutations.     

Measuring spontaneous deleterious mutation process

Parameters of the deleterious mutation process can be estimated using the data on genotypes, phenotypes, or fitnesses. These data can be on long-term evolution, on short-term changes, or on the properties of equilibrium populations. The two most important parameters at the genomic level, the total deleterious mutation rate U and the mutational pressure on fitness P, remain poorly known. Reliable data on the rates of presumably neutral evolution, together with less certain estimates of the functionally important fraction of the genome, suggest that in mammals U > 1. The magnitudes of inbreeding depression in populations of selfers imply U approximately 1 in flowering plants. The straightforward way to estimate P is to assay the decline of fitness in populations with relaxed selection. The relevant data are contradictory, possibly because the results of the measurement of fitness depend strongly on the environmental conditions.     

Muller's ratchet decreases fitness of a DNA-based microbe

Muller proposed that an asexual organism will inevitably accumulate deleterious mutations, resulting in an increase of the mutational load and an inexorable, ratchet-like, loss of the least mutated class [Muller, H.J. (1964) Mutat. Res. 1, 2-9]. The operation of Muller's ratchet on real populations has been experimentally demonstrated only in RNA viruses. However, these cases are exceptional in that the mutation rates of the RNA viruses are extremely high. We have examined whether Muller's ratchet operates in Salmonella typhimurium, a DNA-based organism with a more typical genomic mutation rate. Cells were grown asexually under conditions expected to result in high genetic drift, and the increase in mutational load was determined. S. typhimurium accumulated mutations under these conditions such that after 1700 generations, 1% of the 444 lineages tested had suffered an obvious loss of fitness, as determined by decreased growth rate. These results suggest that in the absence of sex and with high genetic drift, genetic mechanisms, such as back or compensatory mutations, cannot compensate for the accumulation of deleterious mutations. In addition, we measured the appearance of auxotrophs, which allowed us to calculate an average spontaneous mutation rate of approximately 0.3-1.5 x 10(-9) mutations per base pair per generation. This rate is measured for the largest genetic target studied so far, a collection of about 200 genes.     

Thermodynamic volume cycles for electron transfer in the cytochrome c oxidase and for the binding of cytochrome c to cytochrome c oxidase

Determining the way in which deleterious mutations interact in their effects on fitness is crucial to numerous areas in population genetics and evolutionary biology. For example, if each additional mutation leads to a greater decrease in log fitness than the last (synergistic epistasis), then the evolution of sex and recombination may be favored to facilitate the elimination of deleterious mutations. However, there is a severe shortage of relevant data. Three relatively simple experimental methods to test for epistasis between deleterious mutations in haploid species have recently been proposed. These methods involve crossing individuals and examining the mean and/or skew in log fitness of the offspring and parents. The main aim of this paper is to formalize these methods, and determine the most effective way in which tests for epistasis could be carried out. We show that only one of these methods is likely to give useful results: crossing individuals that have very different numbers of deleterious mutations, and comparing the mean log fitness of the parents with that of their offspring. We also reconsider experimental data collected on Chlamydomonas moewussi using two of the three methods. Finally, we suggest how the test could be applied to diploid species.