The action of stabilizing selection, mutation, and drift on epistatic quantitative traits.

For a quantitative trait under stabilizing selection, the effect of epistasis on its genetic architecture and on the changes of genetic variance caused by bottlenecking were investigated using theory and simulation. Assuming empirical estimates of the rate and effects of mutations and the intensity of selection, we assessed the impact of two-locus epistasis (synergistic/antagonistic) among linked or unlinked loci on the distribution of effects and frequencies of segregating loci in populations at the mutation-selection-drift balance. Strong pervasive epistasis did not modify substantially the genetic properties of the trait and, therefore, the most likely explanation for the low amount of variation usually accounted by the loci detected in genome-wide association analyses is that many causal loci will pass undetected. We investigated the impact of epistasis on the changes in genetic variance components when large populations were subjected to successive bottlenecks of different sizes, considering the action of genetic drift, operating singly (D), or jointly with mutation (MD) and selection (MSD). An initial increase of the different components of the genetic variance, as well as a dramatic acceleration of the between-line divergence, were always associated with synergistic epistasis but were strongly constrained by selection.

Regeneration of the variance of metric traits by spontaneous mutation in a Drosophila population.

In the C1 population of Drosophila melanogaster of moderate effective size ( approximately 500), which was genetically invariant in its origin, we studied the regeneration by spontaneous mutation of the genetic variance for two metric traits [abdominal (AB) and sternopleural (ST) bristle number] and that of the concealed mutation load for viability, together with their temporal stability, using alternative selection models based on mutational parameters estimated in the C1 genetic background. During generations 381-485 of mutation accumulation (MA), the additive variances of AB and ST approached the levels observed in standing laboratory populations, fluctuating around their expected equilibrium values under neutrality or under relatively weak causal stabilizing selection. This type of selection was required to simultaneously account for the observed additive variance in our population and for those previously reported in natural and laboratory populations, indicating that most mutations affecting bristle traits would only be subjected to weak selective constraints. Although gene action for bristles was essentially additive, transient situations occurred where inbreeding resulted in a depression of the mean and an increase of the additive variance. This was ascribed to the occasional segregation of mutations of large recessive effects. On the other hand, the observed non-lethal inbreeding depression for viability must be explained by the segregation of alleles of considerable and largely recessive deleterious effects, and the corresponding load concealed in the heterozygous condition was found to be temporally stable, as expected from tighter constraints imposed by natural selection.

The action of purifying selection, mutation and drift on fitness epistatic systems.

For different fitness mutational models, with epistasis introduced, we simulated the consequences of drift (D scenario) or mutation, selection, and drift (MSD scenario) in populations at the MSD balance subsequently subjected to bottlenecks of size N = 2, 10, 50 during 100 generations. No "conversion" of nonadditive into additive variance was observed, all components of the fitness genetic variance initially increasing with the inbreeding coefficient F and subsequently decreasing to zero (D) or to an equilibrium value (MSD). In the D scenario, epistasis had no appreciable effect on inbreeding depression and that on the temporal change of variance components was relevant only for high rates of strong epistatic mutation. In parallel, between-line differentiation in mean fitness accelerated with F and that in additive variance reached a maximum at F approximately 0.6-0.7, both processes being intensified by strong epistasis. In the MSD scenario, however, the increase in additive variance was smaller, as it was used by selection to purge inbreeding depression (N > or = 10), and selection prevented between-line differentiation. Epistasis, either synergistic or antagonistic (this leading to multiple adaptive peaks), had no appreciable effect on MSD results nor, therefore, on the evolutionary rate of fitness change.

The build up of mutation-selection- drift balance in laboratory Drosophila populations.

The build up of an equilibrium between mutation, selection, and drift in populations of moderate size is an important evolutionary issue, and can be critical in the conservation of endangered populations. We studied this process in two Drosophila melanogaster populations initially lacking genetic variability (C1 and C2) that were subsequently maintained during 431 or 165 generations with effective population size N(e) approximately 500 (estimated by lethal complementation analysis). Each population originated synchronously to a companion set of full-sib mutation accumulation (MA) lines, C1 and MA1 were derived from an isogenic origin and C2 and MA2 from a single MA1 line at generation 265. The results suggest that both C1 and C2 populations were close to the mutation-selection-drift balance for viability and bristle traits, and are consistent with a 2.5-fold increase of the mutation rate in C2 and MA2. Despite this increase, the average panmictic viability in C2 was only slightly below that of C1, indicating that the expressed loads due to segregating deleterious mutation were small, in agreement with the low deleterious mutation rate (0.015-0.045) previously reported for the MA1 lines. In C1, the nonlethal inbreeding depression rate for viability was 30% of that usually estimated in segregating populations. The genetic variance for bristles regenerated in C1 and C2 was moderately smaller than the average value reported for natural populations, implying that they have accumulated a substantial adaptive potential. In light of neutral and selective predictions, these results suggest that bristle additive variance was predominantly due to segregation of mutations with deleterious effects of the order of 10(-3), and is consistent with relatively weak causal stabilizing selection (V(s) approximately 30).

Increase of the spontaneous mutation rate in a long-term experiment with Drosophila melanogaster.

In a previous experiment, the effect of 255 generations of mutation accumulation (MA) on the second chromosome viability of Drosophila melanogaster was studied using 200 full-sib MA1 lines and a large C1 control, both derived from a genetically homogeneous base population. At generation 265, one of those MA1 lines was expanded to start 150 new full-sib MA2 lines and a new C2 large control. After 46 generations, the rate of decline in mean viability in MA2 was approximately 2.5 times that estimated in MA1, while the average degree of dominance of mutations was small and nonsignificant by generation 40 and moderate by generation 80. In parallel, the inbreeding depression rate for viability and the amount of additive variance for two bristle traits in C2 were 2-3 times larger than those in C1. The results are consistent with a mutation rate in the line from which MA2 and C2 were derived about 2.5 times larger than that in MA1. The mean viability of C2 remained roughly similar to that of C1, but the rate of MA2 line extinction increased progressively, leading to mutational collapse, which can be ascribed to accelerated mutation and/or synergy after important deleterious accumulation.

The effect of genetic drift on the variance/covariance components generated by multilocus additive x additive epistatic systems.

The effect of population bottlenecks on the components of the genetic variance/covariance generated by n neutral independent additive x additive loci has been studied theoretically. In its simplest version, this situation can be modelled by specifying the allele frequencies and homozygous effects at each locus, and an additional factor measuring the strength of the n-th order epistatic interaction. The variance/covariance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium over replicates randomly derived from the base population, after t bottlenecks of size N (derived components). Formulae were obtained giving the derived components (and the between-line variance) as functions of the ancestral ones (alternatively, in terms of allele frequencies and effects) and the corresponding inbreeding coefficient F(t). The n-th order derived component of the genetic variance/covariance is continuously eroded by inbreeding, but the remaining components may increase initially until a critical F(t) value is attained, which is inversely related to the order of the pertinent component, and subsequently decline to zero. These changes can be assigned to the between-line variances/covariances of gene substitution and epistatic effects induced by drift. Numerical examples indicate that: (1) the derived additive variance/covariance component will generally exceed its ancestral value unless epistasis is weak; (2) the derived epistatic variance/covariance components will generally exceed their ancestral values unless allele frequencies are extreme; (3) for systems showing equal ancestral additive and total non-additive variance/covariance components, those including a smaller number of epistatic loci may generate a larger excess in additive variance/covariance after bottlenecks than others involving a larger number of loci, provided that F(t) is low. Our results indicate that it is unlikely that the rate of evolution may be significantly accelerated after population bottlenecks, in spite of occasional increments of the derived additive variance over its ancestral value.

Epistasis and the temporal change in the additive variance-covariance matrix induced by drift.

The effect of population bottlenecks on the components of the genetic covariance generated by two neutral independent epistatic loci has been studied theoretically (additive, covA; dominance, covD; additive-by-additive, covAA; additive-by-dominance, covAD; and dominance-by-dominance, covDD). The additive-by-additive model and a more general model covering all possible types of marginal gene action at the single-locus level (additive/dominance epistatic model) were considered. The covariance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium over replicates randomly derived from the base population, after t consecutive bottlenecks of equal size N (derived components). Formulae were obtained in terms of the allele frequencies and effects at each locus, the corresponding epistatic effects and the inbreeding coefficient Ft. These expressions show that the contribution of nonadditive loci to the derived additive covariance (covAt) does not linearly decrease with inbreeding, as in the pure additive case, and may initially increase or even change sign in specific situations. Numerical examples were also analyzed, restricted for simplicity to the case of all covariance components being positive. For additive-by-additive epistasis, the condition covAt > covA only holds for high frequencies of the allele decreasing the metric traits at each locus (negative allele) if epistasis is weak, or for intermediate allele frequencies if it is strong. For the additive/dominance epistatic model, however, covAt > covA applies for low frequencies of the negative alleles at one or both loci and mild epistasis, but this result can be progressively extended to intermediate frequencies as epistasis becomes stronger. Without epistasis the same qualitative results were found, indicating that marginal dominance induced by epistasis can be considered as the primary cause of an increase of the additive covariance after bottlenecks. For all models, the magnitude of the ratio covAt/covA was inversely related to N and t.

The effect of neutral nonadditive gene action on the quantitative index of population divergence.

For neutral additive genes, the quantitative index of population divergence (Q(ST)) is equivalent to Wright's fixation index (F(ST)). Thus, divergent or convergent selection is usually invoked, respectively, as a cause of the observed increase (Q(ST) > F(ST)) or decrease (Q(ST) < F(ST)) of Q(ST) from its neutral expectation (Q(ST) = F(ST)). However, neutral nonadditive gene action can mimic the additive expectations under selection. We have studied theoretically the effect of consecutive population bottlenecks on the difference F(ST) - Q(ST) for two neutral biallelic epistatic loci, covering all types of marginal gene action. With simple dominance, Q(ST) < F(ST) for only low to moderate frequencies of the recessive alleles; otherwise, Q(ST) > F(ST). Additional epistasis extends the condition Q(ST) < F(ST) to a broader range of frequencies. Irrespective of the type of nonadditive action, Q(ST) < F(ST) generally implies an increase of both the within-line additive variance after bottlenecks over its ancestral value (V(A)) and the between-line variance over its additive expectation (2F(ST)V(A)). Thus, both the redistribution of the genetic variance after bottlenecks and the F(ST) - Q(ST) value are governed largely by the marginal properties of single loci. The results indicate that the use of the F(ST) - Q(ST) criterion to investigate the relative importance of drift and selection in population differentiation should be restricted to pure additive traits.

The effect of epistasis on the excess of the additive and nonadditive variances after population bottlenecks.

The effect of population bottlenecks on the components of the genetic variance generated by two neutral independent epistatic loci has been studied theoretically (VA, additive; VD, dominant; VAA, additive x additive; VAD, additive x dominant; VDD; dominant x dominant components of variance). Nonoverdominance and overdominance models were considered, covering all possible types of marginal gene action at the single locus level. The variance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium, after t consecutive bottlenecks of equal size N (derived components). Formulae were obtained in terms of allele frequencies and effects at each locus and the corresponding epistatic value. An excess of VA after bottlenecks can be assigned to two sources: (1) the spatiotemporal changes in the marginal average effects of gene substitution alpha(i), which are equal to zero only for additive gene action within and between loci; and (2) the covariance between alpha2(i) and the heterozygosity at the loci involved, which is generated by dominance, with or without epistasis. Numerical examples were analyzed, indicating that an increase in VA after bottlenecks will only occur if its ancestral value is minimal or very small. For the nonoverdominance model with weak reinforcing epistasis, that increase has been detected only for extreme frequencies of the negative allele at one or both loci. With strong epistasis, however, this result can be extended to a broad range of intermediate frequencies. With no epistasis, the same qualitative results were found, indicating that dominance can be considered as the primary cause of an increase in VA following bottlenecks. In parallel, the derived total nonadditive variance exceeded its ancestral value (V(NA) = V(D) + V(AA) + V(AD) + V(DD)) for a range of combinations of allele frequencies covering those for an excess of VA and for very large frequencies of the negative allele at both loci. For the overdominance model, an increase in V(A) and V(NA) was respectively observed for equilibrium (intermediate) frequencies at one or both loci or for extreme frequencies at both loci. For all models, the magnitude of the change of V(A) and V(NA) was inversely related to N and t. At low levels of inbreeding, the between-line variance was not affected by the type of gene action. For the models considered, the results indicate that it is unlikely that the rate of evolution may be accelerated after population bottlenecks, in spite of occasional increments of the derived V(A) over its ancestral value.

SPONTANEOUS MUTATIONAL GENOTYPE-ENVIRONMENT INTERACTION FOR FITNESS-RELATED TRAITS IN DROSOPHILA MELANOGASTER.

Spontaneous mutations were allowed to accumulate for 104-161 generations in 113-176 inbred lines, independently maintained by a single brother-sister mating per generation, all of them derived from a completely homozygous population of Drosophila melanogaster. In each of two to three consecutive generations, all lines were scored for fecundity, egg-to-pupa and pupa-to-adult viabilities, both in the standard laboratory culture medium (ST) and in three harsh media differing from the former by a single factor: higher temperature (HT), higher NaCl concentration (HSC), or a much reduced concentration of nutrients (D). Relative to the standard medium, productivity (fecundity × viability) decreased by 25% (HT), 66% (HSC), and 80% (D). In each medium, mutational variances of those traits and mutational covariances between all possible pairs were calculated from the between-line divergence (codivergence). Mutational correlations between character states in different media were also obtained. Because we used inbred lines, those estimates were mainly due to the accumulation of mildly detrimental mutations, deleterious mutations of large effect being underrepresented. For all traits, mutational heritabilities ranged from 1.41 × 10-4 to 11.24 × 10-4 , and did not increase with intensified environmental harshness. Mutational correlations between character states in different media were usually not large (average absolute value 0.31), reflecting a high degree of environmental specificity of the mutations involved. In our results, mutations quasi-neutral in ST conditions and mildly detrimental in more stressful media were not, as a class, important. Mutational correlations between fecundity and egg-to-pupa viability were small and positive in all media. Those involving pupa-to-adult viability were positive in HT, nonsignificant in HSC, and negative in ST and D, showing how the genetic covariance structure of quantitative traits in populations may change in variable environments.

THE GENETICS OF VIABILITY IN DROSOPHILA MELANOGASTER: EFFECTS OF INBREEDING AND ARTIFICIAL SELECTION.

Inbreeding and artificial selection experiments were conducted to investigate the genetic properties of egg-to-pupa viability in a population of Drosophila melanogaster. The effect of different levels of inbreeding (F = 0, 0.25, 0.50, and 0.73) was studied. Up to F = 0.50, a linear depression of the mean viability was observed, accompanied by a significant increase of both within-line additive variance and between-line variance. At F = 0.73, no further changes were detected. This can be attributed to natural selection opposing high levels of homozygosity. In parallel, artificial selection to increase viability was performed for 27 generations in (1) a single undivided population (U) and (2) two populations with cycles of subdivision and between-line selection, followed by reconstitution of selected lines (SO and SI ). During the first cycle (generations 0-4), most of the final total response was achieved under all selection regimes. An advantage of the SO and SI strategies was observed after the completion of the first cycle. However, the same limit was reached in all cases because of a delayed response experienced by line U. Reverse selection for viability resulted in positive correlated responses for fecundity and mating success. Both inbreeding and selection results are compatible with the genetic variance of viability in the base population being generated by segregation at a few loci with substantial additive effects and several deleterious recessives at low initial frequencies. Possible reasons for the maintenance of that variance in natural populations are discussed.