Pleiotropic Models of Polygenic Variation, Stabilizing Selection, and Epistasis

We show that in polymorphic populations many polygenic traits pleiotropically related to fitness are expected to be under apparent ``stabilizing selection' independently of the real selection acting on the population. This occurs, for example, if the genetic system is at a stable polymorphic equilibrium determined by selection and the nonadditive contributions of the loci to the trait value either are absent, or are random and independent of those to fitness. Stabilizing selection is also observed if the polygenic system is at an equilibrium determined by a balance between selection and mutation (or migration) when both additive and nonadditive contributions of the loci to the trait value are random and independent of those to fitness. We also compare different viability models that can maintain genetic variability at many loci with respect to their ability to account for the strong stabilizing selection on an additive trait. Let V(m) be the genetic variance supplied by mutation (or migration) each generation, V(g) be the genotypic variance maintained in the population, and n be the number of the loci influencing fitness. We demonstrate that in mutation (migration)-selection balance models the strength of apparent stabilizing selection is order V(m)/V(g). In the overdominant model and in the symmetric viability model the strength of apparent stabilizing selection is approximately 1/(2n) that of total selection on the whole phenotype. We show that a selection system that involves pairwise additive by additive epistasis in maintaining variability can lead to a lower genetic load and genetic variance in fitness (approximately 1/(2n) times) than an equivalent selection system that involves overdominance. We show that, in the epistatic model, the apparent stabilizing selection on an additive trait can be as strong as the total selection on the whole phenotype.     

Signals of major histocompatibility complex overdominance in a wild salmonid population

The major histocompatibility complex (MHC) contains the most variable genes in vertebrates, but despite extensive research, the mechanisms maintaining this polymorphism are still unresolved. One hypothesis is that MHC polymorphism is a result of balancing selection operating by overdominance, but convincing evidence for overdominant selection in natural populations has been lacking. We present strong evidence consistent with MHC-specific overdominance in a free-living population of Arctic charr (Salvelinus alpinus) in northernmost Europe. In this population, where just two MHC alleles were observed, MHC heterozygous fish had a lower parasite load, were in better condition (as estimated by a fatness indicator) and had higher survival under stress than either of the homozygotes. Conversely, there was no consistent association between these fitness measures and assumedly neutral microsatellite variability, indicating an MHC-specific effect. Our results provide convincing empirical evidence consistent with the notion that overdominance can be an important evolutionary mechanism contributing to MHC polymorphism in wild animal populations. They also support a recent simulation study indicating that the number of alleles expected to be maintained at an MHC loci can be low, even under strong heterozygote advantage.     

The significance of over- and underdominance for the maintenance of genetic polymorphisms. I. Underdominance and stability

It is pointed out that the standard selection models in population genetics all require some form of heterozygote advantage in fitness in order to guarantee the maintenance or stability of genetic polymorphisms. Even more recent results demonstrating the existence of stable two-locus polymorphisms with marginal underdominance at both loci are based on certain epistatically acting heterosis assumptions. This raises the question as to whether heterozygote advantage in fitness is indeed a generally valid principle of maintaining polymorphisms. To avoid ambiguity in definition of heterozygote advantage (overdominance) as it appears in multiallele or multilocus systems, a one-locus-two-allele model is considered. This model allows for sexually asymmetric selection and random mating. It is shown that the model produces globally stable polymorphisms exhibiting underdominance in fitness for a considerable and biologically reasonable range of selection values. Having thus properly refuted the general validity of the common overdominance principle, a modified version is suggested which covers the classical viability selection model and its extension to arbitrary, sexually asymmetric viability and fertility selection. This modified overdominance principle is based on the notion of fractional fitnesses and relates protectedness of biallelic polymorphisms to the extent to which each genotype reproduces its own type. The fact that the model treated displays frequency dependent fitnesses which may change in ranking while approaching equilibrium is discussed in relation to problems of the evolution of overdominance and underdominance.     

Marginal Overdominance in Drosophila

A reanalysis of Drosophila viability data was undertaken to determine the role of genotype-environment interactions in the maintenance of polymorphism. Between-replicate variances of viabilities in chromosomal homozygotes and heterozygotes with the same mean fitnesses were compared, with the expectation that if the heterozygote variance were on the average greater, conditional overdominance would be prevalent; if it were less, partial dominance would be prevalent; and if it were the same, marginal overdominance of the type considered by Wallace (1968) would be the prevalent type of variation. In fact, heterozygote variance was slightly less. The work of Dempster (1955) and of Gillespie and Langley (1974) is cited to show that this situation can still lead to balanced polymorphisms. Their general model for genetic variation in populations, consistent with the viability data, is reinforced.     

Testing for beneficial reversal of dominance during salinity shifts in the invasive copepod Eurytemora affinis,and implications for the maintenance of genetic variation

Maintenance of genetic variation at loci under selection has profound implications for adaptation under environmental change. In temporally and spatially varying habitats, non‐neutral polymorphism could be maintained by heterozygote advantage across environments (marginal overdominance), which could be greatly increased by beneficial reversal of dominance across conditions. We tested for reversal of dominance and marginal overdominance in salinity tolerance in the saltwater‐to‐freshwater invading copepod Eurytemora affinis. We compared survival of F1 offspring generated by crossing saline and freshwater inbred lines (between‐salinity F1 crosses) relative to within‐salinity F1 crosses, across three salinities. We found evidence for both beneficial reversal of dominance and marginal overdominance in salinity tolerance. In support of reversal of dominance, survival of between‐salinity F1 crosses was not different from that of freshwater F1 crosses under freshwater conditions and saltwater F1 crosses under saltwater conditions. In support of marginal overdominance, between‐salinity F1 crosses exhibited significantly higher survival across salinities relative to both freshwater and saltwater F1 crosses. Our study provides a rare empirical example of complete beneficial reversal of dominance associated with environmental change. This mechanism might be crucial for maintaining genetic variation in salinity tolerance in E. affinis populations, allowing rapid adaptation to salinity changes during habitat invasions.     

Mate choice for non-additive genetic benefits: a resolution to the lek paradox

In promiscuous mating systems, females often show a consistent preference to mate with one or a few males, presumably to acquire heritable genetic benefits for their offspring. However, strong directional selection should deplete additive genetic variation in fitness and consequently any benefit to expressing the preference by females (referred to as the lek paradox). Here, we provide a novel resolution that examines non-additive genetic benefits, such as overdominance or inbreeding, as a source of genetic variation. Focusing on the inbreeding coefficient f and overdominance effects, we use dynamic models to show that (1) f can be inherited from sire to offspring, (2) populations with females that express a mating preferences for outbred males (low f) maintain higher genetic variation than populations with females that mate randomly, and (3) preference alleles for outbred males can invade populations even when the alleles are associated with a fecundity cost. We show that non-additive genetic variation due to overdominance can be converted to additive genetic variation and becomes “heritable” when the frequencies of alternative homozygous genotypes at fitness loci deviate from equality. Unlike previous models that assume an infinite population size, we now show that genetic drift in finite populations can lead to the necessary deviations in the frequencies of homozygous genotypes. We also show that the “heritability of f,” and hence the benefit to a mating preference for non-additive genetic benefits, is highest in small populations and populations in which a smaller number of loci contribute to fitness via overdominance. Our model contributes to the solution of the lek paradox.     

The maintenance (or not) of polygenic variation by soft selection in heterogeneous environments

On the basis of single-locus models, spatial heterogeneity of the environment coupled with strong population regulation within each habitat (soft selection) is considered an important mechanism maintaining genetic variation. We studied the capacity of soft selection to maintain polygenic variation for a trait determined by several additive loci, selected in opposite directions in two habitats connected by dispersal. We found three main types of stable equilibria. Extreme equilibria are characterized by extreme specialization to one habitat and loss of polymorphism. They are analogous to monomorphic equilibria in singe-locus models and are favored by similar factors: high dispersal, weak selection, and low marginal average fitness of intermediate genotypes. At the remaining two types of equilibria the population mean is intermediate but variance is very different. At fully polymorphic equilibria all loci are polymorphic, whereas at low-variance equilibria at most one locus remains polymorphic. For most parameters only one type of equilibrium is stable; the transition between the domains of fully polymorphic and low-variance equilibria is typically sharp. Low-variance equilibria are favored by high marginal average fitness of intermediate genotypes, in contrast to single-locus models, in which marginal overdominance is particularly favorable for maintenance of polymorphism. The capacity of soft selection to maintain polygenic variation is thus more limited than extrapolation from single-locus models would suggest, in particular if dispersal is high and selection weak. This is because in a polygenic model, variance can evolve independently of the mean, whereas in the single-locus two-allele case, selection for an intermediate mean automatically leads to maintenance of polymorphism.     

The effects of deleterious mutations on linked, neutral variation in small populations.

The effects of recessive, deleterious mutations on genetic variation at linked neutral loci can be heterozygosity-decreasing because of reduced effective population sizes or heterozygosity-increasing because of associative overdominance. Here we examine the balance between these effects by simulating individual diploid genotypes in small panmictic populations. The haploid genome consists of one linkage group with 1000 loci that can have deleterious mutations and a neutral marker. Combinations of the following parameters are studied: gametic mutation rate to harmful alleles (U), population size (N), recombination rate (r), selection coefficient (s), and dominance (h). Tight linkage (r 相似文献   

A population genetic model of selection that maintains specific trinucleotides at a specific location

Summary Periodic appearances of specific trinucleotides along the DNA sequence have been reported in the chicken core DNA and the phenomenon has been suggested to be related to the supercoiling of DNA around nucleosomes. A population genetic model is constructed in which selection is operating to maintain specific trinucleotides at a specific location on the DNA sequence. Assuming low mutation rates, equilibrium probabilities of the appearances of respective trinucleotides were computed. Vague patterns appeared if the product of the effective size and the selection coefficient was 0.1–2.0. The genetic load and substitution rates in the equilibrium state were also computed. When the model was applied to the chicken DNA data, the product of the effective size and the selection coefficient was estimated to be 0.1–0.2. With this intensity of selection, the substitution rate was hardly different from that in the case without selection. However, the genetic load became fairly large. Considering the large number of times that DNA coils about nucleosomes, the number of trinucleotide sites must be very large, and thus the total load might be too large. Epistasis among these sites to reduce the total load is suggested to exist if selection is responsible for this periodic pattern observed in the chicken core DNA.     

Effect of linkage on behavior of mutant genes in finite populations

In this paper, the effectiveness of the apparent or “associated” overdominance caused by linked selected loci on maintaining genetic variability was investigated using diffusion models. It was shown that when a population is subdivided, the amount of linkage disequilibrium is determined by the local population size if the recombination fraction is much larger than the migration rates. Also, it was shown that the associative overdominance temporarily creates a sort of inertia against perturbation in gene frequencies even if it cannot endow any definite equilibrium values. Hence, it has no long term effect on the rate of mutant substitution in evolution.     

Patterns of differentiation in a colour polymorphism and in neutral markers reveal rapid genetic changes in natural damselfly populations

The existence and mode of selection operating on heritable adaptive traits can be inferred by comparing population differentiation in neutral genetic variation between populations (often using F(ST) values) with the corresponding estimates for adaptive traits. Such comparisons indicate if selection acts in a diversifying way between populations, in which case differentiation in selected traits is expected to exceed differentiation in neutral markers [F(ST )(selected) > F(ST )(neutral)], or if negative frequency-dependent selection maintains genetic polymorphisms and pulls populations towards a common stable equilibrium [F(ST) (selected) < F(ST) (neutral)]. Here, we compared F(ST) values for putatively neutral data (obtained using amplified fragment length polymorphism) with estimates of differentiation in morph frequencies in the colour-polymorphic damselfly Ischnura elegans. We found that in the first year (2000), population differentiation in morph frequencies was significantly greater than differentiation in neutral loci, while in 2002 (only 2 years and 2 generations later), population differentiation in morph frequencies had decreased to a level significantly lower than differentiation in neutral loci. Genetic drift as an explanation for population differentiation in morph frequencies could thus be rejected in both years. These results indicate that the type and/or strength of selection on morph frequencies in this system can change substantially between years. We suggest that an approach to a common equilibrium morph frequency across all populations, driven by negative frequency-dependent selection, is the cause of these temporal changes. We conclude that inferences about selection obtained by comparing F(ST) values from neutral and adaptive genetic variation are most useful when spatial and temporal data are available from several populations and time points and when such information is combined with other ecological sources of data.     

The significance of over- and underdominance for the maintenance of genetic polymorphisms. II. Overdominance and instability with random mating

Part I of the present series demonstrates that globally stable polymorphic equilibria may show underdominance in Darwinian fitness. Hence, overdominance in fitness can no longer be conceived of as a necessary condition for the stability of a polymorphism. In the present paper, the question is posed as to whether overdominance is at least sufficient for this stability. A population of randomly mating individuals is considered, where selection operates uniquely through differential fecundities of particular mating types and may generate either a heterozygote excess or deficit relative to Hardy-Weinberg proportions. It turns out that both unstable central overdominance and stable central underdominance are possible and that their occurrence is strongly related to an excess or a deficiency of heterozygotes in the vicinity of the regions of instability or stability. As one consequence, the above suggested sufficiency of heterozygote superiority is not valid, even in random mating populations. Based on the results of both papers of this series, which demonstrate the inadequacy of over- and underdominance as indicators of stability or instability, a modified overdominance principle is discussed. This principle states that a biallelic polymorphism is maintained if the heterozygote is superior in its degree of "heterogamous self-replication" to the degrees of "autogamous self-replication" of the corresponding homozygotes. It is derived with the help of fractional fitnesses, and it is pointed out that certain ratios of these may be more useful for finding evolutionary constants which govern the maintenance of genetic polymorphisms than are ratios of total fitnesses.     

Levels of inbreeding depression over seven generations of selfing in the androdioecious clam shrimp, Eulimnadia texana

Androdioecy (mixtures of males and hermaphrodites) is a rare mating system in both plants and animals. Theory suggests that high levels of inbreeding depression can maintain males in androdioecious populations if hermaphrodites commonly self-fertilize. However, if inbreeding depression (delta) can be 'purged' from selfing populations, maintaining males is more difficult. In the androdioecious clam shrimp, Eulimnadia texana, delta is estimated to be as high as 0.7. Previous work suggests that this high level is maintained in the face of high levels of inbreeding due to an associative overdominance of fitness-related loci with the sex-determining locus. Such associative overdominance would make purging of inbreeding depression difficult to impossible. The current experiment was designed to determine if delta can be purged in these shrimp by tracking fitness across seven generations in selfing and outcrossing treatments. Evidence of purging was found in one of four populations, but the remaining populations demonstrated a consistent pattern of delta across generations. Although the experimental design allowed ample opportunity for purging, the majority of populations were unable to purge their genetic load. Therefore, delta in this species is likely due to associative overdominance caused by deleterious recessive alleles linked to the sex determining locus.     

Recent approaches into the genetic basis of inbreeding depression in plants

Predictions for the evolution of mating systems and genetic load vary, depending on the genetic basis of inbreeding depression (dominance versus overdominance, epistasis and the relative frequencies of genes of large and small effect). A distinction between the dominance and overdominance hypotheses is that deleterious recessive mutations should be purged in inbreeding populations. Comparative studies of populations differing in their level of inbreeding and experimental approaches that allow selection among inbred lines support this prediction. More direct biometric approaches provide strong support for the importance of partly recessive deleterious alleles. Investigators using molecular markers to study quantitative trait loci (QTL) often find support for overdominance, though pseudo-overdominance (deleterious alleles linked in repulsion) may bias this perception. QTL and biometric studies of inbred lines often find evidence for epistasis, which may also contribute to the perception of overdominance, though this may be because of the divergent lines initially crossed in QTL studies. Studies of marker segregation distortion commonly uncover genes of major effect on viability, but these have only minor contributions to inbreeding depression. Although considerable progress has been made in understanding the genetic basis of inbreeding depression, we feel that all three aspects merit more study in natural plant populations.     

Stability analysis of the partial selfing selection model

We undertake a detailed study of the one-locus two-allele partial selfing selection model. We show that a polymorphic equilibrium can exist only in the cases of overdominance and underdominance and only for a certain range of selfing rates. Furthermore, when it exists, we show that the polymorphic equilibrium is unique. The local stability of the polymorphic equilibrium is investigated and exact analytical conditions are presented. We also carry out an analysis of local stability of the fixation states and then conclude that only overdominance can maintain polymorphism in the population. When the linear local analysis is inconclusive, a quadratic analysis is performed. For some sets of selective values, we demonstrate global convergence. Finally, we compare and discuss results under the partial selfing model and the random mating model.     

Dynamics of inbreeding depression due to deleterious mutations in small populations: mutation parameters and inbreeding rate

A multilocus stochastic model is developed to simulate the dynamics of mutational load in small populations of various sizes. Old mutations sampled from a large ancestral population at mutation-selection balance and new mutations arising each generation are considered jointly, using biologically plausible lethal and deleterious mutation parameters. The results show that inbreeding depression and the number of lethal equivalents due to partially recessive mutations can be partly purged from the population by inbreeding, and that this purging mainly involves lethals or detrimentals of large effect. However, fitness decreases continuously with inbreeding, due to increased fixation and homozygosity of mildly deleterious mutants, resulting in extinctions of very small populations with low reproductive rates. No optimum inbreeding rate or population size exists for purging with respect to fitness (viability) changes, but there is an optimum inbreeding rate at a given final level of inbreeding for reducing inbreeding depression or the number of lethal equivalents. The interaction between selection against partially recessive mutations and genetic drift in small populations also influences the rate of decay of neutral variation. Weak selection against mutants relative to genetic drift results in apparent overdominance and thus an increase in effective size (Ne) at neutral loci, and strong selection relative to drift leads to a decrease in Ne due to the increased variance in family size. The simulation results and their implications are discussed in the context of biological conservation and tests for purging.     

WHY WE ARE NOT DEAD ONE HUNDRED TIMES OVER

The possibility of pervasive weak selection at tens or hundreds of millions of sites across the genome, suggested by recent studies of silent site DNA sequence variation and divergence, raises the problem of the survival of the population in the face of the large genetic load that may result. Two alternative resolutions of this problem are presented for populations where recombination is sufficiently frequent that different sites under selection evolve independently. One invokes weak stabilizing selection, of the magnitude compatible with abundant silent site variability. This can be shown to produce only a modest genetic load, due to the effectiveness of even weak stabilizing selection in keeping the trait mean close to the optimum. The other invokes soft selection, whereby individuals compete for a limiting resource whose abundance determines the absolute fitness of the population. Weak purifying selection at a large number of sites produces only a small variance in fitness among individuals within the population, due to the fact that most sites are fixed rather than polymorphic. Even when it produces a large genetic load, it is compatible with the observations on fitness variance when selection is soft. It may be very difficult to distinguish between these two possibilities.     

Genomic selection of purebred animals for crossbred performance in the presence of dominant gene action

Background

Genomic selection is an appealing method to select purebreds for crossbred performance. In the case of crossbred records, single nucleotide polymorphism (SNP) effects can be estimated using an additive model or a breed-specific allele model. In most studies, additive gene action is assumed. However, dominance is the likely genetic basis of heterosis. Advantages of incorporating dominance in genomic selection were investigated in a two-way crossbreeding program for a trait with different magnitudes of dominance. Training was carried out only once in the simulation.

Results

When the dominance variance and heterosis were large and overdominance was present, a dominance model including both additive and dominance SNP effects gave substantially greater cumulative response to selection than the additive model. Extra response was the result of an increase in heterosis but at a cost of reduced purebred performance. When the dominance variance and heterosis were realistic but with overdominance, the advantage of the dominance model decreased but was still significant. When overdominance was absent, the dominance model was slightly favored over the additive model, but the difference in response between the models increased as the number of quantitative trait loci increased. This reveals the importance of exploiting dominance even in the absence of overdominance. When there was no dominance, response to selection for the dominance model was as high as for the additive model, indicating robustness of the dominance model. The breed-specific allele model was inferior to the dominance model in all cases and to the additive model except when the dominance variance and heterosis were large and with overdominance. However, the advantage of the dominance model over the breed-specific allele model may decrease as differences in linkage disequilibrium between the breeds increase. Retraining is expected to reduce the advantage of the dominance model over the alternatives, because in general, the advantage becomes important only after five or six generations post-training.

Conclusion

Under dominance and without retraining, genomic selection based on the dominance model is superior to the additive model and the breed-specific allele model to maximize crossbred performance through purebred selection.     

Population Genetic Studies Revealed Local Adaptation in a High Gene-Flow Marine Fish,the Small Yellow Croaker (Larimichthys polyactis)

The genetic differentiation of many marine fish species is low. Yet local adaptation may be common in marine fish species as the vast and changing marine environment provides more chances for natural selection. Here, we used anonymous as well as known protein gene linked microsatellites and mitochondrial DNA to detect the population structure of the small yellow croaker (Larimichthys polyactis) in the Northwest Pacific marginal seas. Among these loci, we detected at least two microsatellites, anonymous H16 and HSP27 to be clearly under diversifying selection in outlier tests. Sequence cloning and analysis revealed that H16 was located in the intron of BAHCC1 gene. Landscape genetic analysis showed that H16 mutations were significantly associated with temperature, which further supported the diversifying selection at this locus. These marker types presented different patterns of population structure: (i) mitochondrial DNA phylogeny showed no evidence of genetic divergence and demonstrated only one glacial linage; (ii) population differentiation using putatively neutral microsatellites presented a pattern of high gene flow in the L. polyactis. In addition, several genetic barriers were identified; (iii) the population differentiation pattern revealed by loci under diversifying selection was rather different from that revealed by putatively neutral loci. The results above suggest local adaptation in the small yellow croaker. In summary, population genetic studies based on different marker types disentangle the effects of demographic history, migration, genetic drift and local adaptation on population structure and also provide valuable new insights for the design of management strategies in L. polyactis.