Population models of genomic imprinting. I. Differential viability in the sexes and the analogy with genetic dominance

Population-genetic models of sex-limited genomic imprinting

Genomic imprinting is a form of epigenetic modification involving parent-of-origin-dependent gene expression, usually the inactivation of one gene copy in some tissues, at least, for some part of the diploid life cycle. Occurring at a number of loci in mammals and flowering plants, this mode of non-Mendelian expression can be viewed more generally as parentally-specific differential gene expression. The effects of natural selection on genetic variation at imprinted loci have previously been examined in a several population-genetic models. Here we expand the existing one-locus, two-allele population-genetic models of viability selection with genomic imprinting to include sex-limited imprinting, i.e., imprinted expression occurring only in one sex, and differential viability between the sexes. We first consider models of complete inactivation of either parental allele and these models are subsequently generalized to incorporate differential expression. Stable polymorphic equilibrium was possible without heterozygote advantage as observed in some prior models of imprinting in both sexes. In contrast to these latter models, in the sex-limited case it was critical whether the paternally inherited or maternally inherited allele was inactivated. The parental origin of inactivated alleles had a different impact on how the population responded to the different selection pressures between the sexes. Under the same fitness parameters, imprinting in the other sex altered the number of possible equilibrium states and their stability. When the parental origin of imprinted alleles and the sex in which they are inactive differ, an allele cannot be inactivated in consecutive generations. The system dynamics became more complex with more equilibrium points emerging. Our results show that selection can interact with epigenetic factors to maintain genetic variation in previously unanticipated ways.

Genomic imprinting leads to less selectively maintained polymorphism on X chromosomes

Population-genetic models are developed to investigate the consequences of viability selection at a diallelic X-linked locus subject to genomic imprinting. Under complete paternal-X inactivation, a stable polymorphism is possible under the same conditions as for paternal-autosome inactivation with differential selection on males and females. A necessary but not sufficient condition is that there is sexual conflict, with selection acting in opposite directions in males and females. In contrast, models of complete maternal-X inactivation never admit a stable polymorphism and alleles will either be fixed or lost from the population. Models of complete paternal-X inactivation are more complex than corresponding models of maternal-X inactivation, as inactivation of paternally derived X chromosomes in females screens these chromosomes from selection for a generation. We also demonstrate that polymorphism is possible for incomplete X inactivation, but that the parameter conditions are more restrictive than for complete paternal-X inactivation. Finally, we investigate the effects of recurrent mutation in our models and show that deleterious alleles in mutation-selection balance at imprinted X-linked loci are at frequencies rather similar to those with corresponding selection pressures and mutation rates at unimprinted loci. Overall, our results add to the reasons for expecting less selectively maintained allelic variation on X chromosomes.

One- and two-locus population models with differential viability between sexes: parallels between haploid parental selection and genomic imprinting

A model of genomic imprinting with complete inactivation of the imprinted allele is shown to be formally equivalent to the haploid model of parental selection. When single-locus dynamics are considered, an internal equilibrium is possible only if selection acts in the opposite directions in males and females. I study a two-locus version of the latter model, in which maternal and paternal effects are attributed to the single alleles at two different loci. A necessary condition for the allele frequency equilibria to remain on the linkage equilibrium surface is the multiplicative interaction between maternal and paternal fitness parameters. In this case the equilibrium dynamics are independent at both loci and results from the single-locus model apply. When fitness parameters are additive, analytic treatment was not possible but numerical simulations revealed that stable polymorphism characterized by association between loci is possible only in several special cases in which maternal and paternal fitness contributions are precisely balanced. As in the single-locus case, antagonistic selection in males and females is a necessary condition for the maintenance of polymorphism. I also show that the above two-locus results of the parental selection model are very sensitive to the inclusion of weak directional selection on the individual's own genotypes.

Genetic and environmental contributions to body mass index: comparative analysis of monozygotic twins, dizygotic twins and same-age unrelated siblings

BACKGROUND

Earlier studies have established that a substantial percentage of variance in obesity-related phenotypes is explained by genetic components. However, only one study has used both virtual twins (VTs) and biological twins and was able to simultaneously estimate additive genetic, non-additive genetic, shared environmental and unshared environmental components in body mass index (BMI). Our current goal was to re-estimate four components of variance in BMI, applying a more rigorous model to biological and virtual multiples with additional data. Virtual multiples share the same family environment, offering unique opportunities to estimate common environmental influence on phenotypes that cannot be separated from the non-additive genetic component using only biological multiples.

METHODS

Data included 929 individuals from 164 monozygotic twin pairs, 156 dizygotic twin pairs, five triplet sets, one quadruplet set, 128 VT pairs, two virtual triplet sets and two virtual quadruplet sets. Virtual multiples consist of one biological child (or twins or triplets) plus one same-aged adoptee who are all raised together since infancy. We estimated the additive genetic, non-additive genetic, shared environmental and unshared random components in BMI using a linear mixed model. The analysis was adjusted for age, age(2), age(3), height, height(2), height(3), gender and race.

RESULTS

Both non-additive genetic and common environmental contributions were significant in our model (P-values<0.0001). No significant additive genetic contribution was found. In all, 63.6% (95% confidence interval (CI) 51.8-75.3%) of the total variance of BMI was explained by a non-additive genetic component, 25.7% (95% CI 13.8-37.5%) by a common environmental component and the remaining 10.7% by an unshared component.

CONCLUSION

Our results suggest that genetic components play an essential role in BMI and that common environmental factors such as diet or exercise also affect BMI. This conclusion is consistent with our earlier study using a smaller sample and shows the utility of virtual multiples for separating non-additive genetic variance from common environmental variance.

Effects of genomic imprinting on quantitative traits

Standard Mendelian genetic processes incorporate several symmetries, one of which is that the level of expression of a gene inherited from an organism's mother is identical to the level should that gene have been inherited paternally. For a small number of loci in a variety of taxa, this symmetry does not hold; such genes are said to be "genomically imprinted" (or simply "imprinted"). The best known examples of imprinted loci come from mammals and angiosperms, although there are also cases from several insects and some data suggesting that imprinting exists in zebra fish. Imprinting means that reciprocal heterozygotes need not be, on average, phenotypically identical. When this difference is incorporated into the standard quantitative-genetic model for two alleles at a single locus, a number of standard expressions are altered in fundamental ways. Most importantly, in contrast to the case with euMendelian expression, the additive and dominance deviations are correlated. It would clearly be of interest to be able to separate imprinting effects from maternal genetic effects, but when the latter are added to the model, the well-known generalized least-squares approach to deriving breeding values cannot be applied. Distinguishing these two types of parent-of-origin effects is not a simple problem and requires further research.

Reciprocally imprinted genes and the response to selection on one sex

We explore the theoretical consequences of limiting selection to males for the evolution of imprinted genes. We find that the efficiency of male-limited selection depends on the pattern of imprinting at an imprinted locus. When selection is strong, the maternally expressed pattern of imprinting allows faster genetic change than the reciprocal, paternally expressed pattern. When selection is relatively weak, the pattern of imprinting that permits a greater rate of genetic response to selection depends on the frequency of the favored allele: the paternally expressed pattern permits faster genetic change than does the maternally expressed pattern at low frequencies of a favored allele; at higher frequencies of a favored allele, however, the maternally expressed pattern is again more conducive to a genetic response. To our knowledge, this is the first theoretical description of a difference between the two reciprocal patterns of imprinting. The selective efficiency bias we identify between the two patterns of imprinting has implications for natural and livestock populations, which we discuss.

Sex: differences in mutation, recombination, selection, gene flow, and genetic drift

In many instances, there are large sex differences in mutation rates, recombination rates, selection, rates of gene flow, and genetic drift. Mutation rates are often higher in males, a difference that has been estimated both directly and indirectly. The higher male mutation rate appears related to the larger number of cell divisions in male lineages but mutation rates also appear gene- and organism-specific. When there is recombination in only one sex, it is always the homogametic sex. When there is recombination in both sexes, females often have higher recombination but there are many exceptions. There are a number of hypotheses to explain the sex differences in recombination. Sex-specific differences in selection may result in stable polymorphisms or for sex chromosomes, faster evolutionary change. In addition, sex-dependent selection may result in antagonistic pleiotropy or sexually antagonistic genes. There are many examples of sex-specific differences in gene flow (dispersal) and a number of adaptive explanations for these differences. The overall effective population size (genetic drift) is dominated by the lower sex-specific effective population size. The mean of the mutation, recombination, and gene flow rates over the two sexes can be used in a population genetics context unless there are sex-specific differences in selection or genetic drift. Sex-specific differences in these evolutionary factors appear to be unrelated to each other. The evolutionary explanations for sex-specific differences for each factor are multifaceted and, in addition, explanations may include chance, nonadaptive differences, or mechanistic, nonevolutionary factors.

Sex-specific viability, sex linkage and dominance in genomic imprinting

Genomic imprinting is a phenomenon by which the expression of an allele at a locus depends on the parent of origin. Two different two-locus evolutionary models are presented in which a second locus modifies the imprinting status of the primary locus, which is under differential selection in males and females. In the first model, a modifier allele that imprints the primary locus invades the population when the average dominance coefficient among females and males is >12 and selection is weak. The condition for invasion is always heavily contingent upon the extent of dominance. Imprinting is more likely in the sex experiencing weaker selection only under some parameter regimes, whereas imprinting by either sex is equally likely under other regimes. The second model shows that a modifier allele that induces imprinting will increase when imprinting has a direct selective advantage. The results are not qualitatively dependent on whether the modifier locus is autosomal or X linked.

Intralocus sexual conflict can drive the evolution of genomic imprinting

Genomic imprinting is a phenomenon whereby the expression of an allele differs depending upon its parent of origin. There is an increasing number of examples of this form of epigenetic inheritance across a wide range of taxa, and imprinting errors have also been implicated in several human diseases. Various hypotheses have been put forward to explain the evolution of genomic imprinting, but there is not yet a widely accepted general hypothesis for the variety of imprinting patterns observed. Here a new evolutionary hypothesis, based on intralocus sexual conflict, is proposed. This hypothesis provides a potential explanation for much of the currently available empirical data, and it also makes new predictions about patterns of genomic imprinting that are expected to evolve but that have not, as of yet, been looked for in nature. This theory also provides a potential mechanism for the resolution of intralocus sexual conflict in sexually selected traits and a novel pathway for the evolution of sexual dimorphism.

The correlation between relatives on the supposition of genomic imprinting

Standard genetic analyses assume that reciprocal heterozygotes are, on average, phenotypically identical. If a locus is subject to genomic imprinting, however, this assumption does not hold. We incorporate imprinting into the standard quantitative-genetic model for two alleles at a single locus, deriving expressions for the additive and dominance components of genetic variance, as well as measures of resemblance among relatives. We show that, in contrast to the case with Mendelian expression, the additive and dominance deviations are correlated. In principle, this correlation allows imprinting to be detected solely on the basis of different measures of familial resemblances, but in practice, the standard error of the estimate is likely to be too large for a test to have much statistical power. The effects of genomic imprinting will need to be incorporated into quantitative-genetic models of many traits, for example, those concerned with mammalian birthweight.

The evolution of X-linked genomic imprinting

We develop a quantitative genetic model to investigate the evolution of X-imprinting. The model compares two forces that select for X-imprinting: genomic conflict caused by polygamy and sex-specific selection. Genomic conflict can only explain small reductions in maternal X gene expression and cannot explain silencing of the maternal X. In contrast, sex-specific selection can cause extreme differences in gene expression, in either direction (lowered maternal or paternal gene expression), even to the point of gene silencing of either the maternal or paternal copy. These conclusions assume that the Y chromosome lacks genetic activity. The presence of an active Y homologue makes imprinting resemble the autosomal pattern, with active paternal alleles (X- and Y-linked) and silenced maternal alleles. This outcome is likely to be restricted as Y-linked alleles are subject to the accumulation of deleterious mutations. Experimental evidence concerning X-imprinting in mouse and human is interpreted in the light of these predictions and is shown to be far more easily explained by sex-specific selection.

Population genetics and evolution of genomic imprinting

At a small number of mammalian loci, only one of the two copies of a gene is expressed. Just which copy is expressed depends on the sex of the parent from which that copy was inherited. Such genes are said to be imprinted. The functional haploidy implied by imprinting has a number of population genetic consequences. Moreover, since diploidy is widely believed to be advantageous, the evolution of this non-Mendelian form of expression requires an explanation. Here I examine some of the theoretical and mathematical models investigating these two aspects of imprinting. For instance, the dynamics and equilibrium properties of many models of natural selection at imprinted loci are formally equivalent to models without imprinting. And different approaches to modeling the problem of the evolution of imprinting reveal the weakness of several of the apparent predictions of various verbal hypotheses about why imprinting has evolved.