Effect of heterogeneity in recombination rate on variation in realised relationship.

Individuals of a specified pedigree relationship vary in the proportion of the genome they share identical by descent, i.e. in their realised or actual relationship. Predictions of the variance in realised relationship have previously been based solely on the proportion of the map length shared, which requires the implicit assumption that both recombination rate and genetic information are uniformly distributed along the genome. This ignores the possible existence of recombination hotspots, and fails to distinguish between coding and non-coding sequences. In this paper, we therefore quantify the effects of heterogeneity in recombination rate at broad and fine-scale levels on the variation in realised relationship. Variance is usually greater on a chromosome with a non-uniform recombination rate than on a chromosome with the same map length and uniform recombination rate, especially if recombination rates are higher towards chromosome ends. Reductions in variance can also be obtained, however, and the overall pattern of change is quite complex. In general, local (fine-scale) variation in recombination rate, e.g. hotspots, has a small influence on the variance in realised relationship. Differences in rates across longer regions and between chromosome ends can increase or decrease the variance in a realised relationship, depending on the genomic architecture.

Dominance genetic variation contributes little to the missing heritability for human complex traits.

For human complex traits, non-additive genetic variation has been invoked to explain "missing heritability," but its discovery is often neglected in genome-wide association studies. Here we propose a method of using SNP data to partition and estimate the proportion of phenotypic variance attributed to additive and dominance genetic variation at all SNPs (hSNP(2) and δSNP(2)) in unrelated individuals based on an orthogonal model where the estimate of hSNP(2) is independent of that of δSNP(2). With this method, we analyzed 79 quantitative traits in 6,715 unrelated European Americans. The estimate of δSNP(2) averaged across all the 79 quantitative traits was 0.03, approximately a fifth of that for additive variation (average hSNP(2) = 0.15). There were a few traits that showed substantial estimates of δSNP(2), none of which were replicated in a larger sample of 11,965 individuals. We further performed genome-wide association analyses of the 79 quantitative traits and detected SNPs with genome-wide significant dominance effects only at the ABO locus for factor VIII and von Willebrand factor. All these results suggest that dominance variation at common SNPs explains only a small fraction of phenotypic variation for human complex traits and contributes little to the missing narrow-sense heritability problem.

Limits to sustained energy intake. XXII. Reproductive performance of two selected mouse lines with different thermal conductance.

Maximal sustained energy intake (SusEI) appears limited, but the factors imposing the limit are disputed. We studied reproductive performance in two lines of mice selected for high and low food intake (MH and ML, respectively), and known to have large differences in thermal conductance (29% higher in the MH line at 21°C). When these mice raised their natural litters, their metabolisable energy intake significantly increased over the first 13 days of lactation and then reached a plateau. At peak lactation, MH mice assimilated on average 45.3% more energy than ML mice (222.9±7.1 and 153.4±12.5 kJ day(-1), N=49 and 24, respectively). Moreover, MH mice exported on average 62.3 kJ day(-1) more energy as milk than ML mice (118.9±5.3 and 56.6±5.4 kJ day(-1), N=subset of 32 and 21, respectively). The elevated milk production of MH mice enabled them to wean litters (65.2±2.1 g) that were on average 50.2% heavier than litters produced by ML mothers (43.4±3.0 g), and pups that were on average 27.2% heavier (9.9±0.2 and 7.8±0.2 g, respectively). Lactating mice in both lines had significantly longer and heavier guts compared with non-reproductive mice. However, inconsistent with the 'central limit hypothesis', the ML mice had significantly longer and heavier intestines than MH mice. An experiment where the mice raised litters of the opposing line demonstrated that lactation performance was not limited by the growth capacity of offspring. Our findings are consistent with the idea that the SusEI at peak lactation is constrained by the capacity of the mothers to dissipate body heat.

Heritability in the genomics era--concepts and misconceptions.

Heritability allows a comparison of the relative importance of genes and environment to the variation of traits within and across populations. The concept of heritability and its definition as an estimable, dimensionless population parameter was introduced by Sewall Wright and Ronald Fisher nearly a century ago. Despite continuous misunderstandings and controversies over its use and application, heritability remains key to the response to selection in evolutionary biology and agriculture, and to the prediction of disease risk in medicine. Recent reports of substantial heritability for gene expression and new estimation methods using marker data highlight the relevance of heritability in the genomics era.

On estimation of genetic variance within families using genome-wide identity-by-descent sharing.

BACKGROUND: Traditionally, heritability and other genetic parameters are estimated from between-family variation. With the advent of dense genotyping, it is now possible to compute the proportion of the genome that is shared by pairs of sibs and thus undertake the estimation within families, thereby avoiding environmental covariances of family members. Formulae for the sampling variance of estimates have been derived previously for families with two sibs, which are relevant for humans, but sampling errors are large. In livestock and plants much larger families can be obtained, and simulation has shown sampling variances are then much smaller. METHODS: Based on the assumptions that realised relationship of sibs can be obtained from genomic data and that data are analyzed by restricted maximum likelihood, formulae were derived for the sampling variance of the estimates of genetic variance for arbitrary family sizes. The analysis used statistical differentiation, assuming the variance of relationships is small. RESULTS: The variance of the estimate of the additive genetic variance was approximately proportional to 1/ (fn2σR2), for f families of size n and variance of relationships σR2. CONCLUSIONS: Because the standard error of the estimate of heritability decreased in proportion to family size, the use of within-family information becomes increasingly efficient as the family size increases. There are however, limitations, such as near complete confounding of additive and dominance variances in full sib families.

The limits of individual identification from sample allele frequencies: theory and statistical analysis.

It was shown recently using experimental data that it is possible under certain conditions to determine whether a person with known genotypes at a number of markers was part of a sample from which only allele frequencies are known. Using population genetic and statistical theory, we show that the power of such identification is, approximately, proportional to the number of independent SNPs divided by the size of the sample from which the allele frequencies are available. We quantify the limits of identification and propose likelihood and regression analysis methods for the analysis of data. We show that these methods have similar statistical properties and have more desirable properties, in terms of type-I error rate and statistical power, than test statistics suggested in the literature.

Data and theory point to mainly additive genetic variance for complex traits.

The relative proportion of additive and non-additive variation for complex traits is important in evolutionary biology, medicine, and agriculture. We address a long-standing controversy and paradox about the contribution of non-additive genetic variation, namely that knowledge about biological pathways and gene networks imply that epistasis is important. Yet empirical data across a range of traits and species imply that most genetic variance is additive. We evaluate the evidence from empirical studies of genetic variance components and find that additive variance typically accounts for over half, and often close to 100%, of the total genetic variance. We present new theoretical results, based upon the distribution of allele frequencies under neutral and other population genetic models, that show why this is the case even if there are non-additive effects at the level of gene action. We conclude that interactions at the level of genes are not likely to generate much interaction at the level of variance.

Change and maintenance of variation in quantitative traits in the context of the Price equation.

The Price equation is a general description of evolutionary change in any character from one generation to the next due to natural selection and other forces such as mutation and recombination. Recently it has been widely utilised in many fields including quantitative genetics, but these applications have focused mainly on the response to selection in the mean of characters. Many different and, in some cases, conflicting models have been investigated by quantitative geneticists to examine the change and maintenance of both genetic and environmental variance of quantitative traits under selection and other forces. In this study, we use the Price equation to derive many such well-known results for the dynamics and equilibria of variances in a straightforward way and to develop them further.

Genetic analysis of environmental variation.

Environmental variation (VE) in a quantitative trait - variation in phenotype that cannot be explained by genetic variation or identifiable genetic differences - can be regarded as being under some degree of genetic control. Such variation may be either between repeated expressions of the same trait within individuals (e.g. for bilateral traits), in the phenotype of different individuals, where variation within families may differ, or in both components. We consider alternative models for defining the distribution of phenotypes to include a component due to heterogeneity of VE. We review evidence for the presence of genetic variation in VE and estimates of its magnitude. Typically the heritability of VE is under 10%, but its genetic coefficient of variation is typically 20% or more. We consider experimental designs appropriate for estimating genetic variance in VE and review alternative methods of estimation. We consider the effects of stabilizing and directional selection on VE and review both the forces that might be maintaining levels of VE and heritability found in populations. We also evaluate the opportunities for reducing VE in breeding programmes. Although empirical and theoretical studies have increased our understanding of genetic control of environmental variance, many issues remain unresolved.

The anomalous effects of biased mutation revisited: mean-optimum deviation and apparent directional selection under stabilizing selection.

Empirical evidence indicates that the distribution of the effects of mutations on quantitative traits is not symmetric about zero. Under stabilizing selection in infinite populations with normally distributed mutant effects having a nonzero mean, Waxman and Peck showed that the deviation of the population mean from the optimum is expected to be small. We show by simulation that genetic drift, leptokurtosis of mutational effects, and pleiotropy can increase the mean-optimum deviation greatly, however, and that the apparent directional selection thereby caused can be substantial.

Inheritance of fertility in broiler chickens.

BACKGROUND: The fertility of a chicken's egg is a trait which depends on both the hen that lays the egg and on her mate. It is also known that fertility of an individual changes over the laying period. METHODS: Longitudinal models including both random genetic and permanent environmental effects of both the female and her male mate were used to model the proportion of fertile eggs in a pedigree broiler population over the ages 29-54 weeks. RESULTS: Both the male and the female contribute to variation in fertility. Estimates of heritability of weekly records were typically 7% for female and 10% for male contributions to fertility. Repeatability estimates ranged from 24 to 33%, respectively. The estimated genetic variance remained almost constant for both sexes over the laying period and the genetic correlations between different ages were close to 1.0. The permanent environment components increased substantially towards the end of the analyzed period, and correlations between permanent environment effects at different ages declined with increasing age difference The heritability of mean fertility over the whole laying period was estimated at 13% for females and 17% for males. A small positive correlation between genetic effects for male and female fertility was found. CONCLUSION: Opportunities to improve fertility in broiler stocks by selection on both sexes exist and should have an impact throughout the laying period.

Publisher Correction: Selective effects of heterozygous protein-truncating variants.

In the version of this article initially published, reference 10 incorrectly cited Seplyarskiy, V. B. et al. Weghorn, D. et al. is the correct reference. The error has been corrected in the HTML and PDF version of the article.

Mutation-selection balance for environmental variance.

The role of mutation-selection balance in maintaining environmental variance (V(E)) of quantitative traits is investigated under the assumption that genotypes differ in the magnitude of phenotypic variance, given genotypic value. Thus, V(E) can be regarded as a quantitative trait. As stabilizing selection on phenotype favors genotypes contributing low V(E), mutations that decrease V(E) are more likely to become fixed than those that increase it, and therefore V(E) should decline. If, however, essentially all mutants increase V(E) and overall selection is sufficiently strong that no mutants become fixed, then V(E) can be maintained. The heritability of the trait is determined by the relative sizes of mutational effects on phenotypic mean and residual variance and is independent of mutation rate and pleiotropic effects. This conclusion is not robust for small populations because some mutants may become fixed, which indicates that other selective forces must be involved, such as an intrinsic cost of homogeneity.

Prediction of multilocus identity-by-descent.

Previous studies have enabled exact prediction of probabilities of identity-by-descent (IBD) in random-mating populations for a few loci (up to four or so), with extension to more using approximate regression methods. Here we present a precise predictor of multiple-locus IBD using simple formulas based on exact results for two loci. In particular, the probability of non-IBD X(ABC) at each of ordered loci A, B, and C can be well approximated by X(ABC) = X(AB)X(BC)/X(B) and generalizes to X(123...k) = X(12)X(23...)X(k)(-1,k)/X(k-2), where X is the probability of non-IBD at each locus. Predictions from this chain rule are very precise with population bottlenecks and migration, but are rather poorer in the presence of mutation. From these coefficients, the probabilities of multilocus IBD and non-IBD can also be computed for genomic regions as functions of population size, time, and map distances. An approximate but simple recurrence formula is also developed, which generally is less accurate than the chain rule but is more robust with mutation. Used together with the chain rule it leads to explicit equations for non-IBD in a region. The results can be applied to detection of quantitative trait loci (QTL) by computing the probability of IBD at candidate loci in terms of identity-by-state at neighboring markers.

Genetic variation and quantitative trait loci associated with developmental stability and the environmental correlation between traits in maize.

There is limited experimental information about the genetic basis of micro-environmental variance (V(E)) (developmental stability) and environmental correlations. This study, by using a population of maize recombinant inbred lines (RIL) and simple sequence repeat (SSR) polymorphic markers, aims at the following: firstly, to quantify the genetic component of the V(E) or developmental stability for four traits in maize and the environmental correlation between these traits, and secondly, to identify quantitative trait loci (QTLs) that influence these quantities. We found that, when estimating variances and correlations and testing their homogeneity, estimates and tests are needed that are not highly dependent on normality assumptions. There was significant variation among the RILs in V(E) and in the environmental correlation for some of the traits, implying genetic heterogeneity in the V(E) and environmental correlations. The genetic coefficient of variation of the environmental variance (GCV(V(E))) was estimated to be 20%, which is lower than estimates obtained for other species. A few genomic regions involved in the stability of one trait or two traits were detected, and these did not have an important influence on the mean of the trait. One region that could be associated with the environmental correlations between traits was also detected.

One Hundred Years of Linkage Disequilibrium.

One hundred years ago, the first population genetic calculations were made for two loci. They indicated that populations should settle down to a state where the frequency of an allele at one locus is independent of the frequency of an allele at a second locus, even if these loci are linked. Fifty years later it was realized what is obvious in retrospect, that these calculations ignored the effect of chance segregation of linked loci, an effect now widely recognized following the association of closely linked markers (SNPs) with rare genetic diseases. Linkage disequilibrium is now accepted as the norm for closely linked loci, leading to powerful applications in the mapping of disease alleles and quantitative trait loci, in the detection of sites of selection in the human genome, in the application of genomic prediction of quantitative traits in animal and plant breeding, in the estimation of population size, and in the dating of population divergence.

Competition can maintain genetic but not environmental variance in the presence of stabilizing selection.

A population in which there is stabilizing selection acting on quantitative traits toward an intermediate optimum becomes monomorphic in the absence of mutation. Further, genotypes that show least environmental variation are also favored, such that selection is likely to reduce both genetic and environmental components of phenotypic variance. In contrast, intraspecific competition for resources is more severe between phenotypically similar individuals, such that those deviating from prevailing phenotypes have a selective advantage. It has been shown previously that polymorphism and phenotypic variance can be maintained if competition between individuals is "effectively" stronger than stabilizing selection. Environmental variance is generally observed in quantitative traits, so mechanisms to explain its maintenance are sought, but the impact of competition on its magnitude has not previously been studied. Here we assume that a quantitative trait is subject to selection for an optimal value and to selection due to competition. Further, we assume that both the mean and variance of the phenotypic value depend on genotype, such that both may be affected by selection. Theoretical analysis and numerical simulations reveal that environmental variance can be maintained only when the genetic variance (in mean phenotypic value) is constrained to a very low level. Environmental variance will be replaced entirely by genotypic variance if a range of genotypes that vary widely in mean phenotype are present or become so by mutation. The distribution of mean phenotypic values is discrete when competition is strong relative to stabilizing selection; but more genotypes segregate and the distribution can approach continuity as competition becomes extremely strong. If the magnitude of the environmental variance is not under genetic control, there is a complementary relationship between the levels of environmental and genetic variance such that the level of phenotypic variance is little affected.