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.

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.

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.

Oxidative costs of reproduction in mouse strains selected for different levels of food intake and which differ in reproductive performance.

Oxidative damage caused by reactive oxygen species has been hypothesised to underpin the trade-off between reproduction and somatic maintenance, i.e., the life-history-oxidative stress theory. Previous tests of this hypothesis have proved equivocal, and it has been suggested that the variation in responses may be related to the tissues measured. Here, we measured oxidative damage (protein carbonyls, 8-OHdG) and antioxidant protection (enzymatic antioxidant activity and serum antioxidant capacity) in multiple tissues of reproductive (R) and non-reproductive (N) mice from two mouse strains selectively bred for high (H) or low (L) food intake, which differ in their reproductive performance, i.e., H mice have increased milk energy output (MEO) and wean larger pups. Levels of oxidative damage were unchanged (liver) or reduced (brain and serum) in R versus N mice, and no differences in multiple measures of oxidative protection were found between H and L mice in liver (except for Glutathione Peroxidase), brain or mammary glands. Also, there were no associations between an individual's energetic investment (e.g., MEO) and most of the oxidative stress measures detected in various tissues. These data are inconsistent with the oxidative stress theory, but were more supportive of, but not completely consistent, with the 'oxidative shielding' hypothesis.

Is Continued Genetic Improvement of Livestock Sustainable?

Large genetic improvements in the quantitative traits of growth, production, and efficiency of farmed livestock have been made over recent decades, and by introduction of genomic technology these are being enhanced. Such continued improvement requires that there be available variation to utilize. The evidence is that little variation has been lost and such rates are indeed sustainable in the future.

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.

Heritable environmental variance causes nonlinear relationships between traits: application to birth weight and stillbirth of pigs.

There is recent evidence from laboratory experiments and analysis of livestock populations that not only the phenotype itself, but also its environmental variance, is under genetic control. Little is known about the relationships between the environmental variance of one trait and mean levels of other traits, however. A genetic covariance between these is expected to lead to nonlinearity between them, for example between birth weight and survival of piglets, where animals of extreme weights have lower survival. The objectives were to derive this nonlinear relationship analytically using multiple regression and apply it to data on piglet birth weight and survival. This study provides a framework to study such nonlinear relationships caused by genetic covariance of environmental variance of one trait and the mean of the other. It is shown that positions of phenotypic and genetic optima may differ and that genetic relationships are likely to be more curvilinear than phenotypic relationships, dependent mainly on the environmental correlation between these traits. Genetic correlations may change if the population means change relative to the optimal phenotypes. Data of piglet birth weight and survival show that the presence of nonlinearity can be partly explained by the genetic covariance between environmental variance of birth weight and survival. The framework developed can be used to assess effects of artificial and natural selection on means and variances of traits and the statistical method presented can be used to estimate trade-offs between environmental variance of one trait and mean levels of others.

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.

Influence of gene interaction on complex trait variation with multilocus models.

Although research effort is being expended into determining the importance of epistasis and epistatic variance for complex traits, there is considerable controversy about their importance. Here we undertake an analysis for quantitative traits utilizing a range of multilocus quantitative genetic models and gene frequency distributions, focusing on the potential magnitude of the epistatic variance. All the epistatic terms involving a particular locus appear in its average effect, with the number of two-locus interaction terms increasing in proportion to the square of the number of loci and that of third order as the cube and so on. Hence multilocus epistasis makes substantial contributions to the additive variance and does not, per se, lead to large increases in the nonadditive part of the genotypic variance. Even though this proportion can be high where epistasis is antagonistic to direct effects, it reduces with multiple loci. As the magnitude of the epistatic variance depends critically on the heterozygosity, for models where frequencies are widely dispersed, such as for selectively neutral mutations, contributions of epistatic variance are always small. Epistasis may be important in understanding the genetic architecture, for example, of function or human disease, but that does not imply that loci exhibiting it will contribute much genetic variance. Overall we conclude that theoretical predictions and experimental observations of low amounts of epistatic variance in outbred populations are concordant. It is not a likely source of missing heritability, for example, or major influence on predictions of rates of evolution.

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.

Applications of population genetics to animal breeding, from wright, fisher and lush to genomic prediction.

Although animal breeding was practiced long before the science of genetics and the relevant disciplines of population and quantitative genetics were known, breeding programs have mainly relied on simply selecting and mating the best individuals on their own or relatives' performance. This is based on sound quantitative genetic principles, developed and expounded by Lush, who attributed much of his understanding to Wright, and formalized in Fisher's infinitesimal model. Analysis at the level of individual loci and gene frequency distributions has had relatively little impact. Now with access to genomic data, a revolution in which molecular information is being used to enhance response with "genomic selection" is occurring. The predictions of breeding value still utilize multiple loci throughout the genome and, indeed, are largely compatible with additive and specifically infinitesimal model assumptions. I discuss some of the history and genetic issues as applied to the science of livestock improvement, which has had and continues to have major spin-offs into ideas and applications in other areas.

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.

Assumptions and properties of limiting pathway models for analysis of epistasis in complex traits.

For most complex traits, results from genome-wide association studies show that the proportion of the phenotypic variance attributable to the additive effects of individual SNPs, that is, the heritability explained by the SNPs, is substantially less than the estimate of heritability obtained by standard methods using correlations between relatives. This difference has been called the "missing heritability". One explanation is that heritability estimates from family (including twin) studies are biased upwards. Zuk et al. revisited overestimation of narrow sense heritability from twin studies as a result of confounding with non-additive genetic variance. They propose a limiting pathway (LP) model that generates significant epistatic variation and its simple parametrization provides a convenient way to explore implications of epistasis. They conclude that over-estimation of narrow sense heritability from family data ('phantom heritability') may explain an important proportion of missing heritability. We show that for highly heritable quantitative traits large phantom heritability estimates from twin studies are possible only if a large contribution of common environment is assumed. The LP model is underpinned by strong assumptions that are unlikely to hold, including that all contributing pathways have the same mean and variance and are uncorrelated. Here, we relax the assumptions that underlie the LP model to be more biologically plausible. Together with theoretical, empirical, and pragmatic arguments we conclude that in outbred populations the contribution of additive genetic variance is likely to be much more important than the contribution of non-additive variance.

Identification of pedigree relationship from genome sharing.

Determination of degree of relationship traditionally has been undertaken using genotypic data on individual loci, typically assumed to be independent. With dense marker data as now available, it is possible to identify the regions of the genome shared identical by descent (ibd). This information can be used to determine pedigree relationship (R), e.g., cousins vs. second cousins, and also to distinguish pedigrees that have the same Wright's relationship (R) such as half-sibs and uncle-nephew. We use simulation to investigate the accuracy with which pedigree relationship can be inferred from genome sharing for uniparental relatives (a common ancestor on only one side of their pedigree), specifically the number, position (whether at chromosome ends), and length of shared regions ibd on each chromosome. Moments of the distribution of the likelihood ratio (including its expectation, the Kullback-Leibler distance) for alternative relationships are estimated for model human genomes, with the ratio of the mean to the SD of the likelihood ratio providing a useful reference point. Two relationships differing in R can be readily distinguished provided at least one has high R, e.g., approximately 98.5% correct assignment of cousins and half-cousins, but only approximately 75% for second cousins once removed and third cousins. Two relationships with the same R can be distinguished only if R is high, e.g., half-sibs and uncle-nephew, with probability of correct assignment being approximately 5/6.

Quantitative genetics in the genomics era.

The genetic analysis of quantitative or complex traits has been based mainly on statistical quantities such as genetic variances and heritability. These analyses continue to be developed, for example in studies of natural populations. Genomic methods are having an impact on progress and prospects. Actual relationships of individuals can be estimated enabling novel quantitative analyses. Increasing precision of linkage mapping is feasible with dense marker panels and designed stocks allowing multiple generations of recombination, and large SNP panels enable the use of genome wide association analysis utilising historical recombination. Whilst such analyses are identifying many loci for disease genes and traits such as height, typically each individually contributes a small amount of the variation. Only by fitting all SNPs without regard to significance can a high proportion be accounted for, so a classical polygenic model with near infinitesimally small effects remains a useful one. Theory indicates that a high proportion of variants will have low minor allele frequency, making detection difficult. Genomic selection, based on simultaneously fitting very dense markers and incorporating these with phenotypic data in breeding value prediction is revolutionising breeding programmes in agriculture and has a major potential role in human disease prediction.

On the pleiotropic structure of the genotype-phenotype map and the evolvability of complex organisms.

Analyses of effects of mutants on many traits have enabled estimates to be obtained of the magnitude of pleiotropy, and in reviews of such data others have concluded that the degree of pleiotropy is highly restricted, with implications on the evolvability of complex organisms. We show that these conclusions are highly dependent on statistical assumptions, for example significance levels. We analyze models with pleiotropic effects on all traits at all loci but by variable amounts, considering distributions of numbers of traits declared significant, overall pleiotropic effects, and extent of apparent modularity of effects. We demonstrate that these highly pleiotropic models can give results similar to those obtained in analyses of experimental data and that conclusions on limits to evolvability through pleiotropy are not robust.