Using mating designs to uncover QTL and the genetic architecture of complex traits

Analysis of quantitative trait loci (QTL) affecting complex traits is often pursued in single-cross experiments. For most purposes, including breeding, some assessment is desired of the generalizability of the QTL findings and of the overall genetic architecture of the trait. Single-cross experiments provide a poor basis for these purposes, as comparison across experiments is hampered by segregation of different allelic combinations among different parents and by context-dependent effects of QTL. To overcome this problem, we combined the benefits of QTL analysis (to identify genomic regions affecting trait variation) and classic diallel analysis (to obtain insight into the general inheritance of the trait) by analyzing multiple mapping families that are connected via shared parents. We first provide a theoretical derivation of main (general combining ability (GCA)) and interaction (specific combining ability (SCA)) effects on F(2) family means relative to variance components in a randomly mating reference population. Then, using computer simulations to generate F(2) families derived from 10 inbred parents in different partial-diallel designs, we show that QTL can be detected and that the residual among-family variance can be analyzed. Standard diallel analysis methods are applied in order to reveal the presence and mode of action (in terms of GCA and SCA) of undetected polygenes. Given a fixed experiment size (total number of individuals), we demonstrate that QTL detection and estimation of the genetic architecture of polygenic effects are competing goals, which should be explicitly accounted for in the experimental design. Our approach provides a general strategy for exploring the genetic architecture, as well as the QTL underlying variation in quantitative traits.     

Mapping genetic loci that interact with myostatin to affect growth traits

Myostatin, or GDF8, is an inhibitor of skeletal muscle growth. A non-functional myostatin mutation leads to a double muscling phenotype in some species, for example, mice, cattle and humans. Previous studies have indicated that there are loci in the genome that interact with myostatin to control backfat depth and other complex traits. We now report a quantitative trait loci (QTL) mapping study designed to identify loci that interact with myostatin to impact growth traits in mice. Body weight and average daily gain traits were collected on F2 progeny derived from a myostatin-null C57BL/6 strain by M16i cross. In all, 44 main effect QTL were detected above a 5% genome-wide significance threshold when an interval mapping method was used. An additional 37 QTL were identified to significantly interact with myostatin, sex or reciprocal cross. A total of 12 of these QTL interacted with myostatin genotype. These results provide a foundation for the further fine mapping of genome regions that harbor loci that interact with myostatin.     

Generalized character process models: estimating the genetic basis of traits that cannot be observed and that change with age or environmental conditions

The genetic analysis of characters that change as a function of some independent and continuous variable has received increasing attention in the biological and statistical literature. Previous work in this area has focused on the analysis of normally distributed characters that are directly observed. We propose a framework for the development and specification of models for a quantitative genetic analysis of function-valued characters that are not directly observed, such as genetic variation in age-specific mortality rates or complex threshold characters. We employ a hybrid Markov chain Monte Carlo algorithm involving a Monte Carlo EM algorithm coupled with a Markov chain approximation to the likelihood, which is quite robust and provides accurate estimates of the parameters in our models. The methods are investigated using simulated data and are applied to a large data set measuring mortality rates in the fruit fly, Drosophila melanogaster.     

Non-linear recursive models for growth traits in the Pirenaica beef cattle breed

One of the main goals of selection schemes in beef cattle populations is to increase carcass weight at slaughter. Live weights at different growth stages are frequently used as selection criteria under the hypothesis that they usually have a high and positive genetic correlation with weight at slaughter. However, the presence of compensatory growth may bias the prediction ability of early weights for selection purposes. Recursive models may represent an interesting alternative for understanding the genetic and phenotypic relationship between weight traits during growth. For the purposes of this study, the analysis was performed for three different set of data from the Pirenaica beef cattle breed: weight at 120 days (W120) and at 210 days (W210); W120 and carcass weight at slaughter at 365 days (CW365); W210 and CW365. The number of records for each analysis was 8592, 4648 and 3234, respectively. A pedigree composed of 56323 individuals was also included. The statistical model comprised sex, year-season of birth, herd and slaughterhouse, plus a non-linear recursive dependency between traits. The dependency was modeled as a polynomial up to the 4th degree and models were compared using a Logarithm of Conditional Predictive Ordinates. The results of model comparison suggest that the best models were the 3rd degree polynomial for W120-W210 and W120-CW365 and the 2nd degree polynomial for W210-CW365. The posterior mean estimates for heritabilities ranged between 0.29 and 0.44 and the posterior mean estimates of the genetic correlations were null or very low, indicating that the relationship between traits is fully captured by the recursive dependency. The results imply that the predictive ability of the performance of future growth is low if it is only based on records of early weights. The usefulness of slaughterhouse records in beef cattle breeding evaluation is confirmed.     

Evaluating alternate models to estimate genetic parameters of calving traits in United Kingdom Holstein-Friesian dairy cattle

Background

The focus in dairy cattle breeding is gradually shifting from production to functional traits and genetic parameters of calving traits are estimated more frequently. However, across countries, various statistical models are used to estimate these parameters. This study evaluates different models for calving ease and stillbirth in United Kingdom Holstein-Friesian cattle.

Methods

Data from first and later parity records were used. Genetic parameters for calving ease, stillbirth and gestation length were estimated using the restricted maximum likelihood method, considering different models i.e. sire (−maternal grandsire), animal, univariate and bivariate models. Gestation length was fitted as a correlated indicator trait and, for all three traits, genetic correlations between first and later parities were estimated. Potential bias in estimates was avoided by acknowledging a possible environmental direct-maternal covariance. The total heritable variance was estimated for each trait to discuss its theoretical importance and practical value. Prediction error variances and accuracies were calculated to compare the models.

Results and discussion

On average, direct and maternal heritabilities for calving traits were low, except for direct gestation length. Calving ease in first parity had a significant and negative direct-maternal genetic correlation. Gestation length was maternally correlated to stillbirth in first parity and directly correlated to calving ease in later parities. Multi-trait models had a slightly greater predictive ability than univariate models, especially for the lowly heritable traits. The computation time needed for sire (−maternal grandsire) models was much smaller than for animal models with only small differences in accuracy. The sire (−maternal grandsire) model was robust when additional genetic components were estimated, while the equivalent animal model had difficulties reaching convergence.

Conclusions

For the evaluation of calving traits, multi-trait models show a slight advantage over univariate models. Extended sire models (−maternal grandsire) are more practical and robust than animal models. Estimated genetic parameters for calving traits of UK Holstein cattle are consistent with literature. Calculating an aggregate estimated breeding value including direct and maternal values should encourage breeders to consider both direct and maternal effects in selection decisions.     

Predicting complex traits using a diffusion kernel on genetic markers with an application to dairy cattle and wheat data

Background

Arguably, genotypes and phenotypes may be linked in functional forms that are not well addressed by the linear additive models that are standard in quantitative genetics. Therefore, developing statistical learning models for predicting phenotypic values from all available molecular information that are capable of capturing complex genetic network architectures is of great importance. Bayesian kernel ridge regression is a non-parametric prediction model proposed for this purpose. Its essence is to create a spatial distance-based relationship matrix called a kernel. Although the set of all single nucleotide polymorphism genotype configurations on which a model is built is finite, past research has mainly used a Gaussian kernel.

Results

We sought to investigate the performance of a diffusion kernel, which was specifically developed to model discrete marker inputs, using Holstein cattle and wheat data. This kernel can be viewed as a discretization of the Gaussian kernel. The predictive ability of the diffusion kernel was similar to that of non-spatial distance-based additive genomic relationship kernels in the Holstein data, but outperformed the latter in the wheat data. However, the difference in performance between the diffusion and Gaussian kernels was negligible.

Conclusions

It is concluded that the ability of a diffusion kernel to capture the total genetic variance is not better than that of a Gaussian kernel, at least for these data. Although the diffusion kernel as a choice of basis function may have potential for use in whole-genome prediction, our results imply that embedding genetic markers into a non-Euclidean metric space has very small impact on prediction. Our results suggest that use of the black box Gaussian kernel is justified, given its connection to the diffusion kernel and its similar predictive performance.     

应用VCE4.0估计长白猪生长性状的遗传参数

应用PEST和VCE4.0对温氏长白猪的主要生长性状进行了遗传分析。利用温氏水台原种猪场1998～2002年的6344头长白猪生长性能测定记录,运用多性状动物模型REML方法估计主要生长性状的遗传参数。估计遗传力的变化范围为0.207～0.493,性状达30kg体重日龄（AGE30）、达100kg体重日龄（AGE100）、30～100kg平均日增重（ADG）和100kg体重活体背膘厚（FAT）的估计遗传力分别是0.207、0.396、0.304和0.493;FAT/ADG、FAT/AGE100、ADG/AGE100、ADG/AGE30和AGE30/AGE100的各自遗传相关为-0.343、0.180、-0.941、-0.48和0.745;它们的表型相关分别为-0.139、0.138、-0.829、-0.026 和 0.565;AGE30、AGE100、ADG和FAT的窝效应估计结果分别为0.194、0.156、0.157和0.043。     

Non-additive genetic variation in growth,carcass and fertility traits of beef cattle

Background

A better understanding of non-additive variance could lead to increased knowledge on the genetic control and physiology of quantitative traits, and to improved prediction of the genetic value and phenotype of individuals. Genome-wide panels of single nucleotide polymorphisms (SNPs) have been mainly used to map additive effects for quantitative traits, but they can also be used to investigate non-additive effects. We estimated dominance and epistatic effects of SNPs on various traits in beef cattle and the variance explained by dominance, and quantified the increase in accuracy of phenotype prediction by including dominance deviations in its estimation.

Methods

Genotype data (729 068 real or imputed SNPs) and phenotypes on up to 16 traits of 10 191 individuals from Bos taurus, Bos indicus and composite breeds were used. A genome-wide association study was performed by fitting the additive and dominance effects of single SNPs. The dominance variance was estimated by fitting a dominance relationship matrix constructed from the 729 068 SNPs. The accuracy of predicted phenotypic values was evaluated by best linear unbiased prediction using the additive and dominance relationship matrices. Epistatic interactions (additive × additive) were tested between each of the 28 SNPs that are known to have additive effects on multiple traits, and each of the other remaining 729 067 SNPs.

Results

The number of significant dominance effects was greater than expected by chance and most of them were in the direction that is presumed to increase fitness and in the opposite direction to inbreeding depression. Estimates of dominance variance explained by SNPs varied widely between traits, but had large standard errors. The median dominance variance across the 16 traits was equal to 5% of the phenotypic variance. Including a dominance deviation in the prediction did not significantly increase its accuracy for any of the phenotypes. The number of additive × additive epistatic effects that were statistically significant was greater than expected by chance.

Conclusions

Significant dominance and epistatic effects occur for growth, carcass and fertility traits in beef cattle but they are difficult to estimate precisely and including them in phenotype prediction does not increase its accuracy.     

Assessing models for genetic prediction of complex traits: a comparison of visualization and quantitative methods

Background

In silico models have recently been created in order to predict which genetic variants are more likely to contribute to the risk of a complex trait given their functional characteristics. However, there has been no comprehensive review as to which type of predictive accuracy measures and data visualization techniques are most useful for assessing these models.

Methods

We assessed the performance of the models for predicting risk using various methodologies, some of which include: receiver operating characteristic (ROC) curves, histograms of classification probability, and the novel use of the quantile-quantile plot. These measures have variable interpretability depending on factors such as whether the dataset is balanced in terms of numbers of genetic variants classified as risk variants versus those that are not.

Results

We conclude that the area under the curve (AUC) is a suitable starting place, and for models with similar AUCs, violin plots are particularly useful for examining the distribution of the risk scores.

Electronic supplementary material

The online version of this article (doi:10.1186/s12864-015-1616-z) contains supplementary material, which is available to authorized users.     

Using the realized relationship matrix to disentangle confounding factors for the estimation of genetic variance components of complex traits

Background

In the analysis of complex traits, genetic effects can be confounded with non-genetic effects, especially when using full-sib families. Dominance and epistatic effects are typically confounded with additive genetic and non-genetic effects. This confounding may cause the estimated genetic variance components to be inaccurate and biased.

Methods

In this study, we constructed genetic covariance structures from whole-genome marker data, and thus used realized relationship matrices to estimate variance components in a heterogenous population of ~ 2200 mice for which four complex traits were investigated. These mice were genotyped for more than 10,000 single nucleotide polymorphisms (SNP) and the variances due to family, cage and genetic effects were estimated by models based on pedigree information only, aggregate SNP information, and model selection for specific SNP effects.

Results and conclusions

We show that the use of genome-wide SNP information can disentangle confounding factors to estimate genetic variances by separating genetic and non-genetic effects. The estimated variance components using realized relationship were more accurate and less biased, compared to those based on pedigree information only. Models that allow the selection of individual SNP in addition to fitting a relationship matrix are more efficient for traits with a significant dominance variance.     

Dissecting the complex genetic basis of mate choice

The genetic analysis of mate choice is fraught with difficulties. Males produce complex signals and displays that can consist of a combination of acoustic, visual, chemical and behavioural phenotypes. Furthermore, female preferences for these male traits are notoriously difficult to quantify. During mate choice, genes not only affect the phenotypes of the individual they are in, but can influence the expression of traits in other individuals. How can genetic analyses be conducted to encompass this complexity? Tighter integration of classical quantitative genetic approaches with modern genomic technologies promises to advance our understanding of the complex genetic basis of mate choice.     

Quantitative genetic dissection of complex traits in a QTL-mapping pedigree

This paper summarizes and modifies quantitative genetic analyses on a pedigree used to map genetic factors (i.e., QTLs) underlying a complex trait. The total genetic variance can be exactly estimated based on the F₂ family derived from two homozygous parents for alternative alleles at all QTLs of interest. The parents, F₁ hybrids, and two backcrosses are combined to each parent, and the total number of QTLs and the number of dominant QTLs are estimated under the assumptions of gene association with the two parents, equal gene effect, no linkage, and no epistasis among QTLs. Further relaxation for each of the assumptions are made in detail. The biometric estimator for the QTL number and action mode averaged over the entire genome could provide some basic and complementary information to QTL mapping designed to detect the effect and location of specific genetic factors.     

The genetic dissection of complex traits in a founder population

We estimated broad heritabilities (H(2)) and narrow heritabilities (h(2)) and conducted genomewide screens, using a novel association-based mapping approach for 20 quantitative trait loci (QTLs) among the Hutterites, a founder population that practices a communal lifestyle. Heritability estimates ranged from.21 for diastolic blood pressure (DBP) to.99 for whole-blood serotonin levels. Using a multipoint method to detect association under a recessive model we found evidence of major QTLs for six traits: low-density lipoprotein (LDL), triglycerides, lipoprotein (a) (Lp[a]), systolic blood pressure (SBP), serum cortisol, and whole-blood serotonin. Second major QTLs for Lp(a) and for cortisol were identified using a single-point method to detect association under a general two-allele model. The heritabilities for these six traits ranged from.37 for triglycerides to.99 for serotonin, and three traits (LDL, SBP, and serotonin) had significant dominance variances (i.e., H(2) > h(2)). Surprisingly, there was little correlation between measures of heritability and the strength of association on a genomewide screen (P>.50), suggesting that heritability estimates per se do not identify phenotypes that are influenced by genes with major effects. The present study demonstrates the feasibility of genomewide association studies for QTL mapping. However, even in this young founder population that has extensive linkage disequilibrium, map densities <5 cM may be required to detect all major QTLs.     

Using genetic networks and homology to understand the evolution of phenotypic traits

Homology can have different meanings for different kinds of biologists. A phylogenetic view holds that homology, defined by common ancestry, is rigorously identified through phylogenetic analysis. Such homologies are taxic homologies (=synapomorphies). A second interpretation, "biological homology" emphasizes common ancestry through the continuity of genetic information underlying phenotypic traits, and is favored by some developmental geneticists. A third kind of homology, deep homology, was recently defined as "the sharing of the genetic regulatory apparatus used to build morphologically and phylogenetically disparate features." Here we explain the commonality among these three versions of homology. We argue that biological homology, as evidenced by a conserved gene regulatory network giving a trait its "essential identity" (a Character Identity Network or "ChIN") must also be a taxic homology. In cases where a phenotypic trait has been modified over the course of evolution such that homology (taxic) is obscured (e.g. jaws are modified gill arches), a shared underlying ChIN provides evidence of this transformation. Deep homologies, where molecular and cellular components of a phenotypic trait precede the trait itself (are phylogenetically deep relative to the trait), are also taxic homologies, undisguised. Deep homologies inspire particular interest for understanding the evolutionary assembly of phenotypic traits. Mapping these deeply homologous building blocks on a phylogeny reveals the sequential steps leading to the origin of phenotypic novelties. Finally, we discuss how new genomic technologies will revolutionize the comparative genomic study of non-model organisms in a phylogenetic context, necessary to understand the evolution of phenotypic traits.