A finite locus effect diffusion model for the evolution of a quantitative trait

A diffusion model is constructed for the joint distribution of absolute locus effect sizes and allele frequencies for loci contributing to an additive quantitative trait under selection in a haploid, panmictic population. The model is designed to approximate a discrete model exactly in the limit as both population size and the number of loci affecting the trait tend to infinity. For the case when all loci have the same absolute effect size, formal multiple-timescale asymptotics are used to predict the long-time response of the population trait mean to selection. For the case where loci can take on either of two distinct effect sizes, not necessarily with equal probability, numerical solutions of the system indicate that response to selection of a quantitative trait is insensitive to the variability of the distribution of effect sizes when mutation is negligible.     

A general mixture model for mapping quantitative trait loci by using molecular markers

Summary In a segregating population a quantitative trait may be considered to follow a mixture of (normal) distributions, the mixing proportions being based on Mendelian segregation rules. A general and flexible mixture model is proposed for mapping quantitative trait loci (QTLs) by using molecular markers. A method is discribed to fit the model to data. The model makes it possible to (1) analyse non-normally distributed traits such as lifetimes, counts or percentages in addition to normally distributed traits, (2) reduce environmental variation by taking into account the effects of experimental design factors and interaction between genotype and environment, (3) reduce genotypic variation by taking into account the effects of two or more QTLs simultaneously, (4) carry out a (combined) analysis of different population types, (5) estimate recombination frequencies between markers or use known marker distances, (6) cope with missing marker observations, (7) use markers as covariables in detection and mapping of QTLs, and finally to (8) implement the mapping in standard statistical packages.     

Mapping loci influencing blood pressure in the Framingham pedigrees using model-free LOD score analysis of a quantitative trait

This paper presents a method of performing model-free LOD-score based linkage analysis on quantitative traits. It is implemented in the QMFLINK program. The method is used to perform a genome screen on the Framingham Heart Study data. A number of markers that show some support for linkage in our study coincide substantially with those implicated in other linkage studies of hypertension. Although the new method needs further testing on additional real and simulated data sets we can already say that it is straightforward to apply and may offer a useful complementary approach to previously available methods for the linkage analysis of quantitative traits.     

Estimating genetic variance contributed by a quantitative trait locus: A random model approach

Detecting quantitative trait loci (QTL) and estimating QTL variances (represented by the squared QTL effects) are two main goals of QTL mapping and genome-wide association studies (GWAS). However, there are issues associated with estimated QTL variances and such issues have not attracted much attention from the QTL mapping community. Estimated QTL variances are usually biased upwards due to estimation being associated with significance tests. The phenomenon is called the Beavis effect. However, estimated variances of QTL without significance tests can also be biased upwards, which cannot be explained by the Beavis effect; rather, this bias is due to the fact that QTL variances are often estimated as the squares of the estimated QTL effects. The parameters are the QTL effects and the estimated QTL variances are obtained by squaring the estimated QTL effects. This square transformation failed to incorporate the errors of estimated QTL effects into the transformation. The consequence is biases in estimated QTL variances. To correct the biases, we can either reformulate the QTL model by treating the QTL effect as random and directly estimate the QTL variance (as a variance component) or adjust the bias by taking into account the error of the estimated QTL effect. A moment method of estimation has been proposed to correct the bias. The method has been validated via Monte Carlo simulation studies. The method has been applied to QTL mapping for the 10-week-body-weight trait from an F₂ mouse population.     

A non-parametric mixture model for genome-enabled prediction of genetic value for a quantitative trait

A Bayesian nonparametric form of regression based on Dirichlet process priors is adapted to the analysis of quantitative traits possibly affected by cryptic forms of gene action, and to the context of SNP-assisted genomic selection, where the main objective is to predict a genomic signal on phenotype. The procedure clusters unknown genotypes into groups with distinct genetic values, but in a setting in which the number of clusters is unknown a priori, so that standard methods for finite mixture analysis do not work. The central assumption is that genetic effects follow an unknown distribution with some “baseline” family, which is a normal process in the cases considered here. A Bayesian analysis based on the Gibbs sampler produces estimates of the number of clusters, posterior means of genetic effects, a measure of credibility in the baseline distribution, as well as estimates of parameters of the latter. The procedure is illustrated with a simulation representing two populations. In the first one, there are 3 unknown QTL, with additive, dominance and epistatic effects; in the second, there are 10 QTL with additive, dominance and additive × additive epistatic effects. In the two populations, baseline parameters are inferred correctly. The Dirichlet process model infers the number of unique genetic values correctly in the first population, but it produces an understatement in the second one; here, the true number of clusters is over 900, and the model gives a posterior mean estimate of about 140, probably because more replication of genotypes is needed for correct inference. The impact on inferences of the prior distribution of a key parameter (M), and of the extent of replication, was examined via an analysis of mean body weight in 192 paternal half-sib families of broiler chickens, where each sire was genotyped for nearly 7,000 SNPs. In this small sample, it was found that inference about the number of clusters was affected by the prior distribution of M. For a set of combinations of parameters of a given prior distribution, the effects of the prior dissipated when the number of replicate samples per genotype was increased. Thus, the Dirichlet process model seems to be useful for gauging the number of QTLs affecting the trait: if the number of clusters inferred is small, probably just a few QTLs code for the trait. If the number of clusters inferred is large, this may imply that standard parametric models based on the baseline distribution may suffice. However, priors may be influential, especially if sample size is not large and if only a few genotypic configurations have replicate phenotypes in the sample.     

Smoothing of the bivariate LOD score for non-normal quantitative traits

Variance component analysis provides an efficient method for performing linkage analysis for quantitative traits. However, type I error of variance components-based likelihood ratio testing may be affected when phenotypic data are non-normally distributed (especially with high values of kurtosis). This results in inflated LOD scores when the normality assumption does not hold. Even though different solutions have been proposed to deal with this problem with univariate phenotypes, little work has been done in the multivariate case. We present an empirical approach to adjust the inflated LOD scores obtained from a bivariate phenotype that violates the assumption of normality. Using the Collaborative Study on the Genetics of Alcoholism data available for the Genetic Analysis Workshop 14, we show how bivariate linkage analysis with leptokurtotic traits gives an inflated type I error. We perform a novel correction that achieves acceptable levels of type I error.     

Fine mapping of a major quantitative trait locus that regulates pod shattering in soybean

Legumes represent the second most important family of crop plants, accounting for ~27 % of the world’s crop production. While some legumes are grown as forages or vegetables, most crop legumes are grown for harvesting their nutritious seeds. The legume seeds are contained in the pod, which is composed of a single seed-bearing carpel that, when matures, splits open along two seams, a process called pod dehiscence or pod shattering. Pod shattering before or during harvest causes yield losses of grain legumes. Moreover, the dominant shattering trait of the wild progenitors is a limiting factor for efficient introgression of value-added traits into elite breeding lines. Knowledge of the genetic mechanisms underlying pod shattering will facilitate breeding of shattering-resistant varieties, expedite introgression of agronomically favorable traits from wild species to elite breeding lines, and enrich our understanding of the evolution of seed dispersal and crop domestication in diverse crop species. Here we report fine mapping of a major quantitative trait locus (designated as qPDH1) that regulates pod shattering in soybean (Glycine max). A combination of linkage and association mapping allowed us to delimit the qPDH1 locus within a 47-kb region on chromosome 16. The data reported here will facilitate positional cloning of the underlying gene and the development of breeder-friendly genetic markers for marker-assisted selection in soybean.     

Zero-inflated generalized Poisson regression mixture model for mapping quantitative trait loci underlying count trait with many zeros

Phenotypes measured in counts are commonly observed in nature. Statistical methods for mapping quantitative trait loci (QTL) underlying count traits are documented in the literature. The majority of them assume that the count phenotype follows a Poisson distribution with appropriate techniques being applied to handle data dispersion. When a count trait has a genetic basis, “naturally occurring” zero status also reflects the underlying gene effects. Simply ignoring or miss-handling the zero data may lead to wrong QTL inference. In this article, we propose an interval mapping approach for mapping QTL underlying count phenotypes containing many zeros. The effects of QTLs on the zero-inflated count trait are modelled through the zero-inflated generalized Poisson regression mixture model, which can handle the zero inflation and Poisson dispersion in the same distribution. We implement the approach using the EM algorithm with the Newton-Raphson algorithm embedded in the M-step, and provide a genome-wide scan for testing and estimating the QTL effects. The performance of the proposed method is evaluated through extensive simulation studies. Extensions to composite and multiple interval mapping are discussed. The utility of the developed approach is illustrated through a mouse F₂ intercross data set. Significant QTLs are detected to control mouse cholesterol gallstone formation.     

Complex genetic interactions in a quantitative trait locus

Whether in natural populations or between two unrelated members of a species, most phenotypic variation is quantitative. To analyze such quantitative traits, one must first map the underlying quantitative trait loci. Next, and far more difficult, one must identify the quantitative trait genes (QTGs), characterize QTG interactions, and identify the phenotypically relevant polymorphisms to determine how QTGs contribute to phenotype. In this work, we analyzed three Saccharomyces cerevisiae high-temperature growth (Htg) QTGs (MKT1, END3, and RHO2). We observed a high level of genetic interactions among QTGs and strain background. Interestingly, while the MKT1 and END3 coding polymorphisms contribute to phenotype, it is the RHO2 3′UTR polymorphisms that are phenotypically relevant. Reciprocal hemizygosity analysis of the Htg QTGs in hybrids between S288c and ten unrelated S. cerevisiae strains reveals that the contributions of the Htg QTGs are not conserved in nine other hybrids, which has implications for QTG identification by marker-trait association. Our findings demonstrate the variety and complexity of QTG contributions to phenotype, the impact of genetic background, and the value of quantitative genetic studies in S. cerevisiae.     

A quantitative trait locus analysis of personality in wild bighorn sheep

Personality, the presence of persistent behav105 ioral differences among individuals over time or contexts, potentially has important ecological and evolutionary consequences. However, a lack of knowledge about its genetic architecture limits our ability to understand its origin, evolution, and maintenance. Here, we report on a genome‐wide quantitative trait locus (QTL) analysis for two personality traits, docility and boldness, in free‐living female bighorn sheep from Ram Mountain, Alberta, Canada. Our variance component linkage analysis based on 238 microsatellite loci genotyped in 310 pedigreed individuals identified suggestive docility and boldness QTL on sheep chromosome 2 and 6, respectively. A lack of QTL overlap indicated that genetic covariance between traits was not modulated by pleiotropic effects at a major locus and may instead result from linkage disequilibrium or pleiotropic effects at QTL of small effects. To our knowledge, this study represents the first attempt to dissect the genetic architecture of personality in a free‐living wildlife population, an important step toward understanding the link between molecular genetic variation in personality and fitness and the evolutionary processes maintaining this variation.     

The X chromosome in quantitative trait locus mapping

The X chromosome requires special treatment in the mapping of quantitative trait loci (QTL). However, most QTL mapping methods, and most computer programs for QTL mapping, have focused exclusively on autosomal loci. We describe a method for appropriate treatment of the X chromosome for QTL mapping in experimental crosses. We address the important issue of formulating the null hypothesis of no linkage appropriately. If the X chromosome is treated like an autosome, a sex difference in the phenotype can lead to spurious linkage on the X chromosome. Further, the number of degrees of freedom for the linkage test may be different for the X chromosome than for autosomes, and so an X chromosome-specific significance threshold is required. To address this issue, we propose a general procedure to obtain chromosome-specific significance thresholds that controls the genomewide false positive rate at the desired level. We apply our methods to data on gut length in a large intercross of mice carrying the Sox10Dom mutation, a model of Hirschsprung disease. We identified QTL contributing to variation in gut length on chromosomes 5 and 18. We found suggestive evidence of linkage to the X chromosome, which would be viewed as strong evidence of linkage if the X chromosome was treated as an autosome. Our methods have been implemented in the package R/qtl.     

棉花数量性状基因定位研究进展

棉花的许多重要性状,包括产量、纤维品质、株型、抗病抗逆性、生理生化等都是数量性状,受遗传和环境因子的共同作用。近年来,随着分子生物学技术的进步,棉花基因组研究得到迅速发展,为棉花数量性状基因（quantitative trait locus,QTL）定位奠定了坚实的基础。概述了近十几年来棉花QTL定位研究及分子标记辅助选择的进展,结合研究实践指出了棉花QTL定位及标记辅助选择存在的问题,并对其发展方向做出了初步探讨。     

Rank-based statistical methodologies for quantitative trait locus mapping

This article addresses the identification of genetic loci (QTL and elsewhere) that influence nonnormal quantitative traits with focus on experimental crosses. QTL mapping is typically based on the assumption that the traits follow normal distributions, which may not be true in practice. Model-free tests have been proposed. However, nonparametric estimation of genetic effects has not been studied. We propose an estimation procedure based on the linear rank test statistics. The properties of the new procedure are compared with those of traditional likelihood-based interval mapping and regression interval mapping via simulations and a real data example. The results indicate that the nonparametric method is a competitive alternative to the existing parametric methodologies.     

Quantitative trait locus analysis of longitudinal quantitative trait data in complex pedigrees

There is currently considerable interest in genetic analysis of quantitative traits such as blood pressure and body mass index. Despite the fact that these traits change throughout life they are commonly analyzed only at a single time point. The genetic basis of such traits can be better understood by collecting and effectively analyzing longitudinal data. Analyses of these data are complicated by the need to incorporate information from complex pedigree structures and genetic markers. We propose conducting longitudinal quantitative trait locus (QTL) analyses on such data sets by using a flexible random regression estimation technique. The relationship between genetic effects at different ages is efficiently modeled using covariance functions (CFs). Using simulated data we show that the change in genetic effects over time can be well characterized using CFs and that including parameters to model the change in effect with age can provide substantial increases in power to detect QTL compared with repeated measure or univariate techniques. The asymptotic distributions of the methods used are investigated and methods for overcoming the practical difficulties in fitting CFs are discussed. The CF-based techniques should allow efficient multivariate analyses of many data sets in human and natural population genetics.     

A power study of bivariate LOD score analysis of a complex trait and fear/discomfort with strangers

Complex diseases are often reported along with disease-related traits (DRT). Sometimes investigators consider both disease and DRT phenotypes separately and sometimes they consider individuals as affected if they have either the disease or the DRT, or both. We propose instead to consider the joint distribution of the disease and the DRT and do a linkage analysis assuming a pleiotropic model. We evaluated our results through analysis of the simulated datasets provided by Genetic Analysis Workshop 14. We first conducted univariate linkage analysis of the simulated disease, Kofendrerd Personality Disorder and one of its simulated associated traits, phenotype b (fear/discomfort with strangers). Subsequently, we considered the bivariate phenotype, which combined the information on Kofendrerd Personality Disorder and fear/discomfort with strangers. We developed a program to perform bivariate linkage analysis using an extension to the Elston-Stewart peeling method of likelihood calculation. Using this program we considered the microsatellites within 30 cM of the gene pleiotropic for this simulated disease and DRT. Based on 100 simulations of 300 families we observed excellent power to detect linkage within 10 cM of the disease locus using the DRT and the bivariate trait.     

A quantitative trait locus on chromosome 1 modulates intermale aggression in mice

Aggression between male conspecifics is a complex social behavior that is likely modulated by multiple gene variants. In this study, the BXD recombinant inbred mouse strains (RIS) were used to map quantitative trait loci (QTLs) underlying behaviors associated with intermale aggression. Four hundred and fifty‐seven males from 55 strains (including the parentals) were observed at an age of 13 ± 1 week in a resident‐intruder test following 10 days of isolation. Attack latency was measured directly within a 10‐minute time period and the test was repeated 24 hours later. The variables we analyzed were the proportion of attacking males in a given strain as well as the attack latency (on days 1 and 2, and both days combined). On day 1, 29% of males attacked, and this increased to 37% on day 2. Large strain differences were obtained for all measures of aggression, indicating substantial heritability (intraclass correlations 0.10‐0.18). We identified a significant QTL on chromosome (Chr) 1 and suggestive QTLs on mouse Chrs 1 and 12 for both attack and latency variables. The significant Chr 1 locus maps to a gene‐sparse region between 82 and 88.5 Mb with the C57BL/6J allele increasing aggression and explaining about 18% of the variance. The most likely candidate gene modulating this trait is Htr2b which encodes the serotonin 2B receptor and has been implicated in aggressive and impulsive behavior in mice, humans and other species.