Multiple Quantitative Trait Research Articles

Detection of multiple QTL with epistatic effects under a mixed inheritance model in an outbred population.

A quantitative trait depends on multiple quantitative trait loci (QTL) and on the interaction between two or more QTL, named epistasis. Several methods to detect multiple QTL in various types of design have been proposed, but most of these are based on the assumption that each QTL works independently and epistasis has not been explored sufficiently. The objective of the study was to propose an integrated method to detect multiple QTL with epistases using Bayesian inference via a Markov chain Monte Carlo (MCMC) algorithm. Since the mixed inheritance model is assumed and the deterministic algorithm to calculate the probabilities of QTL genotypes is incorporated in the method, this can be applied to an outbred population such as livestock. Additionally, we treated a pair of QTL as one variable in the Reversible jump Markov chain Monte Carlo (RJMCMC) algorithm so that two QTL were able to be simultaneously added into or deleted from a model. As a result, both of the QTL can be detected, not only in cases where either of the two QTL has main effects and they have epistatic effects between each other, but also in cases where neither of the two QTL has main effects but they have epistatic effects. The method will help ascertain the complicated structure of quantitative traits.

Structured antedependence models for genetic analysis of repeated measures on multiple quantitative traits

Simultaneous analysis of correlated traits that change with time is an important issue in genetic analyses. Several methodologies have already been proposed for the genetic analysis of longitudinal data on single traits, in particular random regression and character process models. Although the latter proved, in most cases, to compare favourably to alternative approaches for analysis of single function-valued traits, they do not allow a straightforward extension to the multivariate case. In this paper, another methodology (structured antedependence models) is proposed, and methods are derived for the genetic analysis of two or more correlated function-valued traits. Multivariate analyses are presented of fertility and mortality in Drosophila and of milk, fat and protein yields in dairy cattle. These models offer a substantial flexibility for the correlation structure, even in the case of complex non-stationary patterns, and perform better than multivariate random regression models, with fewer parameters.

Multi-trait Selection, Adaptation, and Constraints on the Evolution of Burst Swimming Performance

Whole organism performance represents the integration of numerous physiological, morphological, and behavioral traits. How adaptive changes in performance evolve therefore requires an understanding of how selection acts on multiple integrated traits. Two approaches that lend themselves to studying the evolution of performance in natural populations are the use of quantitative genetics models for estimating the strength of selection acting on multiple quantitative traits and ecological genetic comparisons of populations exhibiting phenotypic differences correlated with environmental variation. In both cases, the ultimate goal is to understand how suites of traits and trade-offs between competing functions respond to natural selection. Here we consider how these two complimentary approaches can be applied to study the adaptive evolution of escape performance in fish. We first present an extension of Arnold's (1983) quantitative genetic approach that explicitly considers how trade-offs between different components of performance interact with the underlying genetics. We propose that such a model can reveal the conditions under which multiple selection pressures will cause adaptive change in traits that influence more than one component of fitness. We then review work on the Atlantic silversides and Trinidadian guppies as two case studies where an ecological genetics approach has been successfully applied to evaluate how the evolution of escape performance trades-off with other components of fitness. We conclude with the general lesson that whole organism performance is embedded in a complex phenotype, and that the net outcome of selection acting on different aspects of the organism will often result in a compromise among competing influences.

Stochastic search variable selection for identifying multiple quantitative trait loci.

In this article, we utilize stochastic search variable selection methodology to develop a Bayesian method for identifying multiple quantitative trait loci (QTL) for complex traits in experimental designs. The proposed procedure entails embedding multiple regression in a hierarchical normal mixture model, where latent indicators for all markers are used to identify the multiple markers. The markers with significant effects can be identified as those with higher posterior probability included in the model. A simple and easy-to-use Gibbs sampler is employed to generate samples from the joint posterior distribution of all unknowns including the latent indicators, genetic effects for all markers, and other model parameters. The proposed method was evaluated using simulated data and illustrated using a real data set. The results demonstrate that the proposed method works well under typical situations of most QTL studies in terms of number of markers and marker density.

Quantitative traits in plants: beyond the QTL

Phenotypic variation for quantitative traits results from segregation at multiple quantitative trait loci (QTL), the effects of which are modified by the internal and external environments. Because of their favorable genetic attributes (e.g. short generation time, large families and tolerance to inbreeding), plants are often used to test new concepts in quantitative trait analysis. Thus far, the molecular basis underlying allelic variation at QTL is similar to the identified variation for simple mendelian loci; namely, alterations in gene expression or protein function. Further comprehensive dissection of complex phenotypes will depend on our ability to link genetic components of the QTL variation to genomic databases.

On flexible finite polygenic models for multiple-trait evaluation.

Finite polygenic models (FPM) might be an alternative to the infinitesimal model (TIM) for the genetic evaluation of pedigreed multiple-generation populations for multiple quantitative traits. I present a general flexible Bayesian method that includes the number of genes in the FPM as an additional random variable. Markov-chain Monte Carlo techniques such as Gibbs sampling and the reversible jump sampler are used for implementation. Sampling of genotypes of all genes in the FPM is done via the use of segregation indicators. A broad range of FPM models, some combined with TIM, are empirically tested for the estimation of variance components and the number of genes in the FPM. Four simulation scenarios were studied, including genetic models with 5 or 50 additive independent diallelic genes affecting the traits, and random selection or selection on one of the traits was performed. The results in this study were based on ten replicates per simulation scenario. In the case of random selection, uniform priors on additive gene effects led to posterior mean estimates of genetic variance that were positively correlated with the number of genes fitted in the FPM. In the case of trait selection, assuming normal priors on gene effects also led to genetic variance estimates for the selected trait that were negatively correlated with the number of genes in the FPM. This negative correlation was not observed for the unselected trait. Treating the number of genes in the FPM as random revealed a positive correlation between prior and posterior mean estimates of this number, but the prior hardly affected the posterior estimates of genetic variance. Posterior inferences about the number of genes should be considered to be indicative where trait selection seems to improve the power of distinguishing between TIM and FPM. Based on the results of this study, I suggest not replacing TIM by the FPM, but combining TIM and FPM with the number of genes treated as random, to facilitate a highly flexible and thereby robust method for variance component estimation in pedigreed populations. Further study is required to explore the full potential of these models under different genetic model assumptions.

Angiotensin-1-converting enzyme (ACE) plasma concentration is influenced by multiple ACE-linked quantitative trait nucleotides.

Circulating angiotensin-1-converting enzyme (ACE) is a highly heritable trait, and a major component of the genetic variance maps to the region of the ACE gene. The strong effect of the locus, and the interest in ACE as a candidate gene for cardiovascular disorders, has led to extensive investigation of its relationship to the ACE phenotype, providing one of the most complete examples of quantitative trait locus (QTL) analysis in humans. Resequencing of ACE followed by haplotype analysis in families of British and French origin has shown that the genetic variants that are primarily associated with the ACE trait map to an 18 kb interval flanked by two intragenic, ancestral recombination breakpoints. This critical interval contains dozens of ACE-associated variants in Caucasians, but identification of which of these directly influence ACE concentration is ambiguous because of the almost complete linkage disequilibrium in European populations. In a complementary sequencing and genotyping study of individuals from West African families, we show that this population has much greater haplotype diversity across the gene. Through analysis of the contrasting relationships of the trait phenotype with haplotypes that carry different allelic combinations from those observed in Caucasians, we demonstrate that (at least) two major intragenic sites within the critical interval and (at least) one minor promoter site are associated with the ACE quantitative trait through additive effects. These results point to the importance of analysing diverse populations with different gene genealogies in gene-association studies.

A Unified Approach to Joint Modeling of Multiple Quantitative and Qualitative Traits in Gene Mapping

Using graph theory, we present a theoretical basis for mapping oligogenes in the joint presence of multiple phenotypic measurements of both quantitative and qualitative types. Various statistical models proposed earlier for several traits of solely single type are special cases of the unified approach given here. Our emphasis is on the generality of the framework, without specifying explicit assumptions about a sampling design. When information about environmental factors potentially affecting the traits is available, it can be incorporated into the genetic model. We adopt the Bayesian inferential machinery due to its firm theoretical basis and its capability of handling uncertain quantities; such as unobserved model parameters, missing marker data, and even different putative genetic models, probabilistically within a single framework. It is shown here that biological hypotheses about single gene affecting simultaneously multiple traits (pleiotropy) can be intuitively imposed as parameter constraints, leading to pleiotropic models for which posterior probabilities can be calculated. Outline of the possible implementation of the Bayesian method is described using the general reversible-jump Markov chain Monte Carlo algorithm. Some future challenges and extensions are also discussed.

A Unified Approach to Joint Modeling of Multiple Quantitative and Qualitative Traits in Gene Mapping

Using graph theory, we present a theoretical basis for mapping oligogenes in the joint presence of multiple phenotypic measurements of both quantitative and qualitative types. Various statistical models proposed earlier for several traits of solely single type are special cases of the unified approach given here. Our emphasis is on the generality of the framework, without specifying explicit assumptions about a sampling design. When information about environmental factors potentially affecting the traits is available, it can be incorporated into the genetic model. We adopt the Bayesian inferential machinery due to its firm theoretical basis and its capability of handling uncertain quantities; such as unobserved model parameters, missing marker data, and even different putative genetic models, probabilistically within a single framework. It is shown here that biological hypotheses about single gene affecting simultaneously multiple traits (pleiotropy) can be intuitively imposed as parameter constraints, leading to pleiotropic models for which posterior probabilities can be calculated. Outline of the possible implementation of the Bayesian method is described using the general reversible-jump Markov chain Monte Carlo algorithm. Some future challenges and extensions are also discussed.

Mapping quantitative trait loci with epistatic effects.

Epistatic variance can be an important source of variation for complex traits. However, detecting epistatic effects is difficult primarily due to insufficient sample sizes and lack of robust statistical methods. In this paper, we develop a Bayesian method to map multiple quantitative trait loci (QTLs) with epistatic effects. The method can map QTLs in complicated mating designs derived from the cross of two inbred lines. In addition to mapping QTLs for quantitative traits, the proposed method can even map genes underlying binary traits such as disease susceptibility using the threshold model. The parameters of interest are various QTL effects, including additive, dominance and epistatic effects of QTLs, the locations of identified QTLs and even the number of QTLs. When the number of QTLs is treated as an unknown parameter, the dimension of the model becomes a variable. This requires the reversible jump Markov chain Monte Carlo algorithm. The utility of the proposed method is demonstrated through analysis of simulation data.

Congenic rat strains are important tools for the genetic dissection of essential hypertension.

The identification of mutated genes and the characterization of disease pathways in monogenetic forms of human arterial hypertension has been very successful during the past decade, although only little progress has been made with regard to the genetic analysis of essential hypertension. Inbred rat strains that display hypertension as an inherited trait represent an attractive substitute for the dissection of the polygenetic basis of human essential hypertension. The power of studying these inbred models with natural allelic variation is that each strain can be thought of as a different subtype of essential hypertension. Thus, to study the genetics of hypertension using a potpourri of inbred hypertensive rat strains may help to identify a set of genes that can give rise to hypertension in the heterogeneous clinical situation of essential hypertension. Indeed, multiple blood pressure quantitative trait loci (QTL) have been identified in the rat genome and a few of those have been implicated in the human disease by homology mapping already. Here, we discuss the role of congenic breeding strategies to further dissect the genetics of hypertension in the rat. Based on recent accomplishments it can be anticipated that by using congenic strains, the genetic sifting of the collection of blood pressure QTLs identified so far will lead to the identification of additional and new candidate genes. This will open the possibility for the development of new diagnostic and therapeutic means contributing to a better control of human essential hypertension.

A method to optimize selection on�multiple identified quantitative trait loci

A mathematical approach was developed to model and optimize selection on multiple known quantitative trait loci (QTL) and polygenic estimated breeding values in order to maximize a weighted sum of responses to selection over multiple generations. The model allows for linkage between QTL with multiple alleles and arbitrary genetic effects, including dominance, epistasis, and gametic imprinting. Gametic phase disequilibrium between the QTL and between the QTL and polygenes is modeled but polygenic variance is assumed constant. Breeding programs with discrete generations, differential selection of males and females and random mating of selected parents are modeled. Polygenic EBV obtained from best linear unbiased prediction models can be accommodated. The problem was formulated as a multiple-stage optimal control problem and an iterative approach was developed for its solution. The method can be used to develop and evaluate optimal strategies for selection on multiple QTL for a wide range of situations and genetic models.

Optimal selection on two quantitative trait loci with linkage

A mathematical approach to optimize selection on multiple quantitative trait loci (QTL) and an estimate of residual polygenic effects was applied to selection on two linked or unlinked additive QTL. Strategies to maximize total or cumulative discounted response over ten generations were compared to standard QTL selection on the sum of breeding values for the QTL and an estimated breeding value for polygenes, and to phenotypic selection. Optimal selection resulted in greater response to selection than standard QTL or phenotypic selection. Tight linkage between the QTL (recombination rate 0.05) resulted in a slightly lower response for standard QTL and phenotypic selection but in a greater response for optimal selection. Optimal selection capitalized on linkage by emphasizing selection on favorable haplotypes. When the objective was to maximize total response after ten generations and QTL were unlinked, optimal selection increased QTL frequencies to fixation in a near linear manner. When starting frequencies were equal for the two QTL, equal emphasis was given to each QTL, regardless of the difference in effects of the QTL and regardless of the linkage, but the emphasis given to each of the two QTL was not additive. These results demonstrate the ability of optimal selection to capitalize on information on the complex genetic basis of quantitative traits that is forthcoming.

A method to optimize selection on multiple identified quantitative trait loci.

A mathematical approach was developed to model and optimize selection on multiple known quantitative trait loci (QTL) and polygenic estimated breeding values in order to maximize a weighted sum of responses to selection over multiple generations. The model allows for linkage between QTL with multiple alleles and arbitrary genetic effects, including dominance, epistasis, and gametic imprinting. Gametic phase disequilibrium between the QTL and between the QTL and polygenes is modeled but polygenic variance is assumed constant. Breeding programs with discrete generations, differential selection of males and females and random mating of selected parents are modeled. Polygenic EBV obtained from best linear unbiased prediction models can be accommodated. The problem was formulated as a multiple-stage optimal control problem and an iterative approach was developed for its solution. The method can be used to develop and evaluate optimal strategies for selection on multiple QTL for a wide range of situations and genetic models.

Gene-expression profiling of experimental autoimmune encephalomyelitis.

Experimental autoimmune encephalomyelitis (EAE) is a mouse model that serves as an experimental tool for studying the etiology, pathogenesis, as well as new therapeutic approaches of multiple sclerosis (MS). EAE is a polygenic chronic inflammatory demyelinating disease of the nervous system that involves the interaction between genetic and environmental factors. Previous studies have identified multiple quantitative trait loci (QTL) controlling different aspects of disease pathogenesis. However, progress in identifying new susceptibility genes outside the MHC locus has been slow. With the advent of new global methods for genetic analysis such as large-scale sequencing, gene expression profiling combined with classic linkage analysis and congenic and physical mapping progress is considerably accelerating. Here we review our preliminary work on the use of gene expression mapping to identify new putative genetic pathways contributing to the pathogenesis of EAE.

Optimal selection on two quantitative trait loci with linkage.

A mathematical approach to optimize selection on multiple quantitative trait loci (QTL) and an estimate of residual polygenic effects was applied to selection on two linked or unlinked additive QTL. Strategies to maximize total or cumulative discounted response over ten generations were compared to standard QTL selection on the sum of breeding values for the QTL and an estimated breeding value for polygenes, and to phenotypic selection. Optimal selection resulted in greater response to selection than standard QTL or phenotypic selection. Tight linkage between the QTL (recombination rate 0.05) resulted in a slightly lower response for standard QTL and phenotypic selection but in a greater response for optimal selection. Optimal selection capitalized on linkage by emphasizing selection on favorable haplotypes. When the objective was to maximize total response after ten generations and QTL were unlinked, optimal selection increased QTL frequencies to fixation in a near linear manner. When starting frequencies were equal for the two QTL, equal emphasis was given to each QTL, regardless of the difference in effects of the QTL and regardless of the linkage, but the emphasis given to each of the two QTL was not additive. These results demonstrate the ability of optimal selection to capitalize on information on the complex genetic basis of quantitative traits that is forthcoming.

The genetic architecture of quantitative traits.

Phenotypic variation for quantitative traits results from the segregation of alleles at multiple quantitative trait loci (QTL) with effects that are sensitive to the genetic, sexual, and external environments. Major challenges for biology in the post-genome era are to map the molecular polymorphisms responsible for variation in medically, agriculturally, and evolutionarily important complex traits; and to determine their gene frequencies and their homozygous, heterozygous, epistatic, and pleiotropic effects in multiple environments. The ease with which QTL can be mapped to genomic intervals bounded by molecular markers belies the difficulty in matching the QTL to a genetic locus. The latter requires high-resolution recombination or linkage disequilibrium mapping to nominate putative candidate genes, followed by genetic and/or functional complementation and gene expression analyses. Complete genome sequences and improved technologies for polymorphism detection will greatly advance the genetic dissection of quantitative traits in model organisms, which will open avenues for exploration of homologous QTL in related taxa.

Bayesian versus frequentist analysis of multiple quantitative trait loci with an application to an outbred apple cross

Two methods, following different statistical paradigms for mapping multiple quantitative trait loci (QTLs), were compared: the first is a frequentist, the second a Bayesian approach. Both methods were applied to previously published experimental data from an outbred progeny of a single cross between two apple cultivars (Malus pumila Mill.). These approaches were compared with respect to (1) the models used, (2) the number of putative QTLs, (3) their estimated map positions and accuracies thereof and (4) the choice of cofactor markers. In general, the strongest evidence for QTLs, provided by both methods, was for the same linkage groups and for similar map positions. However, some differences were found with respect to evidence for QTLs on other linkage groups. The effect of using cofactor markers which were selected differently was also somewhat different.

The nature of quantitative genetic variation for Drosophila longevity

Longevity is a typical quantitative trait: the continuous variation in life span observed in natural populations is attributable to genetic variation at multiple quantitative trait loci (QTL), environmental sensitivity of QTL alleles, and truly continuous environmental variation. To begin to understand the genetic architecture of longevity at the level of individual QTL, we have mapped QTL for Drosophila life span that segregate between two inbred strains that were not selected for longevity. A mapping population of 98 recombinant inbred lines (RIL) was derived from these strains, and life span of virgin male and female flies measured under control culture conditions, chronic heat and cold stress, heat shock and starvation stress, and high and low density larval environments. The genotypes of the RIL were determined for polymorphic roo transposable element insertion sites, and life span QTL were mapped using composite interval mapping methods. A minimum of 19 life span QTL were detected by recombination mapping. The life span QTL exhibited strong genotype by sex, genotype by environment, and genotype by genotype (epistatic) interactions. These interactions complicate mapping efforts, but evolutionary theory predicts such properties of segregating QTL alleles. Quantitative deficiency mapping of four longevity QTL detected in the control environment by recombination mapping revealed a minimum of 11 QTL in these regions. Clearly, longevity is a complex quantitative trait. In the future, linkage disequilibrium mapping can be used to determine which candidate genes in a QTL region correspond to the genetic loci affecting variation in life span, and define the QTL alleles at the molecular level.

Multiple quantitative trait locus analysis of bovine chromosome 6 in the Israeli Holstein population by a daughter design.

Nine Israeli Holstein sire families with 2978 daughters were analyzed for quantitative trait loci effects on chromosome 6 for five milk production traits by a daughter design. All animals were genotyped for 2 markers. The three families with significant effects were genotyped for up to 10 additional markers spanning positions 0-122 cM of BTA6. Two sires were segregating for a locus affecting protein and fat percentage near position 55 cM with an estimated substitution effect of 0.18% protein, which is equivalent to one phenotypic standard deviation. This locus was localized to a confidence interval of 4 cM. One of these sires was also heterozygous for a locus affecting milk, fat, and protein production near the centromere. The hypothesis of two segregating loci was verified by multiple regression analysis. A third sire was heterozygous for a locus affecting milk and protein percentage near the telomeric end of the chromosome. Possible candidates for the major quantitative gene near position 55 cM were determined by comparative mapping. IBSP and SSP1 were used as anchors for the orthologous region on human chromosome 4. Twelve genes were detected within a 2-Mbp sequence. None of these genes have been previously associated with lactogenesis.