Analysis of quantitative trait loci using hybrid pedigrees: Quantitative traits of animals

A method is proposed for analysis of quantitative traits in animal hybrid pedigrees formed by crosses between outbred lines differing in allele frequencies of the genes controlling the trait studied. The method is based on the decomposition of trait variances into components and uses maximization of the likelihood function for estimating model parameters, which allows the estimation of additive and dominance effects of the gene involved in trait determination and its allele frequencies, as well as determination of the chromosomal position of this gene relative to genotyped markers. To test the linkage of this gene with markers, a statistic with the noncentral x ² distribution has been chosen. Analytical expressions for the power of this method have been derived. The method has been tested on small model hybrid pedigrees. Phenotypic values of the trait and information on marker genotypes for each individual in hybrid pedigrees are initial data for the analysis of a quantitative trait.     

Analysis of quantitative trait loci using hybrid pedigrees: quantitative traits of animals

A method is proposed for analysis of quantitative traits in animal hybrid pedigrees formed by crosses between outbred lines differing in allele frequencies of the genes controlling the trait studied. The method is based on the decomposition of trait variances into components and uses maximization of the likelihood function for estimating model parameters, which allows the estimation of additive and dominance effects of the gene involved in trait determination and its allele frequencies, as well as determination of the chromosomal position of this gene relative to genotyped markers. To test the linkage of this gene with markers, a statistic with the noncentral chi(2) distribution has been chosen. Analytical expressions for the power of this method have been derived. The method has been tested on small model hybrid pedigrees. Phenotypic values of the trait and information on marker genotypes for each individual in hybrid pedigrees are original data for the analysis of a quantitative trait.     

An EM algorithm for mapping quantitative resistance loci

Many disease resistance traits in plants have a polygenic background and the disease phenotypes are modified by environmental factors. As a consequence, the phenotypic values usually show a quantitative variation. The phenotypes of such disease traits, however, are often measured in discrete but ordered categories. These traits are called ordinal traits. In terms of disease resistance, they are called quantitative resistance traits, as opposed to qualitative resistance traits, and are controlled by the quantitative resistance loci (QRL). Classical quantitative trait locus mapping methods are not optimal for ordinal trait analysis because the assumption of normal distribution is violated. Methods for mapping binary trait loci are not suitable either because there are more than two categories in ordinal traits. We developed a maximum likelihood method to map these QRL. The method is implemented via a multicycle expectation-conditional-maximization (ECM) algorithm under the threshold model, where we can estimate both the QRL effects and the thresholds that link the disease liability and the categorical phenotype. The method is verified in simulated data under various combinations of the parameters. An SAS program is available to implement the multicycle ECM algorithm. The program can be downloaded from our website at www.statgen.ucr.edu.     

A score test for the linkage analysis of qualitative and quantitative traits based on identity by descent data from sib-pairs

We propose a general likelihood-based approach to the linkage analysis of qualitative and quantitative traits using identity by descent (IBD) data from sib-pairs. We consider the likelihood of IBD data conditional on phenotypes and test the null hypothesis of no linkage between a marker locus and a gene influencing the trait using a score test in the recombination fraction theta between the two loci. This method unifies the linkage analysis of qualitative and quantitative traits into a single inferential framework, yielding a simple and intuitive test statistic. Conditioning on phenotypes avoids unrealistic random sampling assumptions and allows sib-pairs from differing ascertainment mechanisms to be incorporated into a single likelihood analysis. In particular, it allows the selection of sib-pairs based on their trait values and the analysis of only those pairs having the most informative phenotypes. The score test is based on the full likelihood, i.e. the likelihood based on all phenotype data rather than just differences of sib-pair phenotypes. Considering only phenotype differences, as in Haseman and Elston (1972) and Kruglyak and Lander (1995), may result in important losses in power. The linkage score test is derived under general genetic models for the trait, which may include multiple unlinked genes. Population genetic assumptions, such as random mating or linkage equilibrium at the trait loci, are not required. This score test is thus particularly promising for the analysis of complex human traits. The score statistic readily extends to accommodate incomplete IBD data at the test locus, by using the hidden Markov model implemented in the programs MAPMAKER/SIBS and GENEHUNTER (Kruglyak and Lander, 1995; Kruglyak et al., 1996). Preliminary simulation studies indicate that the linkage score test generally matches or outperforms the Haseman-Elston test, the largest gains in power being for selected samples of sib-pairs with extreme phenotypes.     

Molecular-Marker-Facilitated Investigations of Quantitative-Trait Loci in Maize. I. Numbers, Genomic Distribution and Types of Gene Action

Individual genetic factors which underlie variation in quantitative traits of maize were investigated in each of two F2 populations by examining the mean trait expressions of genotypic classes at each of 17-20 segregating marker loci. It was demonstrated that the trait expression of marker locus classes could be interpreted in terms of genetic behavior at linked quantitative trait loci (QTLs). For each of 82 traits evaluated, QTLs were detected and located to genomic sites. The numbers of detected factors varied according to trait, with the average trait significantly influenced by almost two-thirds of the marked genomic sites. Most of the detected associations between marker loci and quantitative traits were highly significant, and could have been detected with fewer than the 1800-1900 plants evaluated in each population. The cumulative, simple effects of marker-linked regions of the genome explained between 8 and 40% of the phenotypic variation for a subset of 25 traits evaluated. Single marker loci accounted for between 0.3% and 16% of the phenotypic variation of traits. Individual plant heterozygosity, as measured by marker loci, was significantly associated with variation in many traits. The apparent types of gene action at the QTLs varied both among traits and between loci for given traits, although overdominance appeared frequently, especially for yield-related traits. The prevalence of apparent overdominance may reflect the effects of multiple QTLs within individual marker-linked regions, a situation which would tend to result in overestimation of dominance. Digenic epistasis did not appear to be important in determining the expression of the quantitative traits evaluated. Examination of the effects of marked regions on the expression of pairs of traits suggests that genomic regions vary in the direction and magnitudes of their effects on trait correlations, perhaps providing a means of selecting to dissociate some correlated traits. Marker-facilitated investigations appear to provide a powerful means of examining aspects of the genetic control of quantitative traits. Modifications of the methods employed herein will allow examination of the stability of individual gene effects in varying genetic backgrounds and environments.     

Functional genetics of intraspecific ecological interactions in Arabidopsis thaliana

Studying the genetic basis of traits involved in ecological interactions is a fundamental part of elucidating the connections between evolutionary and ecological processes. Such knowledge allows one to link genetic models of trait evolution with ecological models describing interactions within and between species. Previous work has shown that connections between genetic and ecological processes in Arabidopsis thaliana may be mediated by the fact that quantitative trait loci (QTL) with 'direct' effects on traits of individuals also have pleiotropic 'indirect' effects on traits expressed in neighbouring plants. Here, we further explore these connections by examining functional relationships between traits affected directly and indirectly by the same QTL. We develop a novel approach using structural equation models (SEMs) to determine whether observed pleiotropic effects result from traits directly affected by the QTL in focal individuals causing the changes in the neighbours' phenotypes. This hypothesis was assessed using SEMs to test whether focal plant phenotypes appear to mediate the connection between the focal plants' genotypes and the phenotypes of their neighbours, or alternatively, whether the connection between the focal plants' genotypes and the neighbours' phenotypes is mediated by unmeasured traits. We implement this analysis using a QTL of major effect that maps to the well-characterized flowering locus, FRIGIDA. The SEMs support the hypothesis that the pleiotropic indirect effects of this locus arise from size and developmental timing-related traits in focal plants affecting the expression of developmental traits in their neighbours. Our findings provide empirical insights into the genetics and nature of intraspecific ecological interactions. Our technique holds promise in directing future work into the genetic basis and functional relationship of traits mediating and responding to ecological interactions.     

The spatial scale of local adaptation in a stochastic environment

The distribution of phenotypes in space will be a compromise between adaptive plasticity and local adaptation increasing the fit of phenotypes to local conditions and gene flow reducing that fit. Theoretical models on the evolution of quantitative characters on spatially explicit landscapes have only considered scenarios where optimum trait values change as deterministic functions of space. Here, these models are extended to include stochastic spatially autocorrelated aspects to the environment, and consequently the optimal phenotype. Under these conditions, the regression of phenotype on the environmental variable becomes steeper as the spatial scale on which populations are sampled becomes larger. Under certain deterministic models – such as linear clines – the regression is constant. The way in which the regression changes with spatial scale is informative about the degree of phenotypic plasticity, the relative scale of effective gene flow and the environmental dependency of selection. Connections to temporal models are discussed.     

Evolution and maintenance of the environmental component of the phenotypic variance: benefit of plastic traits under changing environments

How environmental variances in quantitative traits are influenced by variable environments is an important problem in evolutionary biology. In this study, the evolution and maintenance of phenotypic variance in a plastic trait under stabilizing selection are investigated. The mapping from genotypic value to phenotypic value of the quantitative trait is approximated by a linear reaction norm, with genotypic effects on its phenotypic mean and sensitivity to environment. The environmental deviation is assumed to be decomposed into environmental quality, which interacts with genotypic value, and residual developmental noise, which is independent of genotype. Environmental quality and the optimal phenotype of stabilizing selection are allowed to randomly fluctuate in both space and time, and individuals migrate equally before development and reproduction among different niches. Analyses show that phenotypic plasticity is adaptive within variable environments if correlations have become established between the optimal phenotype and environmental quality in space and/or time. The evolved plasticity increases with variances in optimal phenotypes and correlations between optimal phenotype and environmental quality; this further induces increases in mean fitness and the environmental variance in the trait. Under certain circumstances, however, the environmental variance may decrease with increase in variation in environmental quality.     

Selective Genotyping and Phenotyping Strategies in a Complex Trait Context

Selective genotyping and phenotyping strategies are used to lower the cost of quantitative trait locus studies. Their efficiency has been studied primarily in simplified contexts—when a single locus contributes to the phenotype, and when the residual error (phenotype conditional on the genotype) is normally distributed. It is unclear how these strategies will perform in the context of complex traits where multiple loci, possibly linked or epistatic, may contribute to the trait. We also do not know what genotyping strategies should be used for nonnormally distributed phenotypes. For time-to-event phenotypes there is the additional question of choosing follow-up time duration. We use an information perspective to examine these experimental design issues in the broader context of complex traits and make recommendations on their use.     

Dissecting the correlation structure of a bivariate phenotype: Common genes or shared environment?

High correlations between two quantitative traits may be either due to common genetic factors or common environmental factors or a combination of both. In this study, we develop statistical methods to extract the genetic contribution to the total correlation between the components of a bivariate phenotype. Using data on bivariate phenotypes and marker genotypes for sib-pairs, we propose a test for linkage between a common QTL and a marker locus based on the conditional cross-sib trait correlations (trait 1 of sib 1—trait 2 of sib 2 and conversely) given the identity-by-descent (i.b.d.) sharing at the marker locus. We use Monte-Carlo simulations to evaluate the performance of the proposed test under different trait parameters and quantitative trait distributions. An application of the method is illustrated using data on two alcohol-related phenotypes from a project on the collaborative study on the genetics of alcoholism.     

A stochastic expectation and maximization algorithm for detecting quantitative trait-associated genes

MOTIVATION: Most biological traits may be correlated with the underlying gene expression patterns that are partially determined by DNA sequence variation. The correlations between gene expressions and quantitative traits are essential for understanding the functions of genes and dissecting gene regulatory networks. RESULTS: In the present study, we adopted a novel statistical method, called the stochastic expectation and maximization (SEM) algorithm, to analyze the associations between gene expression levels and quantitative trait values and identify genetic loci controlling the gene expression variations. In the first step, gene expression levels measured from microarray experiments were assigned to two different clusters based on the strengths of their association with the phenotypes of a quantitative trait under investigation. In the second step, genes associated with the trait were mapped to genetic loci of the genome. Because gene expressions are quantitative, the genetic loci controlling the expression traits are called expression quantitative trait loci. We applied the same SEM algorithm to a real dataset collected from a barley genetic experiment with both quantitative traits and gene expression traits. For the first time, we identified genes associated with eight agronomy traits of barley. These genes were then mapped to seven chromosomes of the barley genome. The SEM algorithm and the result of the barley data analysis are useful to scientists in the areas of bioinformatics and plant breeding. Availability and implementation: The R program for the SEM algorithm can be downloaded from our website: http://www.statgen.ucr.edu.     

Bivariate association analysis for quantitative traits using generalized estimation equation

Quantitative traits often underlie risk for complex diseases. Many studies collect multiple correlated quantitative phenotypes and perform univariate analyses on each of them respectively. However, this strategy may not be powerful and has limitations to detect plei- otropic genes that may underlie correlated quantitative traits. In addition, testing multiple traits individually will exacerbate perplexing problem of multiple testing. In this study, generalized estimating equation 2 （GEE2） is applied to association mapping of two correlated quantitative traits. We suppose that a quantitative trait locus is located in a chromosome region that exerts pleiotropic effects on multiple quantitative traits. In that region, multiple SNPs are genotyped. Genotypes of these SNPs and the two quantitative traits affected by a causal SNP were simulated under various parameter values： residual correlation coefficient between two traits, causal SNP heritability, minor allele frequency of the causal SNP, extent of linkage disequilibrium with the causal SNP, and the test sample size. By power ana- lytical analyses, it is showed that the bivariate method is generally more powerful than the univariate method. This method is robust and yields false-positive rates close to the pre-set nominal significance level. Our real data analyses attested to the usefulness of the method.     

Verification of marker–trait associations in biparental winter barley (<Emphasis Type="Italic">Hordeum vulgare</Emphasis> L.) DH populations

In previous genome-wide association studies, marker–trait associations for grain yield and additional traits of agronomic importance were identified in the German winter barley (Hordeum vulgare L.) breeding gene pool. In the present study, seven doubled haploid populations segregating for the relevant alleles at the associated loci were used to get information whether these marker–trait associations can be verified in biparental populations and reliably used in applied barley breeding. The doubled haploid populations were phenotyped in field trials at two to five locations each in 1 year and genotyped by 40 trait-associated single nucleotide polymorphisms using an Illumina VeraCode GoldenGate assay. Large phenotypic variation was observed for all traits within at least one doubled haploid population. For 19 out of 58 marker–trait associations tested, the phenotypic means of both marker classes were significantly (p ≤ 0.005) different, thus confirming the association of the respective marker and the quantitative trait locus detected. For example, doubled haploid lines derived from a cross of ‘Malta’ × ‘Goldmine’ carrying different marker alleles differed by 0.41 t/ha in mean grain yield. The 19 (out of 58) marker–trait associations verified correspond to 10 (out of 27) genomic regions. Markers that were verified to be associated with a quantitative trait locus can be implemented directly in winter barley breeding for the selection of parental lines and marker-assisted pedigree selection.     

DNA-marking of quantitative traits in corn

Methods of ISSR- and RAPD-analyses were used for marking quantitative trait loci (QTLs) determining the development of some morphological and biological traits in maize. Specificity of marker locus alleles was established for certain levels of polygenic trait phenotype manifestation. Criteria of marker locus informativity are discussed. A possibility of marker-assisted selection for valuable genotypes with desired for breeding trait values was demonstrated.     

Trait-based analyses for the detection of linkage between marker loci and quantitative trait loci in crosses between inbred lines

Summary Methods are presented for determining linkage between a marker locus and a nearby locus affecting a quantitative trait (quantitative trait locus=QTL), based on changes in the marker allele frequencies in selection lines derived from the F-2 of a cross between inbred lines, or in the high and low phenotypic classes of an F-2 or BC population. The power of such trait-based (TB) analyses was evaluated and compared with that of methods for determining linkage based on the mean quantitative trait value of marker genotypes in F-2 or BC populations [marker-based (MB) analyses]. TB analyses can be utilized for marker-QTL linkage determination in situations where the MB analysis is not applicable, including analysis of polygenic resistance traits where only a part of the population survives exposure to the Stressor and analysis of marker-allele frequency changes in selection lines. TB analyses may be a useful alternative to MB analyses when interest is centered on a single quantitative trait only and costs of scoring for markers are high compared with costs of raising and obtaining quantitative trait information on F-2 or BC individuals. In this case, a TB analysis will enable equivalent power to be obtained with fewer individuals scored for the marker, but more individuals scored for the quantitative trait. MB analyses remain the method of choice when more than one quantitative trait is to be analyzed in a given population.Contribution from the ARO, Bet Dagan, Israel. No. 1698-E, 1986 series     

Exploiting genomic resources in studies of speciation and adaptive radiation of lizards in the genus Anolis

Lizards in the genus Anolis have radiated extensively within and among islands in the Caribbean. Here, I provide a prospectus for identifying genes underlying adaptive phenotypic traits in anoles. First I review patterns of diversification in Anolis and the important morphological axes along which divergence occurs. Then I discuss two features of anole diversification, the repeated, convergent evolution of ecomorphs, and phenotypic divergence among populations within species, that provide opportunities to identify genes underlying adaptive phenotypic variation. While small clutch size and difficulty with captive rearing currently limit the utility of quantitative trait locus analyses, comparative analyses of gene expression, and population genomic approaches are promising.     

Tests for major genes affecting quantitative traits in wild radish,Raphanus raphanistrum

The number of gene loci coding for quantitative traits is an important issue in genetics. However, there are still very few empirical data on this point, especially in natural populations. I tested for major gene effects on ten quantitative traits in wild radish, using an indirect method based on the patterns of family means and within and between family variances for traits. This method should reveal whether a single locus is responsible for most of the variation in a trait. Eight of the traits measured were morphological dimensions of leaves and flowers; no strong evidence for major gene effects on these traits was found. In contrast, evidence for major gene effects was found in the other two traits, emergence time and flowering time.     

Statistical models for trisomic phenotypes.

Certain genetic disorders are rare in the general population but more common in individuals with specific trisomies, which suggests that the genes involved in the etiology of these disorders may be located on the trisomic chromosome. As with all aneuploid syndromes, however, a considerable degree of variation exists within each phenotype so that any given trait is present only among a subset of the trisomic population. We have previously presented a simple gene-dosage model to explain this phenotypic variation and developed a strategy to map genes for such traits. The mapping strategy does not depend on the simple model but works in theory under any model that predicts that affected individuals have an increased likelihood of disomic homozygosity at the trait locus. This paper explores the robustness of our mapping method by investigating what kinds of models give an expected increase in disomic homozygosity. We describe a number of basic statistical models for trisomic phenotypes. Some of these are logical extensions of standard models for disomic phenotypes, and some are more specific to trisomy. Where possible, we discuss genetic mechanisms applicable to each model. We investigate which models and which parameter values give an expected increase in disomic homozygosity in individuals with the trait. Finally, we determine the sample sizes required to identify the increased disomic homozygosity under each model. Most of the models we explore yield detectable increases in disomic homozygosity for some reasonable range of parameter values, usually corresponding to smaller trait frequencies. It therefore appears that our mapping method should be effective for a wide variety of moderately infrequent traits, even though the exact mode of inheritance is unlikely to be known.     

The application of the entropy-based statistic for genomic association study of QTL

An entropy-based statistic TPE has been proposed for genomic association study for disease-susceptibility locus.The statistic TPE may be directly adopted and/or extended to quantitative-trait locus (QTL)mapping for quantitative traits.In this article,the statistic TPE was extended and applied to quantitative trait for association analysis of QTL by means of selective genotyping.The statistical properties (the type I error rate and the power) were examined under a range of parameters and population-sampling strategies (e.g.,various genetic models,various heritabilities,and various sample-selection threshold values) by simulation studies.The results indicated that the statistic Tee is robust and powerful for genomic association study of QTL.A simulation study based on the haplotype frequencies of 10 single nucleotide polymorphisms (SNPs) of angiotensin-I converting enzyme genes was conducted to evaluate the performance of the statistic TPE for genetic association study.     

Evolutionary Distributions and Competition by Way of Reaction-Diffusion and by Way of Convolution

Evolution by natural selection is the most ubiquitous and well understood process of evolution. We say distribution instead of the distribution of the density of populations of phenotypes across the values of their adaptive traits. A phenotype refers to an organism that exhibits a set of values of adaptive traits. An adaptive trait is a trait that a phenotype exhibits where the trait is subject to natural selection. Natural selection is a process by which populations of different phenotypes decline at different rates. An evolutionary distribution (ED) encapsulates the dynamics of evolution by natural selection. The main results are: (i) ED are derived by way of PDE of reaction-diffusion type and by way of integro-differential equations. The latter capture mutations through convolution of a kernel with the rate of growth of a population. The kernel controls the size and rate of mutations. (ii) The numerical solution of a logistic-like ED driven by competition corresponds to a bounded traveling wave solution of population models based on the logistic. (iii) Competition leads to increase in diversity of phenotypes on a single ED. Diversity refers to change in the number of local maxima (minima) within the bounds of values of adaptive traits. (iv) The principle of competitive exclusion in the context of evolution depends, smoothly, on the size and rate of mutations. (v) We identify the sensitivity—with respect to survival—of phenotypes to changes in values of adaptive traits to be an important parameter: increase in the value of this parameter results in decrease in evolutionary-based diversity. (vi) Stable ED corresponds to Evolutionary Stable Strategy; the latter refers to the outcome of a game of evolution.