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A comparison between methods for linkage disequilibrium fine mapping of quantitative trait loci.

We present a maximum likelihood method for mapping quantitative trait loci that uses linkage disequilibrium information from single and multiple markers. We made paired comparisons between analyses using a single marker, two markers and six markers. We also compared the method to single marker regression analysis under several scenarios using simulated data. In general, our method outperformed regression (smaller mean square error and confidence intervals of location estimate) for quantitative trait loci with dominance effects. In addition, the method provides estimates of the frequency and additive and dominance effects of the quantitative trait locus.

Chromosome Mapping↗

TDT statistics for mapping quantitative trait loci.

The original transmission disequilibrium test (TDT), was introduced to test for linkage between a marker and a disease-susceptibility locus (Spielman et al. 1993). Allison (1997) extended the TDT procedure to quantitative traits. Allison's test, however, is restrictive in that it requires family trios consisting of one heterozygous parent, one homozygous parent and one child, and considers only the situation where the marker locus is analogous to the quantitative trait locus itself. In this paper, we propose, investigate and apply a general TDT for quantitative traits that permits more than one child per family, does not require only one parent to be heterozygous, and allows for the fact that the various alleles at the marker and trait loci may be at varying degree of linkage disequilibrium. We also show that this TDT for quantitative traits is still a valid test of linkage in the presence of population substructure. To provide guidelines for study design, we develop analytic formulae for calculation of the power of the TDT for mapping quantitative trait loci and investigate the impact of various factors on the power. Power calculations show that the proposed TDT for quantitative traits is more powerful than Allison's basic test statistic and the extreme discordant sib pair linkage method. The proposed TDT statistic for quantitative traits is applied to systolic blood pressure variation in the Rochester Family Heart Study using an extremely discordant sibling pair design.

Alleles↗

Power and robustness of linkage tests for quantitative traits in general pedigrees.

There are numerous statistical methods for quantitative trait linkage analysis in human studies. An ideal such method would have high power to detect genetic loci contributing to the trait, would be robust to non-normality in the phenotype distribution, would be appropriate for general pedigrees, would allow the incorporation of environmental covariates, and would be appropriate in the presence of selective sampling. We recently described a general framework for quantitative trait linkage analysis, based on generalized estimating equations, for which many current methods are special cases. This procedure is appropriate for general pedigrees and easily accommodates environmental covariates. In this report, we use computer simulations to investigate the power and robustness of a variety of linkage test statistics built upon our general framework. We also propose two novel test statistics that take account of higher moments of the phenotype distribution, in order to accommodate non-normality. These new linkage tests are shown to have high power and to be robust to non-normality. While we have not yet examined the performance of our procedures in the context of selective sampling via computer simulations, the proposed tests satisfy all of the other qualities of an ideal quantitative trait linkage analysis method.

Algorithms↗

A random model approach to mapping quantitative trait loci for complex binary traits in outbred populations.

Mapping quantitative trait loci (QTL) for complex binary traits is more challenging than for normally distributed traits due to the nonlinear relationship between the observed phenotype and unobservable genetic effects, especially when the mapping population contains multiple outbred families. Because the number of alleles of a QTL depends on the number of founders in an outbred population, it is more appropriate to treat the effect of each allele as a random variable so that a single variance rather than individual allelic effects is estimated and tested. Such a method is called the random model approach. In this study, we develop the random model approach of QTL mapping for binary traits in outbred populations. An EM-algorithm with a Fisher-scoring algorithm embedded in each E-step is adopted here to estimate the genetic variances. A simple Monte Carlo integration technique is used here to calculate the likelihood-ratio test statistic. For the first time we show that QTL of complex binary traits in an outbred population can be scanned along a chromosome for their positions, estimated for their explained variances, and tested for their statistical significance. Application of the method is illustrated using a set of simulated data.

Breeding↗

Correcting for bias in estimation of quantitative trait loci effects.

Estimates of quantitative trait loci (QTL) effects derived from complete genome scans are biased, if no assumptions are made about the distribution of QTL effects. Bias should be reduced if estimates are derived by maximum likelihood, with the QTL effects sampled from a known distribution. The parameters of the distributions of QTL effects for nine economic traits in dairy cattle were estimated from a daughter design analysis of the Israeli Holstein population including 490 marker-by-sire contrasts. A separate gamma distribution was derived for each trait. Estimates for both the alpha and beta parameters and their SE decreased as a function of heritability. The maximum likelihood estimates derived for the individual QTL effects using the gamma distributions for each trait were regressed relative to the least squares estimates, but the regression factor decreased as a function of the least squares estimate. On simulated data, the mean of least squares estimates for effects with nominal 1% significance was more than twice the simulated values, while the mean of the maximum likelihood estimates was slightly lower than the mean of the simulated values. The coefficient of determination for the maximum likelihood estimates was five-fold the corresponding value for the least squares estimates.

Algorithms↗

The genetic architecture of selection response. Inferences from fine-scale mapping of bristle number quantitative trait loci in Drosophila melanogaster.

Quantitative trait loci (QTL) affecting responses and correlated responses to selection for abdominal and sternopleural bristle number have been mapped with high resolution to the X and third chromosomes. Advanced intercross recombinant isogenic chromosomes were constructed from high and low selection lines in an unselected inbred background, and QTL were detected using composite interval mapping and high density transposable element marker maps. We mapped a total of 26 bristle number QTL with large effects, which were in or immediately adjacent to intervals previously inferred to contain bristle number QTL on these chromosomes. The QTL contributing to response to selection for high bristle number were not the same as those contributing to response to selection for low bristle number, suggesting that distributions of allelic effects per locus may be asymmetrical. Correlated responses were more often attributable to loose linkage than pleiotropy or close linkage. Bristle number QTL mapping to the same locations have been inferred in studies with different parental strains. Of the 26 QTL, 20 mapped to locations consistent with candidate genes affecting peripheral nervous system development and/or bristle number. This facilitates determining the molecular basis of quantitative variation and allele frequencies by associating molecular variation at the candidate genes with phenotypic variation in bristle number in samples of alleles from nature.

Alleles↗

Nonparametric estimation of the effects of quantitative trait loci.

Interval mapping of quantitative trait loci from breeding experiments plays an important role in understanding the mechanisms of disease, both in humans and other organisms. Standard approaches to estimation involve parametric assumptions for the component distributions and may be sensitive to model misspecification. Some nonparametric tests have been studied. However, nonparametric estimation of the phenotypic distributions has not been considered in the genetics literature, even though such methods might provide essential nonparametric summaries for comparing different loci. We develop a sufficient condition for identifiability of the phenotypic distributions. Simple nonparametric estimators for the distributions are proposed for uncensored and right censored data. They have a closed form and their small and large sample properties are readily established. Their practical utility as numerical summaries which complement nonparametric tests is demonstrated on two recent genetics examples.

Animals↗

Mapping of quantitative trait loci for growth and carcass traits in commercial sheep populations.

Quantitative trait loci analyses were applied to data from Suffolk and Texel commercial sheep flocks in the United Kingdom. The populations comprised 489 Suffolk animals in three half-sib families and 903 Texel animals in nine half-sib families. Phenotypic data comprised measurements of live weight at 8 and 20 wk of age and ultrasonically measured fat and muscle depth at 20 wk. Lambs and their sires were genotyped across candidate regions on chromosomes 1, 2, 3, 4, 5, 6, 11, 18, and 20. Data were analyzed at the breed level, at the family level, and across extended families when families were genetically related. The breed-level analyses revealed a suggestive QTL on chromosome 1 in the Suffolk breed, between markers BM8246 and McM130, affecting muscle depth, although the effect was only significant in one of the three Suffolk families. A two-QTL analysis suggested that this effect may be due to two adjacent QTL acting in coupling. In total, 24 suggestive QTL were identified from individual family analyses. The most significant QTL affected fat depth and was segregating in a Texel family on chromosome 2, with an effect of 0.62 mm. The QTL was located around marker ILSTS030, 26 cM distal to myostatin. Two of the Suffolk and two of the Texel sires were related, and a three-generation analysis was applied across these two extended families. Seven suggestive QTL were identified in this analysis, including one that had not been detected in the individual family analysis. The most significant QTL, which affected muscle depth, was located on chromosome 18 near the callipyge and Carwell loci. Based on the phenotypic effect and location of the QTL, the data suggest that a locus similar to the Carwell locus may be segregating in the United Kingdom Texel population.

Adipose Tissue↗

Estimating the genetic architecture of quantitative traits.

Understanding and estimating the structure and parameters associated with the genetic architecture of quantitative traits is a major research focus in quantitative genetics. With the availability of a well-saturated genetic map of molecular markers, it is possible to identify a major part of the structure of the genetic architecture of quantitative traits and to estimate the associated parameters. Multiple interval mapping, which was recently proposed for simultaneously mapping multiple quantitative trait loci (QTL), is well suited to the identification and estimation of the genetic architecture parameters, including the number, genomic positions, effects and interactions of significant QTL and their contribution to the genetic variance. With multiple traits and multiple environments involved in a QTL mapping experiment, pleiotropic effects and QTL by environment interactions can also be estimated. We review the method and discuss issues associated with multiple interval mapping, such as likelihood analysis, model selection, stopping rules and parameter estimation. The potential power and advantages of the method for mapping multiple QTL and estimating the genetic architecture are discussed. We also point out potential problems and difficulties in resolving the details of the genetic architecture as well as other areas that require further investigation. One application of the analysis is to improve genome-wide marker-assisted selection, particularly when the information about epistasis is used for selection with mating.

Algorithms↗

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.

Chromosome Mapping↗

Detection and positional cloning of blood pressure quantitative trait loci: is it possible? Identifying the genes for genetic hypertension.

Identification of the quantitative trait loci that influence blood pressure and cause genetic hypertension is a major challenge. Several genetically hypertensive rat strains exist and can be used to locate by linkage analysis broad chromosomal regions containing blood pressure quantitative trait loci. Such broad chromosomal regions, and the narrower subregions, can be moved among strains (ie, production of congenic strains and congenic substrains) to identify small chromosomal regions containing the blood pressure quantitative trait loci. However, ultimate positional cloning of the quantitative trait loci presents a major difficulty because the genetic variants involved are likely to result in subtle changes in function rather than the blatant loss of function characteristic of all mendelian disease genes discovered so far by positional cloning.

Animals↗

Complementation testing identifies genes mediating effects at quantitative trait loci underlying fear-related behavior.

Knowing the genes involved in quantitative traits provides an entry point to understanding the biological bases of behavior, but there are very few examples where the pathway from genetic locus to behavioral change is known. To explore the role of specific genes in fear behavior, we mapped three fear-related traits, tested fourteen genes at six quantitative trait loci (QTLs) by quantitative complementation, and identified six genes. Four genes, Lamp, Ptprd, Nptx2, and Sh3gl, have known roles in synapse function; the fifth, Psip1, was not previously implicated in behavior; and the sixth is a long non-coding RNA, 4933413L06Rik, of unknown function. Variation in transcriptome and epigenetic modalities occurred preferentially in excitatory neurons, suggesting that genetic variation is more permissible in excitatory than inhibitory neuronal circuits. Our results relieve a bottleneck in using genetic mapping of QTLs to uncover biology underlying behavior and prompt a reconsideration of expected relationships between genetic and functional variation.

Animals↗

Mapping and manipulating quantitative traits in maize.

Maize has been used effectively as a model organism in the development and evaluation of molecular markers for the identification, mapping and manipulation of major genes affecting the expression of quantitative traits in plants. Although quantitative geneticists have recognized the possibility of major loci, the general dogma had emerged that quantitative traits were controlled by many loci, each with a small effect. This interpretation sent a quantitative traits because it would be essentially impossible to isolate a gene responsible for the trait. Recent results from numerous mapping studies have shown that quantitative traits are controlled by, at least some, factors with major effects, and have given credibility to the conclusion that major loci exist and that one might be able to study them. Positive results from marker-facilitated selection and introgression studies have further strengthened this conclusion.

Chromosome Mapping↗

Population genetic structure in a Mediterranean pine (Pinus pinaster Ait.): a comparison of allozyme markers and quantitative traits.

F-statistics were employed to analyse quantitative and allozyme variation among 19 native populations of maritime pine (Pinus pinaster Ait.). Fourteen polymorphic allozyme loci were used to provide an empirical basis for constructing a null hypothesis to test natural selection as a determinant of quantitative evolution in stem form, total height growth and survival at 30 years old. Hidden biases, that may result in a difference between quantitative (Q(ST)) and allozyme (F(ST)) differentiation which are not because of the action of natural selection, were avoided by comparing pairs of populations using linear models. All quantitative traits showed higher differentiation than allozymes. The highest divergence was found in stem form, whereas divergences in total height and survival were significantly lower. Differential adaptation to regional and local patterns of precipitation, temperature and soil type seem to be the best explanation of the different structure found in quantitative traits and allozyme loci. Possible bias in the estimation of Q(ST) due to the level of quantitative within-population diversity and the role of adaptation of maritime pine after the last glaciation to highly diverse ecological conditions are discussed with special reference to the actual geographical structure of gene diversity in the species' native range.

Analysis of Variance↗

Identifying candidate genes for blood pressure quantitative trait loci using differential gene expression and a panel of congenic strains.

The most difficult step in dissecting the molecular basis of a quantitative trait is proceeding from chromosomal locations associated with this trait (i.e., quantitative trait locus, QTL) to determining what gene(s) in the QTL region is causative. Using standard positional cloning methodology to identify candidate genes for a particular QTL has three drawbacks: 1) it is labor intensive; 2) defining variants in genes causing quantitative variation from sequence information alone is difficult or impossible; and 3) many (or most) genes in a particular chromosomal interval will not be relevant for a specific disease/trait because they are not expressed in critical candidate organs. Instead of positional cloning, we propose using a panel of congenic strains, where each carries an allele for a different QTL on a similar genetic background, in conjunction with identification of differentially-expressed genes in target organs of inbred strains of contrasting phenotype. This will identify genes having altered expression in organs critical to regulating blood pressure and the development of hypertension. Radiation hybrid mapping of such genes will result in a transcription map of differentially-expressed genes in a target organ of a rat model of genetic hypertension. This approach could rapidly identify genes mapping to genomic regions near QTL, which will be strong candidates to explain, in part, the observed strain differences in blood pressure. This novel approach, which uses a panel of congenic strains to facilitate the mapping and subsequent identification of differentially-expressed and QTL-associated genes, should be applicable to any genetic model for identifying candidate genes located near QTL, given the availability of a panel of congenic strains.

Animals↗

Detection of major genes underlying several quantitative traits associated with a common disease using different ascertainment schemes.

Using the Problem 2A data sets of GAW10, we assessed the power of four ascertainment schemes to localize major genes underlying a disease trait; the schemes were based on disease or quantitative trait status of nuclear families. MAPMAKER/SIBS was used to perform sib-pair analysis for all four data sets using marker data from three chromosomes, 4, 5 and 8. Each scheme varied in power to identify major genes underlying the quantitative traits depending on the genetic architecture of the data set. Three different methods, Haseman-Elston quantitative trait locus (QTL) regression analysis, maximum likelihood variance estimation and a non-parametric method, were used to assess the strength of linkage in all four data sets. False positive mappings localizing to the same region of the genome, verifiable across all three methods did not occur. Two major genes, MG1 and MG2, were successfully assigned to chromosomes 5 and 8, respectively, by at least one of the ascertainment schemes. MG1 was localized under two schemes, selection of families with exactly two affected sibs and selection of families with two sibs who had extremely discordant values for Q1. Additional weak evidence of the location of MG1 was also obtained under the other two ascertainment schemes. MG2 could not be detected by analyzing data sets ascertained either by affected sib pairs or by sib pairs with extremely discordant values for Q1. In the data set ascertained by a third strategy, selection of families with sib pairs extremely discordant for Q2, MG2 could be mapped to chromosome 8. A random ascertainment scheme yielded a data set in which we could find weak evidence for MG1 and no evidence for MG2. Thus our ability to detect major genes underlying the QTL depended on several factors which included the ascertainment scheme, the population allele frequencies, linkage and epistasis.

Chromosome Mapping↗

Joint mapping of quantitative trait Loci for multiple binary characters.

Joint mapping for multiple quantitative traits has shed new light on genetic mapping by pinpointing pleiotropic effects and close linkage. Joint mapping also can improve statistical power of QTL detection. However, such a joint mapping procedure has not been available for discrete traits. Most disease resistance traits are measured as one or more discrete characters. These discrete characters are often correlated. Joint mapping for multiple binary disease traits may provide an opportunity to explore pleiotropic effects and increase the statistical power of detecting disease loci. We develop a maximum-likelihood method for mapping multiple binary traits. We postulate a set of multivariate normal disease liabilities, each contributing to the phenotypic variance of one disease trait. The underlying liabilities are linked to the binary phenotypes through some underlying thresholds. The new method actually maps loci for the variation of multivariate normal liabilities. As a result, we are able to take advantage of existing methods of joint mapping for quantitative traits. We treat the multivariate liabilities as missing values so that an expectation-maximization (EM) algorithm can be applied here. We also extend the method to joint mapping for both discrete and continuous traits. Efficiency of the method is demonstrated using simulated data. We also apply the new method to a set of real data and detect several loci responsible for blast resistance in rice.

Algorithms↗

Contrasting evolutionary forces driving population structure at expressed sequence tag polymorphisms, allozymes and quantitative traits in white spruce.

Patterns of variation in quantitative characters and genetic markers were compared among six regional populations of white spruce [Picea glauca (Moench) Voss]. Although some phenotypic characters were correlated with latitude (r = 0.791), longitude (r = -0.796) and precipitation during the growing season (r = 0.789), variability at genetic markers was not correlated with geographical or bioclimatic variables, and followed neutral expectations. Estimates of genetic diversity and population differentiation for 14 allozymes (translated regions of coding genes) were essentially indistinguishable from those observed for 11 expressed sequence tag polymorphisms (ESTPs) from untranslated regions of coding genes. Variation among populations for quantitative traits such as eighth year height (Q(ST) = 0.082), thirteenth year height (Q(ST) = 0.069), total wood density (Q(ST) = 0.102) and date of budset (Q(ST) = 0.246), was greater than for allozymes (G(ST) = 0.014) and ESTPs (G(ST) = 0.019). These trends suggest a strong adaptive response in quantitative traits, contrasting to allozymes and ESTPs where no selective response could be detected and where populations appeared to be essentially in a migration-drift equilibrium.

DNA, Plant↗