Multiple trait analysis of genetic mapping for quantitative trait loci

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.

Joint multipoint linkage analysis of multivariate qualitative and quantitative traits. II. Alcoholism and event-related potentials

The availability of robust quantitative biological markers that are correlated with qualitative psychiatric phenotypes can potentially improve the power of linkage methods to detect quantitative-trait loci influencing psychiatric disorders. We apply a variance-component method for joint multipoint linkage analysis of multivariate discrete and continuous traits to the extended pedigree data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate analysis of qualitative alcoholism phenotypes and quantitative event-related potentials. Joint consideration of the DSM-IV diagnosis of alcoholism and the amplitude of the P300 component of the Cz event-related potential significantly increases the evidence for linkage of these traits to a chromosome 4 region near the class I alcohol dehydrogenase locus ADH3. A likelihood-ratio test for complete pleiotropy is significant, suggesting that the same quantitative-trait locus influences both risk of alcoholism and the amplitude of the P300 component.

Joint multipoint linkage analysis of multivariate qualitative and quantitative traits. I. Likelihood formulation and simulation results

We describe a variance-components method for multipoint linkage analysis that allows joint consideration of a discrete trait and a correlated continuous biological marker (e.g., a disease precursor or associated risk factor) in pedigrees of arbitrary size and complexity. The continuous trait is assumed to be multivariate normally distributed within pedigrees, and the discrete trait is modeled by a threshold process acting on an underlying multivariate normal liability distribution. The liability is allowed to be correlated with the quantitative trait, and the liability and quantitative phenotype may each include covariate effects. Bivariate discrete-continuous observations will be common, but the method easily accommodates qualitative and quantitative phenotypes that are themselves multivariate. Formal likelihood-based tests are described for coincident linkage (i.e., linkage of the traits to distinct quantitative-trait loci [QTLs] that happen to be linked) and pleiotropy (i.e., the same QTL influences both discrete-trait status and the correlated continuous phenotype). The properties of the method are demonstrated by use of simulated data from Genetic Analysis Workshop 10. In a companion paper, the method is applied to data from the Collaborative Study on the Genetics of Alcoholism, in a bivariate linkage analysis of alcoholism diagnoses and P300 amplitude of event-related brain potentials.

High-resolution mapping of quantitative trait loci in outbred mice

Screening the whole genome of a cross between two inbred animal strains has proved to be a powerful method for detecting genetic loci underlying quantitative behavioural traits, but the level of resolution offered by quantitative trait loci (QTL) mapping is still too coarse to permit molecular cloning of the genetic determinants. To achieve high-resolution mapping, we used an outbred stock of mice for which the entire genealogy is known. The heterogeneous stock (HS) was established 30 years ago from an eight-way cross of C57BL/6, BALB/c, RIII, AKR, DBA/2, I, A/J and C3H inbred mouse strains. At the time of the experiment reported here, the HS mice were at generation 58, theoretically offering at least a 30-fold increase in resolution for QTL mapping compared with a backcross or an F2 intercross. Using the HS mice we have mapped a QTL influencing a psychological trait in mice to a 0.8-cM interval on chromosome 1. This method allows simultaneous fine mapping of multiple QTLs, as shown by our report of a second QTL on chromosome 12. The high resolution possible with this approach makes QTLs accessible to positional cloning.

Interacting quantitative trait loci control phenotypic variation in murine estradiol-regulated responses

The steroid hormone estradiol (E2) elicits a spectrum of systemic and uterotropic responses in vivo. For example, E2 treatment of ovariectomized adult and sexually immature rodents leads to uterine leukocytic infiltration, cell proliferation, and organ growth. E2-regulated growth is also associated with a variety of normal and pathological phenotypes. Historically, the uterine growth response has been used as the key model to understand the molecular and biochemical mechanisms underlying E2-dependent growth. In this study, genome exclusion mapping identified two quantitative trait loci (QTL) in the mouse, Est2 and Est3 on chromosomes 5 and 11, respectively, that control the phenotypic variation in uterine wet weight. Both QTL are linked to a variety of E2-regulated genes, suggesting that they may represent loci within conserved gene complexes that play fundamental roles in mediating the effects of E2. Interaction and multiple trait analyses using the uterine leukocyte response and wet weight suggest that Est4, a QTL on chromosome 10, may encode an interacting factor that influences the quantitative variation in both responses. Our results show that E2-dependent responses can be genetically controlled and that a genetic basis may underlie the variation observed in many E2-dependent phenotypes.

Multiple-trait quantitative trait loci analysis using a large mouse sibship

Quantitative trait loci influencing several phenotypes were assessed using a genetically heterogeneous mouse population. The 145 individuals were produced by a cross between (BALB/cJ x C57BL/6J)F1 females and (C3H/HeJ x DBA/2J)F1 males. The population is genetically equivalent to full siblings derived from heterozygous parents, with known linkage phase. Each individual in the population represents a unique combination of alleles from the inbred grandparents. Quantitative phenotypes for eight T cell measures were obtained at 8 and 18 mo of age. Single-marker locus, repeated measures analysis of variance identified nine marker-phenotype associations with an experimentwise significance level of P < 0.05. Six of the eight quantitative phenotypes could be associated with at least one locus having experiment-wide significance. Composite interval, repeated measures analysis of variance identified 13 chromosomal regions with comparisonwise (nominal) significance associations of P < 0.001. The heterozygous-parent cross provides a reproducible, general method for identification of loci associated with quantitative trait phenotypes or repeated phenotypic measures.

Multiple-trait mapping of quantitative trait loci after selective genotyping using logistic regression

Experiments to map QTL usually measure several traits, and not uncommonly genotype only those animals that are extreme for some trait(s). Analysis of selectively genotyped, multiple-trait data presents special problems, and most simple methods lead to biased estimates of the QTL effects. The use of logistic regression to estimate QTL effects is described, where the genotype is treated as the dependent variable and the phenotype as the independent variable. In this way selection on phenotype does not bias the results. If normally distributed errors are assumed, the logistic-regression analysis is almost equivalent to a maximum-likelihood analysis, but can be carried out with standard statistical packages. Analysis of a simulated half-sib experiment shows that logistic regression can estimate the effect and position of a QTL without bias and confirms the increased power achieved by multiple-trait analysis.

Single- and multiple-trait mapping analysis of linked quantitative trait loci. Some asymptotic analytical approximations

Estimating the resolution power of mapping analysis of linked quantitative trait loci (QTL) remains a difficult problem, which has been previously addressed mainly by Monte Carlo simulations. The analytical method of evaluation of the expected LOD developed in this article spreads the "deterministic sampling" approach for the case of two linked QTL for single- and two-trait analysis. Several complicated questions are addressed through this evaluation: the dependence of QTL detection power on the QTL effects, residual correlation between the traits, and the effect of epistatic interaction between the QTL for one or both traits on expected LOD (ELOD), etc. Although this method gives only an asymptotic estimation of ELOD, it allows one to get an approximate assessment of a broad spectrum of mapping situations. A good correspondence was found between the ELODs predicted by the model and LOD values averaged over Monte Carlo simulations.

Time-related mapping of quantitative trait loci underlying tiller number in rice

Using time-related phenotypic data, methods of composite interval mapping and multiple-trait composite interval mapping based on least squares were applied to map quantitative trait loci (QTL) underlying the development of tiller number in rice. A recombinant inbred population and a corresponding saturated molecular marker linkage map were constructed for the study. Tiller number was recorded every 4 or 5 days for a total of seven times starting at 20 days after sowing. Five QTL were detected on chromosomes 1, 3, and 5. These QTL explained more than half of the genetic variance at the final observation. All the QTL displayed an S-shaped expression curve. Three QTL reached their highest expression rates during active tillering stage, while the other two QTL achieved this either before or after the active tillering stage.

Estimation of the proportion of genetic variance explained by molecular markers

Estimation of the proportion of genetic variance explained by molecular markers (p) plays an important role in basic studies of quantitative traits, as well as in marker-assisted selection (MAS), if the selection index proposed by Lande and Thompson (Genetics 124: 743-756, 1990) is used. Frequently, the coefficient of determination (R2) is used to account for this proportion. In the present study, a simple estimator of p is presented, which is applicable when a multiple regression approach is used, and progenies are evaluated in replicated trials. The associated sampling distribution was obtained and compared with that of R2. Simulations indicated that, when the number of evaluated progenies is small, the statistics are not satisfactory, in general, due to bias and/or low precision. Coefficient R2 was found adequate in situations where p is high. If a large number of progenies is evaluated (say, a few hundreds), then the proposed estimator <img src="http:/img/fbpe/gmb/v21n4/1974f1.jpg" alt="1974f1.jpg (1159 bytes)" align="middle"> appears to be better, with acceptable precision and considerably lower bias than R2. A normal approximation to the sampling distribution of <img src="http:/img/fbpe/gmb/v21n4/1974f1.jpg" alt="1974f1.jpg (1159 bytes)" align="middle"> is given, using Taylor's expansion of the expectation and variance of this statistic. Approximate confidence intervals for p, based on normal distribution, are reasonable, if the number of progenies is large. The use of <img src="http:/img/fbpe/gmb/v21n4/1974f1.jpg" alt="1974f1.jpg (1159 bytes)" align="middle"> in MAS is illustrated for estimation of the weight given to the molecular score, when a selection index is used.

Multiple phenotype modeling in gene-mapping studies of quantitative traits: power advantages

Genomewide searches for loci influencing complex human traits and diseases such as diabetes, hypertension, and obesity are often plagued by low power and interpretive difficulties. Attempts to remedy these difficulties have typically relied on, and have promoted the use of, novel subject-ascertainment schemes, larger sample sizes, a greater density of DNA markers, and more-sophisticated statistical modeling and analysis strategies. Many of these remedies can be costly to implement. We investigate the utility of a simple statistical model for the mapping of quantitative-trait loci that incorporates multiple phenotypic or diagnostic endpoints into a gene-mapping analysis. The approach considers finding a linear combination of multiple phenotypic values that maximizes the evidence for linkage to a locus. Our results suggest that substantial increases in the power to map loci can be obtained with the proposed technique, although the increase in power obtained is a function of the size and direction of the residual correlation among the phenotypes used in the analysis. Extensive simulation studies are described that justify these claims, for cases in which two phenotypic measures are analyzed. This approach can be easily extended to cover more-complex situations and may provide a basis for more insightful genetic-analysis paradigms.

A nonparametric bootstrap method for testing close linkage vs. pleiotropy of coincident quantitative trait loci

A novel method using the nonparametric bootstrap is proposed for testing whether a quantitative trait locus (QTL) at one chromosomal position could explain effects on two separate traits. If the single-QTL hypothesis is accepted, pleiotropy could explain the effect on two traits. If it is rejected, then the effects on two traits are due to linked QTLs. The method can be used in conjunction with several QTL mapping methods as long as they provide a straightforward estimate of the number of QTLs detectable from the data set. A selection step was introduced in the bootstrap procedure to reduce the conservativeness of the test of close linkage vs. pleiotropy, so that the erroneous rejection of the null hypothesis of pleiotropy only happens at a frequency equal to the nominal type I error risk specified by the user. The approach was assessed using computer simulations and proved to be relatively unbiased and robust over the range of genetic situations tested. An example of its application on a real data set from a saline stress experiment performed on a recombinant population of wheat (Triticum aestivum L. ) doubled haploid lines is also provided.

Statistical recovering of incomplete genotypic information of DNA molecular markers

Genetic information provided by a dominant marker about the genotype is partial or incomplete, and a missing marker provides no information at all. In the present study, based on some basic genetic and statistical principles, a general algorithm is proposed to systematically recover the genotypic information of all dominant and missing markers on a genome for individuals from an F(2) population. The recovered information can then increase the efficiency and precision in mapping quantitative trait loci (QTL) and marker assisted selection (MAS). The derived method can be easily extended to other populations consisting of all 3 genotypes on each marker locus, such as populations derived from an F(2) by selfing or random mating.

Multiple marker mapping of quantitative trait loci in a cross between outbred wild boar and large white pigs

A quantitative trait locus (QTL) analysis of growth and fatness data from a three generation pig experiment is presented. The population of 199 F2 animals was derived from a cross between wild boar and Large White pigs. Animals were typed for 240 markers spanning 23 Morgans of 18 autosomes and the X chromosome. A series of analyses are presented within a least squares framework. First, these identify chromosomes containing loci controlling trait variation and subsequently attempt to map QTLs to locations within chromosomes. This population gives evidence for a large QTL affecting back fat and another for abdominal fat segregating on chromosome 4. The best locations for these QTLs are within 4 cM of each other and, hence, this is likely to be a single QTL affecting both traits. The allele inherited from the wild boar causes an increase in fat deposition. A QTL for intestinal length was also located in the same region on chromosome 4 and could be the same QTL with pleiotropic effects. Significant effects, owing to multiple QTLs, for intestinal length were identified on chromosomes 3 and 5. A single QTL affecting growth rate to 30 kg was located on chromosome 13 such that the Large White allele increased early growth rate, another QTL on chromosome 10 affected growth rate from 30 to 70 kg and another on chromosome 4 affected growth rate to 70 kg.

Combining different line crosses for mapping quantitative trait loci using the identical by descent-based variance component method

Mapping quantitative trait loci (QTLs) is usually conducted with a single line cross. The power of such QTL mapping depends highly on the two parental lines. If the two lines are fixed for the same allele at a putative QTL, the QTL is undetectable. On the other hand, if a QTL is segregating in the line cross and is detected, the estimated variance of the QTL cannot be extrapolated beyond the statistical inference space of the two parental lines. To reduce the likelihood of missing a QTL and to increase the statistical inference space of the estimated QTL variance, we present a consensus QTL mapping strategy. We adopt the identical by descent (IBD)-based variance component method originally applied to human linkage analysis by combining multiple line crosses as independent families. We explore the properties of consensus QTL mapping and demonstrate the method with F2, backcross (BC), and full-sib (FS) families. In addition, we examine the effects of the QTL heritability, marker informativeness, QTL position, the number of families, and family size. We show that F2 families notably outperform BC and FS families in detecting a QTL. There is a substantial reduction in the standard deviation of the estimated QTL position and the separation of the QTL and polygenic variance. Finally, we show that the power to detect a QTL is greater when using a small number of large families than a large number of small families.

Quantitative trait locus (QTL) mapping using different testers and independent population samples in maize reveals low power of QTL detection and large bias in estimates of QTL effects

The efficiency of marker-assisted selection (MAS) depends on the power of quantitative trait locus (QTL) detection and unbiased estimation of QTL effects. Two independent samples N = 344 and 107 of F2 plants were genotyped for 89 RFLP markers. For each sample, testcross (TC) progenies of the corresponding F3 lines with two testers were evaluated in four environments. QTL for grain yield and other agronomically important traits were mapped in both samples. QTL effects were estimated from the same data as used for detection and mapping of QTL (calibration) and, based on QTL positions from calibration, from the second, independent sample (validation). For all traits and both testers we detected a total of 107 QTL with N = 344, and 39 QTL with N = 107, of which only 20 were in common. Consistency of QTL effects across testers was in agreement with corresponding genotypic correlations between the two TC series. Most QTL displayed no significant QTL x environment nor epistatic interactions. Estimates of the proportion of the phenotypic and genetic variance explained by QTL were considerably reduced when derived from the independent validation sample as opposed to estimates from the calibration sample. We conclude that, unless QTL effects are estimated from an independent sample, they can be inflated, resulting in an overly optimistic assessment of the efficiency of MAS.

Quantitative trait locus (QTL) mapping using different testers and independent population samples in maize reveals low power of QTL detection and large bias in estimates of QTL effects

The efficiency of marker-assisted selection (MAS) depends on the power of quantitative trait locus (QTL) detection and unbiased estimation of QTL effects. Two independent samples N = 344 and 107 of F2 plants were genotyped for 89 RFLP markers. For each sample, testcross (TC) progenies of the corresponding F3 lines with two testers were evaluated in four environments. QTL for grain yield and other agronomically important traits were mapped in both samples. QTL effects were estimated from the same data as used for detection and mapping of QTL (calibration) and, based on QTL positions from calibration, from the second, independent sample (validation). For all traits and both testers we detected a total of 107 QTL with N = 344, and 39 QTL with N = 107, of which only 20 were in common. Consistency of QTL effects across testers was in agreement with corresponding genotypic correlations between the two TC series. Most QTL displayed no significant QTL x environment nor epistatic interactions. Estimates of the proportion of the phenotypic and genetic variance explained by QTL were considerably reduced when derived from the independent validation sample as opposed to estimates from the calibration sample. We conclude that, unless QTL effects are estimated from an independent sample, they can be inflated, resulting in an overly optimistic assessment of the efficiency of MAS.

Efficiency of multistage marker-assisted selection in the improvement of multiple quantitative traits

The application of marker-assisted selection (MAS) to breeding programmes depends on its relative cost and the expected economic return compared to conventional phenotypic selection. The relative efficiency of MAS can be increased through a two-stage selection scheme or through marker-based, multiple-trait improvement. However, the effectiveness of these alternatives has not been quantified. In this study, we evaluate the efficiency of MAS relative to conventional phenotypic selection and marker-only selection in multistage selection for the improvement of multiple traits. We further incorporate the costs of obtaining measurements on phenotypic characters and marker loci into the objective function to evaluate the efficiency of MAS with respect to the gain per unit cost. Deterministic analyses indicate that excluding costs, multiple-trait MAS can be used to increase the aggregate breeding values in quantitative characters and is expected to be more effective than conventional selection or single-trait MAS. Two-stage MAS has a slightly reduced gain because of culling in the first stage. If the objective function is to maximize the gain per unit cost, multiple-trait MAS is inferior to phenotypic selection in most of the selection schemes investigated when the cost ratio (r) of obtaining measurements on phenotypic characters to scoring marker loci is less than unity (r < or = 1.0) and the heritability (h2) is greater than 0.3. The efficiency of MAS increases as r increases and h2 decreases. For MAS to be more effective, it is necessary to decrease further the cost associated with molecular marker assays.

Approximate analysis of QTL-environment interaction with no limits on the number of environments

An approach is presented here for quantitative trait loci (QTL) mapping analysis that allows for QTL x environment (E) interaction across multiple environments, without necessarily increasing the number of parameters. The main distinction of the proposed model is in the chosen way of approximation of the dependence of putative QTL effects on environmental states. We hypothesize that environmental dependence of a putative QTL effect can be represented as a function of environmental mean value of the trait. Such a description can be applied to take into account the effects of any cosegregating QTLs from other genomic regions that also may vary across environments. The conducted Monte-Carlo simulations and the example of barley multiple environments experiment demonstrate a high potential of the proposed approach for analyzing QTL x E interaction, although the results are only approximated by definition. However, this drawback is compensated by the possibility to utilize information from a potentially unlimited number of environments with a remarkable reduction in the number of parameters, as compared to previously proposed mapping models with QTL x E interactions.

Empirical nonparametric bootstrap strategies in quantitative trait loci mapping: conditioning on the genetic model

Several nonparametric bootstrap methods are tested to obtain better confidence intervals for the quantitative trait loci (QTL) positions, i.e., with minimal width and unbiased coverage probability. Two selective resampling schemes are proposed as a means of conditioning the bootstrap on the number of genetic factors in our model inferred from the original data. The selection is based on criteria related to the estimated number of genetic factors, and only the retained bootstrapped samples will contribute a value to the empirically estimated distribution of the QTL position estimate. These schemes are compared with a nonselective scheme across a range of simple configurations of one QTL on a one-chromosome genome. In particular, the effect of the chromosome length and the relative position of the QTL are examined for a given experimental power, which determines the confidence interval size. With the test protocol used, it appears that the selective resampling schemes are either unbiased or least biased when the QTL is situated near the middle of the chromosome. When the QTL is closer to one end, the likelihood curve of its position along the chromosome becomes truncated, and the nonselective scheme then performs better inasmuch as the percentage of estimated confidence intervals that actually contain the real QTL's position is closer to expectation. The nonselective method, however, produces larger confidence intervals. Hence, we advocate use of the selective methods, regardless of the QTL position along the chromosome (to reduce confidence interval sizes), but we leave the problem open as to how the method should be altered to take into account the bias of the original estimate of the QTL's position.

Experimental strategies for the genetic dissection of complex traits in animal models

Current success in detecting complex trait loci in general, and quantitative trait loci (QTLs) using model organisms in particular, has attracted major biological and biomedical interest. The potential ability to identify genes and their function provides opportunities for new diagnostics and treatments of complex genetic diseases. Despite the success in gene mapping, however, cloning of complex trait loci or QTLs is not straightforward. A major obstacle lies in achieving fine mapping resolution for the detected loci. Compared to the rapid development of sophisticated statistical and molecular tools, development and analysis of experimental designs for various stages in QTL mapping experiments have barely been considered. In this study, novel and existing experimental strategies for QTL analysis are presented and evaluated.

Integrated methods to solve the biological basis of common diseases

Biological variations influence population variations of many common traits. Identification of the biological basis of many common diseases has been particularly difficult, but new reagents and analytical tools will greatly facilitate this process. The goal of this review is to discuss how to identify the biological basis of common traits by using mouse models. No single method will work for all traits. Understanding complex problems will require broadly based holistic approaches that use a wide array of tools and resources. A multiplicity of developed methods together provide the tools needed to identify the biological basis of any common trait. These tools, whole-genome linkage maps, maps of expressed genes, and statistical methods, deal with the complexities of multiple loci or correlated traits. This review provides some criteria for making choices about the likely productive approaches at each stage in the process of finding genes that influence common traits.

Quantitative trait loci differentiating the outbreeding Mimulus guttatus from the inbreeding M. platycalyx

Theoretical predictions about the evolution of selfing depend on the genetic architecture of loci controlling selfing (monogenic vs. polygenic determination, large vs. small effect of alleles, dominance vs. recessiveness), and studies of such architecture are lacking. We inferred the genetic basis of mating system differences between the outbreeding Mimulus guttatus and the inbreeding M. platycalyx by quantitative trait locus (QTL) mapping using random amplified polymorphic DNA and isozyme markers. One to three QTL were detected for each of five mating system characters, and each QTL explained 7.6-28.6% of the phenotypic variance. Taken together, QTL accounted for up to 38% of the variation in mating system characters, and a large proportion of variation was unaccounted for. Inferred QTL often affected more than one trait, contributing to the genetic correlation between those traits. These results are consistent with the hypothesis that quantitative variation in plant mating system characters is primarily controlled by loci with small effect.

Interval-specific congenic strains (ISCS): an experimental design for mapping a QTL into a 1-centimorgan interval

A general experimental design that allows mapping of a quantitative trait locus (QTL) into a 1-cM interval is presented. The design consists of a series of strains, termed "interval-specific congenic strains (ISCS)". Each ISCS is recombinant at a specific 1-cM sub-interval out of an ordered set of sub-intervals, which together comprise a wider interval, to which a QTL was previously mapped. It is shown that a specific and previously detected QTL of moderate or even small effect can be accurately mapped into a 1-cM interval in a program involving a total of no more than 1000 individuals. Consequently, ISCS can serve as the ultimate genetic mapping procedure before the application of physical mapping tools for positional cloning of a QTL.

Transmission-disequilibrium tests for quantitative traits

The transmission-disequilibrium test (TDT) of Spielman et al. is a family-based linkage-disequilibrium test that offers a powerful way to test for linkage between alleles and phenotypes that is either causal (i.e., the marker locus is the disease/trait allele) or due to linkage disequilibrium. The TDT is equivalent to a randomized experiment and, therefore, is resistant to confounding. When the marker is extremely close to the disease locus or is the disease locus itself, tests such as the TDT can be far more powerful than conventional linkage tests. To date, the TDT and most other family-based association tests have been applied only to dichotomous traits. This paper develops five TDT-type tests for use with quantitative traits. These tests accommodate either unselected sampling or sampling based on selection of phenotypically extreme offspring. Power calculations are provided and show that, when a candidate gene is available (1) these TDT-type tests are at least an order of magnitude more efficient than two common sib-pair tests of linkage; (2) extreme sampling results in substantial increases in power; and (3) if the most extreme 20% of the phenotypic distribution is selectively sampled, across a wide variety of plausible genetic models, quantitative-trait loci explaining as little as 5% of the phenotypic variation can be detected at the .0001 alpha level with <300 observations.

The effects of selective genotyping on estimates of proportion of recombination between linked quantitative trait loci

Selective genotyping is the marker assay of only the more extreme phenotypes for a quantitative trait and is intended to increase the efficiency of quantitative trait loci (QTL) mapping. We show that selective genotyping can bias estimates of the recombination frequency between linked QTLs - upwardly when QTLs are in repulsion phase, and downwardly when QTLs are in coupling phase. We examined these biases under simple models involving two QTLs segregating in a backcross or F2 population, using both analytical models and computer simulations. We found that bias is a function of the proportion selected, the magnitude of QTL effects, distance between QTLs and the dominance of QTLs. Selective genotyping thus may decrease the power of mapping multiple linked QTLs and bias the construction of a marker map. We suggest a large proportion than previously suggested (50%) or the entire population be genotyped if linked QTLs of large effects (explain > 10% phenotypic variance) are evident. New models need to be developed to explicitly incorporate selection into QTL map construction.

Computation of the full likelihood function for estimating variance at a quantitative trait locus

The proportion of alleles identical by descent (IBD) determines the genetic covariance between relatives, and thus is crucial in estimating genetic variances of quantitative trait loci (QTL). However, IBD proportions at QTL are unobservable and must be inferred from marker information. The conventional method of QTL variance analysis maximizes the likelihood function by replacing the missing IBDs by their conditional expectations (the expectation method), while in fact the full likelihood function should take into account the conditional distribution of IBDs (the distribution method). The distribution method for families of more than two sibs has not been obvious because there are n(n - 1)/2 IBD variables in a family of size n, forming an n x n symmetrical matrix. In this paper, I use four binary variables, where each indicates the event that an allele from one of the four grandparents has passed to the individual. The IBD proportion between any two sibs is then expressed as a function of the indicators. Subsequently, the joint distribution of the IBD matrix is derived from the distribution of the indicator variables. Given the joint distribution of the unknown IBDs, a method to compute the full likelihood function is developed for families of arbitrary sizes.

Genetic analysis of a morphological shape difference in the male genitalia of Drosophila simulans and D. mauritiana

Two closely related species of Drosophila, D. simulans and D. mauritiana, differ markedly in morphology of the posterior lobe of the male genital arch. Both size and shape aspects of lobe variation can be quantified by a morphometric descriptor based on elliptical Fourier and principal components analyses. The genetic architecture of this quantitative trait (PC1) was investigated by hybridizing inbred lines to produce two backcross populations approximately 200 individuals each, which were analyzed jointly by a composite interval mapping procedure with the aid of 18 marker loci. The parental lines show a large difference in PC1 (30.4 environmental standard deviations), and the markers account for > 80% of the phenotypic variation in backcross populations. Eight of 15 intervals analyzed show convincing evidence of quantitative trait loci (QTL), and the range of estimated QTL effects is 5.7-15.9% of the parental difference (1.7-4.8 environmental standard deviations). These estimates may represent the joint effects of multiple QTL within a single interval (which averaged 23 cM in length). Although there is some evidence of partial dominance of mauritiana alleles and for epistasis, the pattern of inheritance is largely additive.

The geneticist's approach to complex disease

Many studies are in progress worldwide to elucidate the genetics of complex diseases. Nevertheless, few articles are available that provide the scientific rationale and give guidelines for such ambitious endeavours. We describe the methodology and background necessary to study the genetics of complex disease and discuss how to analyze the data. We also provide a table of some ongoing studies. In particular, we wish to emphasize the analysis of intermediate, heritable, quantitative traits as a means of dissecting the genetic basis of a complex trait.

Taking stock of complex trait genetics in mice

The mapping of complex trait loci in mice has recently become very popular thanks to dense genetic maps, better approaches to linkage analysis and the continued value of the mouse as a key model organism for human disease. Nevertheless, the ultimate goal remains very difficult to identify genes that underlie complex traits and to understand their function at a molecular level. In assessing the prospects of current efforts, it helps to review the findings of earlier studies of complex traits and, despite all the technology, to be reminded of the inherent benefits and limitations at the source of genetic variation: the laboratory mouse. With the right perspective it should be possible for geneticists analysing complex traits to take full advantage of the resources that the genome project will provide.

Molecular dissection of quantitative traits: progress and prospects

QTL mapping is an increasingly useful approach to the study and manipulation of complex traits important in agriculture, evolution, and medicine. The molecular dissection of quantitative phenotypes, supplementing the principles of classical quantitative genetics, is accelerating progress in the manipulation of plant and animal genomes. A growing appreciation of the similarities among different organisms and the usefulness of comparative genetic information is making genome analysis more efficient, and providing new opportunities for using model systems to overcome the limitations of less-favorable systems. The expanding repertoire of techniques and information available for studying heredity is removing obstacles to the cloning of QTLs. Although QTL mapping alone is limited to a resolution of 0.1%-1.0% of a genome, use of QTL mapping in conjunction with a search for mapped candidate genes, with emerging technologies for isolation of genes expressed under conditions likely to account for the quantitative phenotype, and with ever more efficient megabase DNA manipulation and characterization bodes well for the prospect of isolating the genetic determinants of QTLs in the foreseeable future. In the words of Thoday (1961), "An extensive attack on quantitative genetics made from this point of view as well as the biometric approach should be a great help in answering questions concerning the nature of polygenes...."