Empirical threshold values for quantitative trait mapping

A major quantitative trait locus influences hyperactivity in the WKHA rat

The syndrome of hyperactivity describes behavioural disorders existing mainly in children and characterized by increased levels of motor activity, inattention and impulsivity. Overall the aetiology is poorly understood due to the heterogeneity of the pathology although psychological, biological and social factors acting singly or in concert are generally thought to be involved. In animal studies the observed hyperactivity phenotype results from relative participation of exploration, emotionality and general activity. Studies using brain lesions, neuropharmacology and gene knock-out strategies have shown that specific elements of the brain dopaminergic system can subserve hyperactivity. Evidence of a genetic contribution comes from family and twin studies but also from the ability to select divergent animal lines on the basis of their differential activity. The Wistar-Kyoto (WKY) and Wistar-Kyoto hyperactive (WKHA) rats are such strains--distinct for their low and high activity scores in a novel environment, respectively. Here, we report the detection of a major hyperactivity-related QTL on chromosome 8, explaining 29% of the variance of an intercross between these strains. This study represents the first behavioural QTL analysis in rat and provides a new starting point for biologically categorizing different forms of hyper-activity.

A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci. I. Methodology

A Bayesian approach to the statistical mapping of Quantitative Trait Loci (QTLs) using single markers was implemented via Markov Chain Monte Carlo (MCMC) algorithms for parameter estimation and hypothesis testing. Parameter estimators were marginal posterior means computed using a Gibbs sampler with data augmentation. Variables sampled included the augmented data (marker-QTL genotypes, polygenic effects), an indicator variable for linkage, and the parameters (allele frequency, QTL substitution effect, recombination rate, polygenic and residual variances). Several MCMC algorithms were derived for computing Bayesian tests of linkage, which consisted of the marginal posterior probability of linkage and the marginal likelihood of the QTL variance associated with the marker.

Detection of putative quantitative trait loci in line crosses under infinitesimal genetic models

Quantitative trait locus (QTL) mapping studies often employ segregating generations derived from a cross between genetically divergent inbred lines. In the analysis of such data it is customary to fit a single QTL and use a null hypothesis which assumes that the genomic region under study contributes no genetic variance. To explore the situation in which multiple linked genes contribute to the genetic variance, we simulated an F2-mapping experiment in which the genetic difference between the two original inbred strains was caused by a large number of loci, each having equal effect on the quantitative trait. QTLs were either in coupling, dispersion or repulsion phase in the base population of inbred lines, with the expected F2 genetic variance explained by the QTLs being equivalent in the three models. Where QTLs were in coupling phase, one inbred line was fixed for all plus alleles, and the other line was fixed for minus alleles. Where QTLs were in dispersion phase, they were assumed to be randomly fixed for one or other allele (as if the inbred lines had evolved from a common ancestor by random drift). Where QTLs were in repulsion phase alleles within an inbred line were alternating plus and minus at adjacent loci, and alternative alleles were fixed in the two inbred lines. In all these genetic models a standard interval mapping test statistic used to determine whether there is a QTL of large effect segregating in the population was inflated on average. Furthermore, the use of a threshold for QTL detection derived under the assumption that no QTLs were segregating would often lead to spurious conclusions regards the presence of genes of large effects (i.e. type I errors). The employment of an alternative model for the analysis, including linked markers as cofactors in the analysis of a single interval, reduced the problem of type I error rate, although test statistics were still inflated relative to the case of no QTLs. It is argued that in practice one should take into account the difference between the strains or the genetic variance in the F2 population when setting significance thresholds. In addition, tests designed to probe the adequacy of a single-QTL model or of an alternative infinitesimal coupling model are described. Such tests should be applied in QTL mapping studies to help dissect the true nature of genetic variation.

A bayesian approach to detect quantitative trait loci using Markov chain Monte Carlo

Markov chain Monte Carlo (MCMC) techniques are applied to simultaneously identify multiple quantitative trait loci (QTL) and the magnitude of their effects. Using a Bayesian approach a multi-locus model is fit to quantitative trait and molecular marker data, instead of fitting one locus at a time. The phenotypic trait is modeled as a linear function of the additive and dominance effects of the unknown QTL genotypes. Inference summaries for the locations of the QTL and their effects are derived from the corresponding marginal posterior densities obtained by integrating the likelihood, rather than by optimizing the joint likelihood surface. This is done using MCMC by treating the unknown QTL, genotypes, and any missing marker genotypes, as augmented data and then by including these unknowns in the Markov chain cycle alone with the unknown parameters. Parameter estimates are obtained as means of the corresponding marginal posterior densities. High posterior density regions of the marginal densities are obtained as confidence regions. We examine flowering time data from double haploid progeny of Brassica napus to illustrate the proposed method.

The use of multiple markers in a Bayesian method for mapping quantitative trait loci

Information on multiple linked genetic markers was used in a Bayesian method for the statistical mapping of quantitative trait loci (QTL). Bayesian parameter estimation and hypothesis testing were implemented via Markov chain Monte Carlo algorithms. Variables sampled were the augmented data (marker-QTL genotypes, polygenic effects), an indicator variable for linkage or nonlinkage, and the parameters. The parameter vector included allele frequencies at the markers and the QTL, map distances of the markers and the QTL, QTL substitution effect, and polygenic and residual variances. The criterion for QTL detection was the marginal posterior probability of a QTL being located on the chromosome carrying the markers. The method was evaluated empirically by analyzing simulated granddaughter designs consisting of 2000 sons, 20 related sires, and their ancestors.

Linkage mapping of quantitative trait loci controlling seed weight in pea (Pisum sativum L.)

Quantitative trait loci (QTLs) affecting seed weight in pea (Pisum sativum L.) were mapped using two populations, a field-grown F2 progeny of a cross between two cultivated types ('Primo' and 'OSU442-15') and glasshouse-grown single-seed-descent recombinant inbred lines (RILs) from a wide cross between a P. sativum ssp. sativum line ('Slow') and a P. sativum ssp. humile accession ('JI1794'). Linkage maps for these crosses consisted of 199 and 235 markers, respectively. QTLs for seed weight in the 'Primo' x 'OSU442-15' cross were identified by interval mapping, bulked segregant analysis, and selective genotyping. Four QTLs were identified in this cross, demonstrating linkage to four intervals on three linkage groups. QTLs for seed weight in the 'JI1794' x 'Slow' cross were identified by single-marker analyses. Linkage were demonstrated to four intervals on three linkage groups plus three unlinked loci. In the two crosses, only one common genomic region was identified as containing seed-weight QTLs. Seed-weight QTLs mapped to the same region of linkage group III in both crosses. Conserved linkage relationships were demonstrated for pea, mungbean (Vigna radiata L.), and cowpea (V. unguiculata L.) genomic regions containing seed-weight QTLs by mapping RFLP loci from the Vigna maps in the 'Primo' x 'OSU442-15' and 'JI1794' x 'Slow' crosses.

Maximum likelihood analysis of rare binary traits under different modes of inheritance

Maximum likelihood methodology was applied to determine the mode of inheritance of rare binary traits with data structures typical for swine populations. The genetic models considered included a monogenic, a digenic, a polygenic, and three mixed polygenic and major gene models. The main emphasis was on the detection of major genes acting on a polygenic background. Deterministic algorithms were employed to integrate and maximize likelihoods. A simulation study was conducted to evaluate model selection and parameter estimation. Three designs were simulated that differed in the number of sires/number of dams within sires (10/10, 30/30, 100/30). Major gene effects of at least one SD of the liability were detected with satisfactory power under the mixed model of inheritance, except for the smallest design. Parameter estimates were empirically unbiased with acceptable standard errors, except for the smallest design, and allowed to distinguish clearly between the genetic models. Distributions of the likelihood ratio statistic were evaluated empirically, because asymptotic theory did not hold. For each simulation model, the Average Information Criterion was computed for all models of analysis. The model with the smallest value was chosen as the best model and was equal to the true model in almost every case studied.

Use of the additive main effects and multiplicative interaction model in QTL mapping for adaptation in barley

The additive main effects and multiplicative interaction (AMMI) model has emerged as a powerful analytical tool for genotype x environment studies. The objective of the present study was to assess its value in quantitative trait locus (QTL) mapping. This was done through the analysis of a large two-way table of genotype-by-environment data of barley (Hordeum vulgare L.) grain yields, where the genotypes constituted a genetic population suitable for mapping studies. Grain yield data of 150 doubled haploid lines derived from the 'Steptoe' x 'Morex' cross, and the two parental lines, were taken by the North American Barley Genome Mapping Project (NABGMP) at 16 environments throughout the barley production areas of the USA and Canada. Four regions of the genome were responsible for most of the differential genotypic expression across environments. They accounted for approximately 50% of the genotypic main effect and 30% of the genotype x environment interaction (GE) sums of squares. The magnitude and sign of AMMI scores for genotypes and sites facilitate inferences about specific interactions. The parallel use of classification (cluster analysis of environments) and ordination (principal component analysis of GE matrix) techniques allowed most of the variation present in the genotype x environment matrix to be summarized in just a few dimensions, specifically four QTLs showing differential adaptation to four clusters of environments. Thus, AMMI genotypic scores, when the genotypes constituted a population suitable for QTL mapping, could provide an adequate way of resolving the magnitude and nature of QTL x environment interactions.

Methods for multiple-marker mapping of quantitative trait loci in half-sib populations

In this paper we consider the detection of individual loci controlling quantitative traits of interest (quantitative trait loci or QTLs) in the large half-sib family structure found in some species. Two simple approaches using multiple markers are proposed, one using least squares and the other maximum likelihood. These methods are intended to provide a relatively fast screening of the entire genome to pinpoint regions of interest for further investigation. They are compared with a more traditional single-marker least-squares approach. The use of multiple markers is shown to increase power and has the advantage of providing an estimate for the location of the QTL. The maximum-likelihood and the least-squares approaches using multiple markers give similar power and estimates for the QTL location, although the likelihood approach also provides estimates of the QTL effect and sire heterozygote frequency. A number of assumptions have been made in order to make the likelihood calculations feasible, however, and computationally it is still more demanding than the least-squares approach. The least-squares approach using multiple markers provides a fast method that can easily be extended to include additional effects.

Mapping quantitative trait loci for complex binary diseases using line crosses

A composite interval gene mapping procedure for complex binary disease traits is proposed in this paper. The binary trait of interest is assumed to be controlled by an underlying liability that is normally distributed. The liability is treated as a typical quantitative character and thus described by the usual quantitative genetics model. Translation from the liability into a binary (disease) phenotype is through the physiological threshold model. Logistic regression analysis is employed to estimate the effects and locations of putative quantitative trait loci (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). Simulation studies show that properties of this mapping procedure mimic those of the composite interval mapping for normally distributed data. Potential utilization of the QTL mapping procedure for resolving alternative genetic models (e.g., single- or two-trait-locus model) is discussed.

Confidence intervals in QTL mapping by bootstrapping

The determination of empirical confidence intervals for the location of quantitative trait loci (QTLs) was investigated using simulation. Empirical confidence intervals were calculated using a bootstrap resampling method for a backcross population derived from inbred lines. Sample sizes were either 200 or 500 individuals, and the QTL explained 1, 5, or 10% of the phenotypic variance. The method worked well in that the proportion of empirical confidence intervals that contained the simulated QTL was close to expectation. In general, the confidence intervals were slightly conservatively biased. Correlations between the test statistic and the width of the confidence interval were strongly negative, so that the stronger the evidence for a QTL segregating, the smaller the empirical confidence interval for its location. The size of the average confidence interval depended heavily on the population size and the effect of the QTL. Marker spacing had only a small effect on the average empirical confidence interval. The LOD drop-off method to calculate empirical support intervals gave confidence intervals that generally were too small, in particular if confidence intervals were calculated only for samples above a certain significance threshold. The bootstrap method is easy to implement and is useful in the analysis of experimental data.

A locus on chromosome 7 determines myocardial cell necrosis and calcification (dystrophic cardiac calcinosis) in mice

Dystrophic cardiac calcinosis, an age-related cardiomyopathy that occurs among certain inbred strains of mice, involves myocardial injury, necrosis, and calcification. Using a complete linkage map approach and quantitative trait locus analysis, we sought to identify genetic loci determining dystrophic cardiac calcinosis in an F2 intercross of resistant C57BL/6J and susceptible C3H/HeJ inbred strains. We identified a single major locus, designated Dyscalc, located on proximal chromosome 7 in a region syntenic with human chromosomes 19q13 and 11p15. The statistical significance of Dyscalc (logarithm of odds score 14.6) was tested by analysis of permuted trait data. Analysis of BxH recombinant inbred strains confirmed the mapping position. The inheritance pattern indicated that this locus influences susceptibility of cells both to enter necrosis and to subsequently undergo calcification.

A genetic map of Gibberella fujikuroi mating population A (Fusarium moniliforme)

We constructed a recombination-based map of the fungal plant pathogen Gibberella fujikuroi mating population A (asexual stage Fusarium moniliforme). The map is based on the segregation of 142 restriction fragment length polymorphism (RFLP) markers, two auxotrophic genes (arg1, nic1), mating type (matA+/matA-), female sterility (ste1), spore-killer (Sk), and a gene governing the production of the mycotoxin fumonisin B1 (fum1) among 121 random ascospore progeny from a single cross. We identified 12 linkage groups corresponding to the 12 chromosome-sized DNAs previously observed in contour-clamped homogeneous electric field (CHEF) gels. Linkage groups and chromosomes were correlated via Southern blots between appropriate RFLP markers and the CHEF gels. Eleven of the 12 chromosomes are meiotically stable, but the 12th (and smallest) is subject to deletions in 3% (4/121) of the progeny. Positive chiasma interference occurred on five of the 12 chromosomes, and nine of the 12 chromosomes averaged more than one crossover per chromosome. The average kb/cM ratio in this cross is approximately 32.

Mapping quantitative trait loci associated with root penetration ability in rice (Oryza sativa L.)

Root penetration ability is an important factor for rice drought resistance in areas with soils subject to both compaction and periodic water deficits. However, breeding for root penetration ability is inhibited by the difficulties associated with measuring root traits. Our objective was to identify restriction fragment length polymorphisms (RFLPs) associated with root penetration ability. Using wax-petrolatum layers as a proxy for compacted soil, we counted the number of vertical root axes penetrating through the layer, the total number of vertical root axes and the number of tillers per plant of 202 recombinant inbred (RI) lines over three replications. As a measure of root penetration ability, we used a root penetration index defined as the percent of the total number of vertical root axes that penetrated through a wax-petrolatum layer. The RI population exhibited a wide range in the number of penetrating roots axes (10-115 roots), the total number of roots axes (74-226 roots), tillers per plant (6-18), and in the root penetration index (0.11-0.71). Single-marker and interval quantitative trait analyses were conducted to identify RFLP loci associated with the number of penetrating roots, total root number, root penetration index, and tiller number. Four quantitative trait loci (QTLs) were associated with the number of penetrated roots, 19 with the total root number, six QTLs with the root penetration index and ten with tiller number. Individually, these QTLs accounted for a maximum of 8% of the variation in the number of penetrating roots, 19% of the variation in total root number, 13% of the variation in root penetration index and 14% of the variation in tiller number as estimated from regressions. The multimarker regression model accounting for the greatest proportion of the variation in the root penetration index was a three-marker model that accounted for 34% of the variation. Two-marker models accounted for 13% of the variation in the number of penetrated roots, 25% of the variation in total root number, and 21% of the variation in tiller number. This is the first research paper to apply RFLP quantitative trait analysis to dissect genetic loci associated with the total number of roots, root penetration ability and tiller number.

QTL analysis of pest resistance in the wild tomato Lycopersicon pennellii: QTLs controlling acylsugar level and composition

Some accessions of Lycopersicon pennellii, a wild relative of the tomato Lycopersicon esculentum, are resistant to a number of important pests of cultivated tomato due to the accumulation of acylsugars, which constitute 90% of the exudate of type-IV trichomes in L. pennellii LA716. An interspecific F2 population, created by the cross L. esculentum x L. pennellii LA 716, was surveyed for acylsugar accumulation and subjected to RFLP/QTL analysis to determine the genomic regions associated with the accumulation of acylglucoses, acylsucroses, and total acylsugars, as well as with acylglucoses as a percentage of total acylsugars (mole percent acylglucoses). Data were analyzed using MAPMAKER/QTL with and without a log10 transformation. A threshold value of 2.4 (default value for MAPMAKER/QTL) was used, as well as 95% empirically derived threshold values. Five genomic regions, two on chromosome 2 and one each on chromosomes 3, 4 and 11, were detected as being associated with one or more aspects of acylsugar production. The L. esculentum allele is partially dominant to the L. pennellii allele in the regions on chromosomes 2 and 11, but the L. pennellii allele is dominant in the region on chromosome 3. Throughout this study, we report the comparative effects of analytical methodology on the identification of acylsugar QTLs. Similarities between our results and published results for the genus Solanum are also discussed.

Nonparametric simulation-based statistics for detecting linkage in general pedigrees

We present here four nonparametric statistics for linkage analysis that test whether pairs of affected relatives share marker alleles more often than expected. These statistics are based on simulating the null distribution of a given statistic conditional on the unaffecteds' marker genotypes. Each statistic uses a different measure of marker sharing: the SimAPM statistic uses the simulation-based affected-pedigree-member measure based on identity-by-state (IBS) sharing. The SimKIN (kinship) measure is 1.0 for identity-by-descent (IBD) sharing, 0.0 for no IBD status sharing, and the kinship coefficient when the IBD status is ambiguous. The simulation-based IBD (SimIBD) statistic uses a recursive algorithm to determine the probability of two affecteds sharing a specific allele IBD. The SimISO statistic is identical to SimIBD, except that it also measures marker similarity between unaffected pairs. We evaluated our statistics on data simulated under different two-locus disease models, comparing our results to those obtained with several other nonparametric statistics. Use of IBD information produces dramatic increases in power over the SimAPM method, which uses only IBS information. The power of our best statistic in most cases meets or exceeds the power of the other nonparametric statistics. Furthermore, our statistics perform comparisons between all affected relative pairs within general pedigrees and are not restricted to sib pairs or nuclear families.

Finding genetic markers for complex phenotypic traits in parasites

The identification, mapping and eventual cloning of genes which determine or influence important epidemiological traits in parasites can have great benefits for the control of parasitic disease. In this review, strategies are outlined for identifying genetic markers for complex, quantitative traits. A genetic marker is a variable DNA sequence which co-occurs with a variable quantitative trait. Candidate markers are chosen because they are thought to directly influence the trait whereas random markers are expected to be linked to another DNA sequence which influences the trait. Association studies compare the value of a quantitative trait between different marker genotype classes in a population, without regard to family structure. Linkage studies compare the value of a quantitative trait between marker genotype classes within families or within a population (usually derived from a cross between inbred lines) which is segregating for both marker and quantitative trait loci. The most commonly used analytical methods for determining the significance of association or linkage between marker and quantitative trait loci, and for estimating parameters such as recombination rate and quantitative gene action, are least-squares and maximum likelihood. Both methods may be used to test either single markers or the interval between flanking markers, and both suffer from the need to minimize type I and type II error rates with multiple tests.

Permutation tests for multiple loci affecting a quantitative character

The problem of detecting minor quantitative trait loci (QTL) responsible for genetic variation not explained by major QTL is of importance in the complete dissection of quantitative characters. Two extensions of the permutation-based method for estimating empirical threshold values are presented. These methods, the conditional empirical threshold (CET) and the residual empirical threshold (RET), yield critical values that can be used to construct tests for the presence of minor QTL effects while accounting for effects of known major QTL. The CET provides a completely nonparametric test through conditioning on markers linked to major QTL. It allows for general nonadditive interactions among QTL, but its practical application is restricted to regions of the genome that are unlinked to the major QTL. The RET assumes a structural model for the effect of major QTL, and a threshold is constructed using residuals from this structural model. The search space for minor QTL is unrestricted, and RET-based tests may be more powerful than the CET-based test when the structural model is approximately true.

Polygenic disease: methods for mapping complex disease traits

Improved genotyping technology has made it feasible to use a genetic approach to map genes involved in the etiology of common human diseases. We discuss here recent developments in several different statistical approaches to linkage analysis of these traits, including affected-sib-pair methods, the affected-pedigree-member method, regressive models and linkage-disequilibrium-based approaches. We discuss advantages and disadvantages of the various approaches, as well as factors influencing study design and the ability to detect loci. Statistical methodology in this area is advancing rapidly and will help enable the mapping and cloning of loci involved in susceptibility to common multifactorial diseases.

QTL mapping in rice

In the past 10 years, interest in applying the tools of molecular genetics to the problem of increasing world rice production has resulted in the generation of two highly saturated, molecular linkage maps of rice, and the localization of numerous genes and quantitative trait loci (QTLs). Primary studies have identified QTLs associated with disease resistance, abiotic stress tolerance and yield potential of rice in a range of ecosystems. The ability to identify, manipulate and potentially clone individual genes involved in quantitatively inherited characters, combined with the demonstrated conservation of numerous linkage blocks among members of the grass family, emphasizes the contribution of map-based genetic analyses both to applied and to basic crop research.

Multifactorial inheritance in type 1 diabetes

To date, twelve separate chromosome regions have been implicated in the development of human type 1 (insulin-dependent) diabetes mellitus. The major disease locus, IDDM1 in the major histocompatibility complex(MHC) on chromosome 6p21, accounts for about 35% of the observed familial clustering and its contribution to disease susceptibility is likely to involve polymorphic residues of class II molecules in T-cell-mediated autoimmunity. IDDM2 is encoded by a minisatellite locus embedded in the 5' regulatory region of the insulin gene. Familial clustering of disease can be explained by the sharing of alleles of at least 10 loci. IDDM1 and IDDM2 interact epistatically. For a multifactorial disease, such as type 1 diabetes, important information concerning the pathways and mechanisms involved can be gained from examining such interactions between loci, using methods that simultaneously take account of the joint effects of the various underlying genetic components.

A random model approach to interval mapping of quantitative trait loci

Mapping quantitative trait loci in outbred populations is important because many populations of organisms are noninbred. Unfortunately, information about the genetic architecture of the trait may not be available in outbred populations. Thus, the allelic effects of genes can not be estimated with ease. In addition, under linkage equilibrium, marker genotypes provide no information about the genotype of a QTL (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). To circumvent this problem, an interval mapping procedure based on a random model approach is described. Under a random model, instead of estimating the effects, segregating variances of QTLs are estimated by a maximum likelihood method. Estimation of the variance component of a QTL depends on the proportion of genes identical-by-descent (IBD) shared by relatives at the locus, which is predicted by the IBD of two markers flanking the QTL. The marker IBD shared by two relatives are inferred from the observed marker genotypes. The procedure offers an advantage over the regression interval mapping in terms of high power and small estimation errors and provides flexibility for large sibships, irregular pedigree relationships and incorporation of common environmental and fixed effects.

Evolutionary consequences of mutation and selection within an individual

Whether in sexual or asexual organisms, selection among cell lineages during development is an effective way of eliminating deleterious mutations. Using a mathematical analysis, we find that relatively small differences in cell replication rates during development can translate into large differences in the proportion of mutant cells within the adult, especially when development involves a large number of cell divisions. Consequently, intraorganismal selection can substantially reduce the deleterious mutation rate observed among offspring as well as the mutation load within a population, because cells rather than individuals provide the selective "deaths" necessary to stem the tide of deleterious mutations. The reduction in mutation rate among offspring is more pronounced in organisms with plastic development than in those with structured development. It is also more pronounced in asexual organisms that produce multicellular rather than unicellular offspring. By effecting the mutation rate, intraorganismal selection may have broad evolutionary implications; as an example, we consider its influence on the evolution of ploidy levels, finding that cell-lineage selection is more effective in haploids and tends to favor their evolution.

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...."

Multiple trait analysis of genetic mapping for quantitative trait loci

We present in this paper models and statistical methods for performing multiple trait analysis on mapping quantitative trait loci (QTL) based on the composite interval mapping method. By taking into account the correlated structure of multiple traits, this joint analysis has several advantages, compared with separate analyses, for mapping QTL, including the expected improvement on the statistical power of the test for QTL and on the precision of parameter estimation. Also this joint analysis provides formal procedures to test a number of biologically interesting hypotheses concerning the nature of genetic correlations between different traits. Among the testing procedures considered are those for joint mapping, pleiotropy, QTL by environment interaction, and pleiotropy vs. close linkage. The test of pleiotropy (one pleiotropic QTL at a genome position) vs. close linkage (multiple nearby nonpleiotropic QTL) can have important implications for our understanding of the nature of genetic correlations between different traits in certain regions of a genome and also for practical applications in animal and plant breeding because one of the major goals in breeding is to break unfavorable linkage. Results of extensive simulation studies are presented to illustrate various properties of the analyses.

Interval mapping of high growth (hg), a major locus that increases weight gain in mice

The high growth locus (hg) causes a major increase in weight gain and body size in mice. As a first step to map-based cloning of hg, we developed a genetic map of the hg-containing region using interval mapping of 403 F2 from a C57BL/6J-hghg x CAST/EiJ cross. The maximum likelihood position of hg was at the chromosome 10 marker D10Mit41 (LOD = 24.8) in the F2 females and 1.5 cM distal to D10Mit41 (LOD = 9.56) in the F2 males with corresponding LOD 2 support intervals of 3.7 and 5.4 cM, respectively. The peak LOD scores were significantly higher than the estimated empirical threshold LOD values. The localization of hg by interval mapping was supported by a test cross of F2 mice recombinant between the LOD 2 support interval and the flanking marker. The interval mapping and test-cross results indicate that hg is not allelic with candidate genes Igf1 or decorin (Dcn), a gene that was mapped close to hg in this study. The hg inheritance was recessive in females, although we could not reject recessive or additive inheritance in males. Possible causes for sex differences in peak LOD scores and for the distortion of transmission ratios observed in F2 males are discussed. The genetic map of the hg region will facilitate further fine mapping and cloning of hg, and allow searches for a homologous quantitative trait locus affecting growth in humans and domestic animals.