Power of QTL mapping experiments in commercial Atlantic salmon populations, exploiting linkage and linkage disequilibrium and effect of limited recombination in males

Whereas detection and positioning of genes that affect quantitative traits (quantitative trait loci (QTL)) using linkage mapping uses only information from recombinants in the genotyped generations, linkage disequilibrium (LD) mapping uses historical recombinants. Thus, whereas linkage mapping requires large family sizes to detect and accurately position QTL, LD mapping is more dependent on the number of families sampled from the population. In commercial Atlantic salmon breeding programmes, only a small number of individuals per family are routinely phenotyped for traits such as disease resistance and meat colour. In this paper, we assess the power and accuracy of combined linkage disequilibrium linkage analysis (LDLA) to detect QTL in the commercial population using simulation. When 15 half-sib sire families (each sire mated to 30 dams, each dam with 10 progeny) were sampled from the population for genotyping, we were able to detect a QTL explaining 10% of the phenotypic variance in 85% of replicates and position this QTL within 3 cM of the true position in 70% of replicates. When recombination was absent in males, a feature of the salmon genome, power to detect QTL increased; however, the accuracy of positioning the QTL was decreased. By increasing the number of sire families sampled from the population to be genotyped to 30, we were able to increase both the proportion of QTL detected and correctly positioned (even with no recombination in males). QTL with much smaller effect could also be detected. The results suggest that even with the existing recording structure in commercial salmon breeding programmes, there is considerable power to detect and accurately position QTL using LDLA.     

Use of the EM algorithm to detect QTL affecting multiple-traits in an across half-sib family analysis

QTL detection experiments in livestock species commonly use the half-sib design. Each male is mated to a number of females, each female producing a limited number of progeny. Analysis consists of attempting to detect associations between phenotype and genotype measured on the progeny. When family sizes are limiting experimenters may wish to incorporate as much information as possible into a single analysis. However, combining information across sires is problematic because of incomplete linkage disequilibrium between the markers and the QTL in the population. This study describes formulæ for obtaining MLEs via the expectation maximization (EM) algorithm for use in a multiple-trait, multiple-family analysis. A model specifying a QTL with only two alleles, and a common within sire error variance is assumed. Compared to single-family analyses, power can be improved up to fourfold with multi-family analyses. The accuracy and precision of QTL location estimates are also substantially improved. With small family sizes, the multi-family, multi-trait analyses reduce substantially, but not totally remove, biases in QTL effect estimates. In situations where multiple QTL alleles are segregating the multi-family analysis will average out the effects of the different QTL alleles.     

Detection of quantitative trait loci in outbred populations with incomplete marker data.

Augmentation of marker genotypes for ungenotyped individuals is implemented in a Bayesian approach via the use of Markov chain Monte Carlo techniques. Marker data on relatives and phenotypes are combined to compute conditional posterior probabilities for marker genotypes of ungenotyped individuals. The presented procedure allows the analysis of complex pedigrees with ungenotyped individuals to detect segregating quantitative trait loci (QTL). Allelic effects at the QTL were assumed to follow a normal distribution with a covariance matrix based on known QTL position and identity by descent probabilities derived from flanking markers. The Bayesian approach estimates variance due to the single QTL, together with polygenic and residual variance. The method was empirically tested through analyzing simulated data from a complex granddaughter design. Ungenotyped dams were related to one or more sons or grandsires in the design. Heterozygosity of the marker loci and size of QTL were varied. Simulation results indicated a significant increase in power when ungenotyped dams were included in the analysis.     

Respective contributions of maternal insulin resistance and diet to metabolic and hypothalamic phenotypes of progeny

Maternal obesity can influence susceptibility to obesity and type 2 diabetes in progeny. We examined the relationship of maternal insulin resistance (IR), a metabolically important consequence of increased adiposity, to adverse consequences of obesity for fetal development. We used mice heterozygous for a null allele of the insulin receptor (Insr) to study the contributions of maternal IR to offspring phenotype without the potential confound of obesity per se, and how maternal consumption of high-fat diet (HFD) may, independently and interactively, affect progeny. In progeny fed a 60% HFD, body weight and adiposity were transiently (5-7 weeks) increased in wild-type (+/+) offspring of Insr(+/-) HFD-fed dams compared to offspring of wild-type HFD-fed dams. Offspring of HFD-fed wild-type dams had increased body weight, blood glucose, and plasma insulin concentrations compared to offspring of chow-fed wild-type dams. Quantification of proopiomelanocortin (POMC) and neuropeptide-Y (NPY) populations in the arcuate nucleus of the hypothalamus (ARH) of offspring of wild-type vs. Insr(+/-) dams was performed to determine whether maternal IR affects the formation of central feeding circuits. We found a 20% increase in the number of Pomc-expressing cells at postnatal day 9 in offspring of Insr(+/-) dams. In conclusion, maternal HFD consumption-distinct from overt obesity per se-was a major contributor to increased body weight, adiposity, IR, and liver triglyceride (TG) phenotypes in progeny. Maternal IR played a minor role in predisposing progeny to obesity and IR, though it acted synergistically with maternal HFD to exacerbate early obesity in progeny.     

Using genetic markers to directly estimate male selection gradients

We present an analysis of Raphanus raphanistrum and simulations illustrating the utility of directly estimating male phenotypic selection gradients using genetic markers. The method offers a much more refined characterization of selection than attempting to assign paternity to individual progeny. Our analysis of R. raphanistrum reveals selection on remarkably fine features of floral morphology, including anther exsertion, that were opaque to previous approaches. The new results also undermine a previous conclusion that selection on wild radish floral morphology acts primarily through female fitness. Simulation results show that selection gradients on the order of beta = 0.1-0.2 can be readily detected with allozyme markers in moderate-sized (< 200 paternal individuals) populations. Highly polymorphic (e.g., microsatellite) markers will likely detect fine scale selection (beta < 0.1) in larger populations (> or = 400 individuals). Increased progeny sample size, by sampling either additional maternal families or more progeny per maternal parent, partly compensates for low exclusion probability. Increasing the number of possible fathers without changing progeny sample size decreases the ability to detect selection, especially at lower exclusion probabilities. Sampling only some male genotypes reduces the power to detect selection and biases (underestimates) the magnitude of the selection gradient estimate.     

Quantifying evidence for candidate gene polymorphisms: Bayesian analysis combining sequence-specific and quantitative trait loci colocation information

We calculate posterior probabilities for candidate genes as a function of genomic location. Posterior probabilities for quantitative trait loci (QTL) presence in a small interval are calculated using a Bayesian model-selection approach based on the Bayesian information criterion (BIC) and used to combine QTL colocation information with sequence-specific evidence, e.g., from differential expression and/or association studies. Our method takes into account uncertainty in estimation of number and locations of QTL and estimated map position. Posterior probabilities for QTL presence were calculated for simulated data with n = 100, 300, and 1200 QTL progeny and compared with interval mapping and composite-interval mapping. Candidate genes that mapped to QTL regions had substantially larger posterior probabilities. Among candidates with a given Bayes factor, those that map near a QTL are more promising for further investigation with association studies and functional testing or for use in marker-aided selection. The BIC is shown to correspond very closely to Bayes factors for linear models with a nearly noninformative Zellner prior for the simulated QTL data with n > or = 100. It is shown how to modify the BIC to use a subjective prior for the QTL effects.     

Detection and verification of quantitative trait loci for resistance to Dothistroma needle blight in<Emphasis Type="Italic"> Pinus radiata</Emphasis>

Six related radiata pine (Pinus radiata) full-sib families were used to detect and independently verify quantitative trait loci (QTLs) for resistance to Dothistroma needle blight, caused by Dothistroma septospora. The detection families had from 26 to 30 individuals each, and had either a common maternal (31053) or paternal (31032) parent; one family (cross 4) consisted of progeny from both parents, 31053×31032. Approximately 200 additional progeny from cross 4 were clonally replicated and planted at two sites, with at least five to seven ramets of each individual per site. Marker segregation data were collected from a total of 250 RFLP and microsatellite markers, and single factor ANOVAs were conducted separately for each family and marker. A number of putative associations were observed, some across more than one family. Permutation tests were used to confirm expected probabilities of multiple associations based on chance alone. Seven markers representing at least four QTLs for resistance to Dothistroma were identified as being significant in more than one family; one of these was significant at P<0.05 in three families and highly significant at P<0.01 in a fourth. Further confirmation was obtained by testing those markers that were significant in more than one of the detection families (or highly significant in cross 4) in the clonally replicated progeny from cross 4. Four QTL positions were verified in the clonal populations, with a total percent variation accounted for of 12.5.Communicated by D.B. Neale     

Detection of agriculturally important QTLs in chickens and analysis of the factors affecting genotyping strategy

Three single cross populations were generated in order to analyze factors affecting the ability to detect true linkage with minimum false positive or false negative associations, and to detect associations between markers and quantitative traits. The three populations are: (1) a broiler x broiler cross of a single sire and 34 dams, resulting in 266 progeny; (2) a broiler x broiler cross of a single sire and 41 dams resulting in 360 progeny; and (3) a broiler x layer cross of a single sire with 56 dams resulting in 1180 progeny. Based on these three resource populations we show that: a) gradient selective genotyping was more effective than the random selective genotyping; b) selective genotyping was significant at a selected proportion less than 62% of the cumulative truncation point; c) as few as 10% of selected individuals (5% of each of the two tails) were sufficient to show significant association between markers and phenotypes; d) a gradient slices approach was more powerful than using replicates of the extreme groups; and e) in resource populations resulting from crosses between lines of different backgrounds, most of the microsatellite markers used are polymorphic. We also used simulation to test factors affecting power to detect true associations between markers and traits that are hard to detect in experimental resource populations. Using defined populations in the simulation, we concluded that the following guidelines provide reliable detection of linked QTLs: 1) the resource population size should be larger than 100; 2) a QTL effect larger than 0.4 SD is detectable with a reasonable number of markers (>100) and resource population size (>200 subjects); 3) the DNA pool from each tail of the trait distribution should contain at least 10% of the resource family; 4) each of the two DNA pools should include more than 35 individuals. Some of these guidelines that were deduced from the simulation analysis have been confirmed in the experimental part of this study.     

QTL detection with bidirectional and unidirectional selective genotyping: marker-based and trait-based analyses

Selective genotyping of one or both phenotypic extremes of a population can be used to detect linkage between markers and quantitative trait loci (QTL) in situations in which full-population genotyping is too costly or not feasible, or where the objective is to rapidly screen large numbers of potential donors for useful alleles with large effects. Data may be subjected to 'trait-based' analysis, in which marker allele frequencies are compared between classes of progeny defined based on trait values, or to 'marker-based' analysis, in which trait means are compared between progeny classes defined based on marker genotypes. Here, bidirectional and unidirectional selective genotyping were simulated, using population sizes and selection intensities relevant to cereal breeding. Control of Type I error was usually adequate with marker-based analysis of variance or trait-based testing using the normal approximation of the binomial distribution. Bidirectional selective genotyping was more powerful than unidirectional. Trait-based analysis and marker-based analysis of variance were about equally powerful. With genotyping of the best 30 out of 500 lines (6%), a QTL explaining 15% of the phenotypic variance could be detected with a power of 0.8 when tests were conducted at a marker 10 cM from the QTL. With bidirectional selective genotyping, QTL with smaller effects and (or) QTL farther from the nearest marker could be detected. Similar QTL detection approaches were applied to data from a population of 436 recombinant inbred rice lines segregating for a large-effect QTL affecting grain yield under drought stress. That QTL was reliably detected by genotyping as few as 20 selected lines (4.5%). In experimental populations, selective genotyping can reduce costs of QTL detection, allowing larger numbers of potential donors to be screened for useful alleles with effects across different backgrounds. In plant breeding programs, selective genotyping can make it possible to detect QTL using even a limited number of progeny that have been retained after selection.     

Contribution of maternal effect QTL to genetic architecture of early growth in mice

Existing approaches to characterizing quantitative trait loci (QTL) utilize a paradigm explicitly focused on the direct effects of genes, where phenotypic variation among individuals is mapped onto genetic variation of those individuals. For many characters, however, the genotype of the mother via its maternal effect accounts for a considerable portion of the genetically based variation in progeny phenotypes. Thus the focus on direct effect QTL may result in an insufficient or misleading characterization of genetic architecture due to the omission of the potentially important source of genetic variance contributed by maternal effects. We analyze the relative contribution of direct and maternal effect (ME) QTL to early growth in mice using a three-generation intercross of the Small (SM/J) and Large (LG/J) inbred mouse lineages. Using interval mapping and composite interval mapping, direct effect (DE) QTL for early growth (change in body mass during the interval from week 1 to 2) were detected in the F(2) generation of the intercross (n = 510), where no maternal genetic effect variance is present (all individuals are progeny of genetically identical F(1) mothers). ME QTL were detected by treating the phenotypes of cross-fostered F(3) pups as a characteristic of their nurse-dam (n = 168 dams with cross-fostered progeny). Five DE QTL, significant at a chromosome wide level (alpha = 0.05), were detected, with two significant at a genome wide level. FourME QTL significant at the chromosome wide level were detected, with three significant at the genome wide level. A model containing only DE QTL accounted for 11.8% of phenotypic variance, while a model containing only ME QTL accounted for 31.5% of the among litter variance in growth. There was no evidence for pleiotropy of DE and ME loci since there was no overlap between loci detected in these two analyses. Epistasis between all pairs of loci was analyzed for both DEs and MEs. Ten pairs of loci showed significant epistasis for MEs (alpha = 0.05 corrected for multiple comparisons) while four pairs showed significant epistasis for DEs on early growth.     

Imputation of non-genotyped sheep from the genotypes of their mates and resulting progeny

Accurate genomic analyses are predicated on access to a large quantity of accurately genotyped and phenotyped animals. Because the cost of genotyping is often less than the cost of phenotyping, interest is increasing in generating genotypes for phenotyped animals. In some instances this may imply the requirement to genotype older animals with greater phenotypic information content. Biological material for these older informative animals may, however, no longer exist. The objective of the present study was to quantify the ability to impute 11 129 single nucleotide polymorphism (SNP) genotypes of non-genotyped animals (in this instance sires) from the genotypes of their progeny with or without including the genotypes of the progenys’ dams (i.e. mates of the sire to be imputed). The impact on the accuracy of genotype imputation by including more progeny (and their dams’) genotypes in the imputation reference population was also quantified. When genotypes of the dams were not available, genotypes of 41 sires with at least 15 genotyped progeny were used for the imputation; when genotypes of the dams were available, genotypes of 21 sires with at least 10 genotyped progeny were used for the imputation. Imputation was undertaken exploiting family and population level information. The mean and variability in the proportion of genotypes per individual that could not be imputed reduced as the number of progeny genotypes used per individual increased. Little improvement in the proportion of genotypes that could not be imputed was achieved once genotypes of seven progeny and their dams were used or genotypes of 11 progeny without their respective dam’s genotypes were used. Mean imputation accuracy per individual (depicted by both concordance rates and correlation between true and imputed) increased with increasing progeny group size. Moreover, the range in mean imputation accuracy per individual reduced as more progeny genotypes were used in the imputation. If the genotype of the mate of the sire was also used, high accuracy of imputation (mean genotype concordance rate per individual of 0.988), with little additional benefit thereafter, was achieved with seven genotyped progeny. In the absence of genotypes on the dam, similar imputation accuracy could not be achieved even using genotypes on up to 15 progeny. Results therefore suggest, at least for the SNP density used in the present study, that it is possible to accurately impute the genotypes of a non-genotyped parent from the genotypes of its progeny and there is a benefit of also including the genotype of the sire’s mate (i.e. dam of the progeny).     

Multi-QTL mapping for quantitative traits using distorted markers

Marker segregation distortion is a common natural phenomenon. However, relatively little is known about utilizing distorted markers for detecting quantitative trait loci (QTL). Therefore, in this study we proposed a multi-QTL mapping approach that uses distorted markers. First, the information from all markers, including distorted markers, was used to detect segregation distortion loci (SDL). Second, the information from the detected SDL was used to correct the conditional probabilities of the QTL genotypes conditional on marker information, and these corrected probabilities were then incorporated into a multi-QTL mapping methodology. Finally, the proposed approach was validated by both Monte Carlo simulation studies and real data analysis. The results from the simulation studies show that as long as one or two SDL are placed around the simulated QTL, there are no differences between the new method and the ordinary interval mapping method in terms of the power of QTL detection or the estimates of the position and dominant effects of the QTL. However, the power of QTL detection is higher under the dominant genetic model of SDL than under the additive genetic model, and the estimate for the additive effect of QTL using the new method is significantly different from the estimate obtained using ordinary interval mapping. The above results were further confirmed by the detection of QTL for dried soymilk in 222 F_2:4 families in soybean.     

Power analysis of QTL detection in half-sib families using selective DNA pooling

Individual loci of economic importance (QTL) can be detected by comparing the inheritance of a trait and the inheritance of loci with alleles readily identifiable by laboratory methods (genetic markers). Data on allele segregation at the individual level are costly and alternatives have been proposed that make use of allele frequencies among progeny, rather than individual genotypes. Among the factors that may affect the power of the set up, the most important are those intrinsic to the QTL: the additive effect of the QTL, and its dominance, and distance between markers and QTL. Other factors are relative to the choice of animals and markers, such as the frequency of the QTL and marker alleles among dams and sires. Data collection may affect the detection power through the size of half-sib families, selection rate within families, and the technical error incurred when estimating genetic frequencies. We present results for a sensitivity analysis for QTL detection using pools of DNA from selected half-sibs. Simulations showed that conclusive detection may be achieved with families of at least 500 half-sibs if sires are chosen on the criteria that most of their marker alleles are either both missing, or one is fixed, among dams.     

Optimal haplotype structure for linkage disequilibrium-based fine mapping of quantitative trait loci using identity by descent

A linkage disequilibrium-based method for fine mapping quantitative trait loci (QTL) has been described that uses similarity between individuals' marker haplotypes to determine if QTL alleles are identical by descent (IBD) to model covariances among individuals' QTL alleles for a mixed linear model. Mapping accuracy with this method was found to be sensitive to the number of linked markers that was included in the haplotype when fitting the model at a putative position of the QTL. The objective of this study was to determine the optimal haplotype structure for this IBD-based method for fine mapping a QTL in a previously identified QTL region. Haplotypes consisting of 1, 2, 4, 6, or all 10 available markers were fit as a "sliding window" across the QTL region under ideal and nonideal simulated population conditions. It was found that using haplotypes of 4 or 6 markers as a sliding "window" resulted in the greatest mapping accuracy under nearly all conditions, although the true IBD state at a putative QTL position was most accurately predicted by IBD probabilities obtained using all markers. Using 4 or 6 markers resulted in greater discrimination of IBD probabilities between positions while maintaining sufficient accuracy of IBD probabilities to detect the QTL. Fitting IBD probabilities on the basis of a single marker resulted in the worst mapping accuracy under all conditions because it resulted in poor accuracy of IBD probabilities. In conclusion, for fine mapping using IBD methods, marker information must be used in a manner that results in sensitivity of IBD probabilities to the putative position of the QTL while maintaining sufficient accuracy of IBD probabilities to detect the QTL. Contrary to expectation, use of haplotypes of 4-6 markers to derive IBD probabilities, rather than all available markers, best fits these criteria. Thus for populations similar to those simulated here, optimal mapping accuracy for this IBD-based fine-mapping method is obtained with a haplotype structure including a subset of all available markers.     

Efficiency of population structures for mapping of Mendelian and imprinted quantitative trait loci in outbred pigs using variance component methods

In a simulation study different designs for a pure line pig population were compared for efficiency of mapping QTL using the variance component method. Phenotypes affected by a Mendelian QTL, a paternally expressed QTL, a maternally expressed QTL or by a QTL without an effect were simulated. In all alternative designs 960 progeny were phenotyped. Given the limited number of animals there is an optimum between the number of families and the family size. Estimation of Mendelian and parentally expressed QTL is more efficient in a design with large family sizes. Too small a number of sires should be avoided to minimize chances of sires to be non-segregating. When a large number of families is used, the number of haplotypes increases which reduces the accuracy of estimating the QTL effect and thereby reduces the power to show a significant QTL and to correctly position the QTL. Dense maps allow for smaller family size due to exploitation of LD-information. Given the different possible modes of inheritance of the QTL using 8 to16 boars, two litters per dam was optimal with respect to determining significance and correct location of the QTL for a data set consisting of 960 progeny. The variance component method combining linkage disequilibrium and linkage analysis seems to be an appropriate choice to analyze data sets which vary in marker density and which contain complex family structures.     

A fast algorithm for estimating transmission probabilities in QTL detection designs with dense maps

Background

In the case of an autosomal locus, four transmission events from the parents to progeny are possible, specified by the grand parental origin of the alleles inherited by this individual. Computing the probabilities of these transmission events is essential to perform QTL detection methods.

Results

A fast algorithm for the estimation of these probabilities conditional to parental phases has been developed. It is adapted to classical QTL detection designs applied to outbred populations, in particular to designs composed of half and/or full sib families. It assumes the absence of interference.

Conclusion

The theory is fully developed and an example is given.     

A model for quantitative trait loci mapping,linkage phase,and segregation pattern estimation for a full-sib progeny

Quantitative trait loci (QTL) mapping is an important approach for the study of the genetic architecture of quantitative traits. For perennial species, inbred lines cannot be obtained due to inbreed depression and a long juvenile period. Instead, linkage mapping can be performed by using a full-sib progeny. This creates a complex scenario because both markers and QTL alleles can have different segregation patterns as well as different linkage phases between them. We present a two-step method for QTL mapping using full-sib progeny based on composite interval mapping (i.e., interval mapping with cofactors), considering an integrated genetic map with markers with different segregation patterns and conditional probabilities obtained by a multipoint approach. The model is based on three orthogonal contrasts to estimate the additive effect (one in each parent) and dominance effect. These estimatives are obtained using the EM algorithm. In the first step, the genome is scanned to detect QTL. After, segregation pattern and linkage phases between QTL and markers are estimated. A simulated example is presented to validate the methodology. In general, the new model is more effective than existing approaches, because it can reveal QTL present in a full-sib progeny that segregates in any pattern present and can also identify dominance effects. Also, the inclusion of cofactors provided more statistical power for QTL mapping.     

Power of three multitrait methods for QTL detection in crossbred populations

The multitrait detections of QTL applied to a mixture of full- and half-sib families require specific strategies. Indeed, the number of parameters estimated by the multivariate methods is excessive compared with the size of the population. Thus, only multitrait methods based on a univariate analysis of a linear combination (LC) of the traits can be extensively performed. We compared three strategies to obtain the LC of the traits. Two linear transformations were performed on the overall population. The last one was performed within each half-sib family. Their powers were compared on simulated data depending on the frequency of the two QTL alleles in each of the grand parental populations of an intercross design. The transformations from the whole population did not lead to a large loss of power even though the frequency of the QTL alleles was similar in the two grand parental populations. In these cases, applying the within-sire family transformation improved the detection when the number of progeny per sire was greater than 100.     

QTL fine mapping with Bayes C(π): a simulation study

Background

Accurate QTL mapping is a prerequisite in the search for causative mutations. Bayesian genomic selection models that analyse many markers simultaneously should provide more accurate QTL detection results than single-marker models. Our objectives were to (a) evaluate by simulation the influence of heritability, number of QTL and number of records on the accuracy of QTL mapping with Bayes Cπ and Bayes C; (b) estimate the QTL status (homozygous vs. heterozygous) of the individuals analysed. This study focussed on the ten largest detected QTL, assuming they are candidates for further characterization.

Methods

Our simulations were based on a true dairy cattle population genotyped for 38 277 phased markers. Some of these markers were considered biallelic QTL and used to generate corresponding phenotypes. Different numbers of records (4387 and 1500), heritability values (0.1, 0.4 and 0.7) and numbers of QTL (10, 100 and 1000) were studied. QTL detection was based on the posterior inclusion probability for individual markers, or on the sum of the posterior inclusion probabilities for consecutive markers, estimated using Bayes C or Bayes Cπ. The QTL status of the individuals was derived from the contrast between the sums of the SNP allelic effects of their chromosomal segments.

Results

The proportion of markers with null effect (π) frequently did not reach convergence, leading to poor results for Bayes Cπ in QTL detection. Fixing π led to better results. Detection of the largest QTL was most accurate for medium to high heritability, for low to moderate numbers of QTL, and with a large number of records. The QTL status was accurately inferred when the distribution of the contrast between chromosomal segment effects was bimodal.

Conclusions

QTL detection is feasible with Bayes C. For QTL detection, it is recommended to use a large dataset and to focus on highly heritable traits and on the largest QTL. QTL statuses were inferred based on the distribution of the contrast between chromosomal segment effects.     

Mapping quantitative trait loci in F2 incorporating phenotypes of F3 progeny

In plants and laboratory animals, QTL mapping is commonly performed using F(2) or BC individuals derived from the cross of two inbred lines. Typical QTL mapping statistics assume that each F(2) individual is genotyped for the markers and phenotyped for the trait. For plant traits with low heritability, it has been suggested to use the average phenotypic values of F(3) progeny derived from selfing F(2) plants in place of the F(2) phenotype itself. All F(3) progeny derived from the same F(2) plant belong to the same F(2:3) family, denoted by F(2:3). If the size of each F(2:3) family (the number of F(3) progeny) is sufficiently large, the average value of the family will represent the genotypic value of the F(2) plant, and thus the power of QTL mapping may be significantly increased. The strategy of using F(2) marker genotypes and F(3) average phenotypes for QTL mapping in plants is quite similar to the daughter design of QTL mapping in dairy cattle. We study the fundamental principle of the plant version of the daughter design and develop a new statistical method to map QTL under this F(2:3) strategy. We also propose to combine both the F(2) phenotypes and the F(2:3) average phenotypes to further increase the power of QTL mapping. The statistical method developed in this study differs from published ones in that the new method fully takes advantage of the mixture distribution for F(2:3) families of heterozygous F(2) plants. Incorporation of this new information has significantly increased the statistical power of QTL detection relative to the classical F(2) design, even if only a single F(3) progeny is collected from each F(2:3) family. The mixture model is developed on the basis of a single-QTL model and implemented via the EM algorithm. Substantial computer simulation was conducted to demonstrate the improved efficiency of the mixture model. Extension of the mixture model to multiple QTL analysis is developed using a Bayesian approach. The computer program performing the Bayesian analysis of the simulated data is available to users for real data analysis.