Genetic response from marker assisted selection in an outbred population for differing marker bracket sizes and with two identified quantitative trait loci.

Effect of flanking quantitative trait loci (QTL)-marker bracket size on genetic response to marker assisted selection in an outbred population was studied by simulation of a nucleus breeding scheme. In addition, genetic response with marker assisted selection (MAS) from two quantitative trait loci on the same and different chromosome(s) was investigated. QTL that explained either 5% or 10% of phenotypic variance were simulated. A polygenic component was simulated in addition to the quantitative trait loci. In total, 35% of the phenotypic variance was due to genetic factors. The trait was measured on females only. Having smaller marker brackets flanking the QTL increased the genetic response from MAS selection. This was due to the greater ability to trace the QTL transmission from one generation to the next with the smaller flanking QTL-marker bracket, which increased the accuracy of estimation of the QTL allelic effects. Greater negative covariance between effects at both QTL was observed when two QTL were located on the same chromosome compared to different chromosomes. Genetic response with MAS was greater when the QTL were on the same chromosome in the early generations and greater when they were on different chromosomes in the later generations of MAS.     

Mapping-Linked Quantitative Trait Loci Using Bayesian Analysis and Markov Chain Monte Carlo Algorithms

A Bayesian method for mapping linked quantitative trait loci (QTL) using multiple linked genetic markers is presented. Parameter estimation and hypothesis testing was implemented via Markov chain Monte Carlo (MCMC) algorithms. Parameters included were allele frequencies and substitution effects for two biallelic QTL, map positions of the QTL and markers, allele frequencies of the markers, and polygenic and residual variances. Missing data were polygenic effects and multi-locus marker-QTL genotypes. Three different MCMC schemes for testing the presence of a single or two linked QTL on the chromosome were compared. The first approach includes a model indicator variable representing two unlinked QTL affecting the trait, one linked and one unlinked QTL, or both QTL linked with the markers. The second approach incorporates an indicator variable for each QTL into the model for phenotype, allowing or not allowing for a substitution effect of a QTL on phenotype, and the third approach is based on model determination by reversible jump MCMC. Methods were evaluated empirically by analyzing simulated granddaughter designs. All methods identified correctly a second, linked QTL and did not reject the one-QTL model when there was only a single QTL and no additional or an unlinked QTL.     

Mapping quantitative trait Loci underlying fitness-related traits in a free-living sheep population

We searched for quantitative trait loci (QTL) underlying fitness-related traits in a free-living pedigree of 588 Soay sheep in which a genetic map using 251 markers with an average spacing of 15 cM had been established previously. Traits examined included birth date and weight, considered both as maternal and offspring traits, foreleg length, hindleg length, and body weight measured on animals in August and jaw length and metacarpal length measured on cleaned skeletal material. In some cases the data were split to consider different age classes separately, yielding a total of 15 traits studied. Genetic and environmental components of phenotypic variance were estimated for each trait and, for those traits showing nonzero heritability (N= 12), a QTL search was conducted by comparing a polygenic model with a model including a putative QTL. Support for a QTL at genome-wide significance was found on chromosome 11 for jaw length; suggestive QTL were found on chromosomes 2 and 5 (for birth date as a trait of the lamb), 8 (birth weight as a trait of the lamb), and 15 (adult hindleg length). We discuss the prospects for refining estimates of QTL position and effect size in the study population, and for QTL searches in free-living pedigrees in general.     

Detection of multiple quantitative trait loci and their pleiotropic effects in outbred pig populations

Background

Simultaneous detection of multiple QTLs (quantitative trait loci) may allow more accurate estimation of genetic effects. We have analyzed outbred commercial pig populations with different single and multiple models to clarify their genetic properties and in addition, we have investigated pleiotropy among growth and obesity traits based on allelic correlation within a gamete.

Methods

Three closed populations, (A) 427 individuals from a Yorkshire and Large White synthetic breed, (B) 547 Large White individuals and (C) 531 Large White individuals, were analyzed using a variance component method with one-QTL and two-QTL models. Six markers on chromosome 4 and five to seven markers on chromosome 7 were used.

Results

Population A displayed a high test statistic for the fat trait when applying the two-QTL model with two positions on two chromosomes. The estimated heritabilities for polygenic effects and for the first and second QTL were 19%, 17% and 21%, respectively. The high correlation of the estimated allelic effect on the same gamete and QTL test statistics suggested that the two separate QTL which were detected on different chromosomes both have pleiotropic effects on the two fat traits. Analysis of population B using the one-QTL model for three fat traits found a similar peak position on chromosome 7. Allelic effects of three fat traits from the same gamete were highly correlated suggesting the presence of a pleiotropic QTL. In population C, three growth traits also displayed similar peak positions on chromosome 7 and allelic effects from the same gamete were correlated.

Conclusion

Detection of the second QTL in a model reduced the polygenic heritability and should improve accuracy of estimated heritabilities for both QTLs.     

Semiparametric variance components models for genetic studies with longitudinal phenotypes

In a family-based genetic study such as the Framingham Heart Study (FHS), longitudinal trait measurements are recorded on subjects collected from families. Observations on subjects from the same family are correlated due to shared genetic composition or environmental factors such as diet. The data have a 3-level structure with measurements nested in subjects and subjects nested in families. We propose a semiparametric variance components model to describe phenotype observed at a time point as the sum of a nonparametric population mean function, a nonparametric random quantitative trait locus (QTL) effect, a shared environmental effect, a residual random polygenic effect and measurement error. One feature of the model is that we do not assume a parametric functional form of the age-dependent QTL effect, and we use penalized spline-based method to fit the model. We obtain nonparametric estimation of the QTL heritability defined as the ratio of the QTL variance to the total phenotypic variance. We use simulation studies to investigate performance of the proposed methods and apply these methods to the FHS systolic blood pressure data to estimate age-specific QTL effect at 62cM on chromosome 17.     

Empirical Bayes factor analyses of quantitative trait loci for gestation length in Iberian × Meishan F2 sows

The aim of this study was to investigate chromosomal regions affecting gestation length in sows. An experimental F2 cross between Iberian and Meishan pig breeds was used for this purpose and we genotyped 119 markers covering the 18 porcine autosomal chromosomes. Within this context, we have developed a new empirical Bayes factor (BF) approach to compare between nested models, with and without the quantitative trait loci (QTL) effect, and after including the location of the QTL as an unknown parameter in the model. This empirical BF can be easily calculated from the output of a Markov chain Monte Carlo sampling by averaging conditional densities at the null QTL effects. Linkage analyses were performed in each chromosome using an animal model to account for infinitesimal genetic effects. Initially, three QTL were detected at chromosomes 6, 8 and 11 although, after correcting for multiple testing, only the additive QTL located in cM 110 of chromosome 8 remained. For this QTL, the allelic effect of substitution of the Iberian allele increased gestation length in 0.521 days, with a highest posterior density region at 95% ranged between 0.121 and 0.972 days. Although future studies are necessary to confirm if detected QTL is relevant and segregating in commercial pig populations, a hot-spot on the genetic regulation of gestation length in pigs seems to be located in chromosome 8.     

A method to optimize selection on multiple identified quantitative trait loci

A mathematical approach was developed to model and optimize selection on multiple known quantitative trait loci (QTL) and polygenic estimated breeding values in order to maximize a weighted sum of responses to selection over multiple generations. The model allows for linkage between QTL with multiple alleles and arbitrary genetic effects, including dominance, epistasis, and gametic imprinting. Gametic phase disequilibrium between the QTL and between the QTL and polygenes is modeled but polygenic variance is assumed constant. Breeding programs with discrete generations, differential selection of males and females and random mating of selected parents are modeled. Polygenic EBV obtained from best linear unbiased prediction models can be accommodated. The problem was formulated as a multiple-stage optimal control problem and an iterative approach was developed for its solution. The method can be used to develop and evaluate optimal strategies for selection on multiple QTL for a wide range of situations and genetic models.     

Inference of genetic architecture from chromosome partitioning analyses is sensitive to genome variation,sample size,heritability and effect size distribution

Genomewide association studies have contributed immensely to our understanding of the genetic basis of complex traits. One major conclusion arising from these studies is that most traits are controlled by many loci of small effect, confirming the infinitesimal model of quantitative genetics. A popular approach to test for polygenic architecture involves so‐called “chromosome partitioning” where phenotypic variance explained by each chromosome is regressed on the size of the chromosome. First developed for humans, this has now been repeatedly used in other species, but there has been no evaluation of the suitability of this method in species that can differ in their genome characteristics such as number and size of chromosomes. Nor has the influence of sample size, heritability of the trait, effect size distribution of loci controlling the trait or the physical distribution of the causal loci in the genome been examined. Using simulated data, we show that these characteristics have major influence on the inferences of the genetic architecture of traits we can infer using chromosome partitioning analyses. In particular, small variation in chromosome size, small sample size, low heritability, a skewed effect size distribution and clustering of loci can lead to a loss of power and consequently altered inference from chromosome partitioning analyses. Future studies employing this approach need to consider and derive an appropriate null model for their study system, taking these parameters into consideration. Our simulation results can provide some guidelines on these matters, but further studies examining a broader parameter space are needed.     

Comparison of whole-genome prediction models for traits with contrasting genetic architecture in a diversity panel of maize inbred lines

ABSTRACT: BACKGROUND: There is increasing empirical evidence that whole-genome prediction (WGP) is a powerful tool for predicting line and hybrid performance in maize. However, there is a lack of knowledge about the sensitivity of WGP models towards the genetic architecture of the trait. Whereas previous studies exclusively focused on highly polygenic traits, important agronomic traits such as disease resistances, nutrifunctional or climate adaptational traits have a genetic architecture which is either much less complex or unknown. For such cases, information about model robustness and guidelines for model selection are lacking. Here, we compared five WGP models with different assumptions about the distribution of the underlying genetic effects. As contrasting model traits, we chose three highly polygenic agronomic traits and three metabolites each with a major QTL explaining 22 to 30 % of the genetic variance in a panel of 289 diverse maize inbred lines genotyped with 56,110 SNPs. RESULTS: We found the five WGP models to be remarkable robust towards trait architecture with the largest differences in prediction accuracies ranging between 0.05 and 0.14 for the same trait, most likely as the result of the high level of linkage disequilibrium prevailing in elite maize germplasm. Whereas RR-BLUP performed best for the agronomic traits, it was inferior to LASSO or elastic net for the three metabolites. We found the approach of genome partitioning of genetic variance, first applied in human genetics, as useful in guiding the breeder which model to choose, if prior knowledge of the trait architecture is lacking. CONCLUSIONS: Our results suggest that in diverse germplasm of elite maize inbred lines with a high level of LD, WGP models differ only slightly in their accuracies, irrespective of the number and effects of QTL found in previous linkage or association mapping studies. However, small gains in prediction accuracies can be achieved if the WGP model is selected according to the genetic architecture of the trait. If the trait architecture is unknown e.g. for novel traits which only recently received attention in breeding, we suggest to inspect the distribution of the genetic variance explained by each chromosome for guiding model selection in WGP.     

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.     

Mapping epigenetic quantitative trait loci (QTL) altering a developmental trajectory.

Genetic variation in a quantitative trait that changes with age is important to both evolutionary biologists and breeders. A traditional analysis of the dynamics of genetic variation is based on the genetic variance-covariance matrix among different ages estimated from a quantitative genetic model. Such an analysis, however, cannot reveal the mechanistic basis of the genetic variation for a growth trait during ontogeny. Age-specific genetic variance at time t conditional on the causal genetic effect at time t - 1 implies the generation of episodes of new genetic variation arising during the interval t - 1 to t. In the present paper, the conditional genetic variance estimated from Zhu's (1995) conditional model was partitioned into its underlying individual quantitative trait loci (QTL) using molecular markers in an F2 progeny of poplars (Populus trichocarpa and Populus deltoides). These QTL, defined as epigenetic QTL, govern the alterations of growth trajectory in a population. Three epigenetic QTL were detected to contribute significantly to variation in growth trajectory during the period from the establishment year to the subsequent year in the field. It is suggested that the activation and expression of epigenetic QTL are influenced by the developmental status of trees and the environment in which they are grown.     

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.     

Rainbow trout resistance to bacterial cold water disease: two new quantitative trait loci identified after a natural disease outbreak on a French farm

In rainbow trout farming, Flavobacterium psychrophilum, the causative agent of bacterial cold water disease, is responsible for important economic losses. Resistance to F. psychrophilum is heritable, and several quantitative trait loci (QTL) with moderate effects have been detected, opening up promising perspectives for the genetic improvement of resistance. In most studies however, resistance to F. psychrophilum was assessed in experimental infectious challenges using injection as the infection route, which is not representative of natural infection. Indeed, injection bypasses external barriers, such as mucus and skin, that likely play a protective role against the infection. In this study, we aimed at describing the genetic architecture of the resistance to F. psychrophilum after a natural disease outbreak. In a 2000‐fish cohort, reared on a French farm, 720 fish were sampled and genotyped using the medium‐throughput Axiom? Trout Genotyping Array. Overall mortality at the end of the outbreak was 25%. Genome‐wide association studies were performed under two different models for time to death measured on 706 fish with validated genotypes for 30 060 SNPs. This study confirms the polygenic inheritance of resistance to F. psychrophilum with a few QTL with moderate effects and a large polygenic background, the heritability of the trait being estimated at 0.34. Two new chromosome‐wide significant QTL and three suggestive QTL were detected, each of them explaining between 1% and 4% of genetic variance.     

Different models of genetic variation and their effect on genomic evaluation

Background

The theory of genomic selection is based on the prediction of the effects of quantitative trait loci (QTL) in linkage disequilibrium (LD) with markers. However, there is increasing evidence that genomic selection also relies on "relationships" between individuals to accurately predict genetic values. Therefore, a better understanding of what genomic selection actually predicts is relevant so that appropriate methods of analysis are used in genomic evaluations.

Methods

Simulation was used to compare the performance of estimates of breeding values based on pedigree relationships (Best Linear Unbiased Prediction, BLUP), genomic relationships (gBLUP), and based on a Bayesian variable selection model (Bayes B) to estimate breeding values under a range of different underlying models of genetic variation. The effects of different marker densities and varying animal relationships were also examined.

Results

This study shows that genomic selection methods can predict a proportion of the additive genetic value when genetic variation is controlled by common quantitative trait loci (QTL model), rare loci (rare variant model), all loci (infinitesimal model) and a random association (a polygenic model). The Bayes B method was able to estimate breeding values more accurately than gBLUP under the QTL and rare variant models, for the alternative marker densities and reference populations. The Bayes B and gBLUP methods had similar accuracies under the infinitesimal model.

Conclusions

Our results suggest that Bayes B is superior to gBLUP to estimate breeding values from genomic data. The underlying model of genetic variation greatly affects the predictive ability of genomic selection methods, and the superiority of Bayes B over gBLUP is highly dependent on the presence of large QTL effects. The use of SNP sequence data will outperform the less dense marker panels. However, the size and distribution of QTL effects and the size of reference populations still greatly influence the effectiveness of using sequence data for genomic prediction.     

Genome-wide association analysis and genetic architecture of egg weight and egg uniformity in layer chickens

The pioneering work by Professor Soller et al., among others, on the use of genetic markers to analyze quantitative traits has provided opportunities to discover their genetic architecture in livestock by identifying quantitative trait loci (QTL). The recent availability of high-density single nucleotide polymorphism (SNP) panels has advanced such studies by capitalizing on population-wide linkage disequilibrium at positions across the genome. In this study, genomic prediction model Bayes-B was used to identify genomic regions associated with the mean and standard deviation of egg weight at three ages in a commercial brown egg layer line. A total of 24,425 segregating SNPs were evaluated simultaneously using over 2900 genotyped individuals or families. The corresponding phenotypic records were represented as individual measurements or family means from full-sib progeny. A novel approach using the posterior distribution of window variances from the Monte Carlo Markov Chain samples was used to describe genetic architecture and to make statistical inferences about regions with the largest effects. A QTL region on chromosome 4 was found to explain a large proportion of the genetic variance for the mean (30%) and standard deviation (up to 16%) of the weight of eggs laid at specific ages. Additional regions with smaller effects on chromosomes 2, 5, 6, 8, 20, 23, 28 and Z showed suggestive associations with mean egg weight and a region on chromosome 13 with the standard deviation of egg weight at 26-28 weeks of age. The genetic architecture of the analyzed traits was characterized by a limited number of genes or genomic regions with large effects and many regions with small polygenic effects. The region on chromosome 4 can be used to improve both the mean and standard deviation of egg weight by marker-assisted selection.     

Mapping multiple QTL of different effects: comparison of a simple sequential testing strategy and multiple QTL mapping

The aim of this study was to explore, by computer simulation, the mapping of QTLs in a realistic but complex situation of many (linked) QTLs with different effects, and to compare two QTL mapping methods. A novel method to dissect genetic variation on multiple chromosomes using molecular markers in backcross and F₂ populations derived from inbred lines was suggested, and its properties tested using simulations. The rationale for this sequential testing method was to explicitly test for alternative genetic models. The method consists of a series of four basic statistical tests to decide whether variance was due to a single QTL, two QTLs, multiple QTLs, or polygenes, starting with a test to detect genetic variance associated with a particular chromosome. The method was able to distinguish between different QTL configurations, in that the probability to `detect' the correct model was high, varying from 0.75 to 1. For example, for a backcross population of 200 and an overall heritability of 50%, in 78% of replicates a polygenic model was detected when that was the underlying true model. To test the method for multiple chromosomes, QTLs were simulated on 10 chromosomes, following a geometric series of allele effects, assuming positive alleles were in coupling in the founder lines For these simulations, the sequential testing method was compared to the established Multiple QTL Mapping (MQM) method. For a backcross population of 400 individuals, power to detect genetic variance was low with both methods when the heritability was 0.40. For example, the power to detect genetic variation on a chromosome on which 6 QTLs explained 12.6% of the genetic variance, was less than 60% for both methods. For a large heritability (0.90), the power of MQM to detect genetic variance and to dissect QTL configurations was generally better, due to the simultaneous fitting of markers on all chromosomes. It is concluded that when testing different QTL configurations on a single chromosome using the sequential testing procedure, regions of other chromosomes which explain a significant amount of variation should be fitted in the model of analysis. This study reinforces the need for large experiments in plants and other species if the aim of a genome scan is to dissect quantitative genetic variation.     

Using mating designs to uncover QTL and the genetic architecture of complex traits

Analysis of quantitative trait loci (QTL) affecting complex traits is often pursued in single-cross experiments. For most purposes, including breeding, some assessment is desired of the generalizability of the QTL findings and of the overall genetic architecture of the trait. Single-cross experiments provide a poor basis for these purposes, as comparison across experiments is hampered by segregation of different allelic combinations among different parents and by context-dependent effects of QTL. To overcome this problem, we combined the benefits of QTL analysis (to identify genomic regions affecting trait variation) and classic diallel analysis (to obtain insight into the general inheritance of the trait) by analyzing multiple mapping families that are connected via shared parents. We first provide a theoretical derivation of main (general combining ability (GCA)) and interaction (specific combining ability (SCA)) effects on F(2) family means relative to variance components in a randomly mating reference population. Then, using computer simulations to generate F(2) families derived from 10 inbred parents in different partial-diallel designs, we show that QTL can be detected and that the residual among-family variance can be analyzed. Standard diallel analysis methods are applied in order to reveal the presence and mode of action (in terms of GCA and SCA) of undetected polygenes. Given a fixed experiment size (total number of individuals), we demonstrate that QTL detection and estimation of the genetic architecture of polygenic effects are competing goals, which should be explicitly accounted for in the experimental design. Our approach provides a general strategy for exploring the genetic architecture, as well as the QTL underlying variation in quantitative traits.     

QTL for tuber morphology traits in diploid potato

A diploid, potato mapping population consisting of 149 individuals was assessed in three consecutive years for important agronomic and quality traits: tuber shape, regularity of tuber shape, eye depth, mean tuber weight, and tuber flesh color. Analysis of variance showed that the genotype had the largest influence on the phenotypic scores but effect of the genotype × year interactions was also strong. Using this data and an existing genetic map, a quantitative trait loci (QTL) analysis was conducted. From four to seven QTL were detected for each trait except tuber flesh color, which was determined by a major QTL on chromosome III explaining 76.8% of the trait variance. Additionally, a minor QTL for flesh color was localized on chromosome II. For the other traits, significant QTL were detected: for tuber shape on chromosome X, for regularity of tuber shape on chromosome III, for eye depth on chromosome IV, and for tuber weight on chromosome I. Some detected QTL confirmed previous studies, but new ones were also identified.     

Contrasting results from GWAS and QTL mapping on wing length in great reed warblers

A major goal in evolutionary biology is to understand the genetic basis of adaptive traits. In migratory birds, wing morphology is such a trait. Our previous work on the great reed warbler (Acrocephalus arundinaceus) shows that wing length is highly heritable and under sexually antagonistic selection. Moreover, a quantitative trait locus (QTL) mapping analysis detected a pronounced QTL for wing length on chromosome 2, suggesting that wing morphology is partly controlled by genes with large effects. Here, we re‐evaluate the genetic basis of wing length in great reed warblers using a genomewide association study (GWAS) approach based on restriction site‐associated DNA sequencing (RADseq) data. We use GWAS models that account for relatedness between individuals and include covariates (sex, age and tarsus length). The resulting association landscape was flat with no peaks on chromosome 2 or elsewhere, which is in line with expectations for polygenic traits. Analysis of the distribution of p‐values did not reveal biases, and the inflation factor was low. Effect sizes were however not uniformly distributed on some chromosomes, and the Z chromosome had weaker associations than autosomes. The level of linkage disequilibrium (LD) in the population decayed to background levels within c. 1 kbp. There could be several reasons to why our QTL study and GWAS gave contrasting results including differences in how associations are modelled (cosegregation in pedigree vs. LD associations), how covariates are accounted for in the models, type of marker used (multi‐ vs. biallelic), difference in power or a combination of these. Our study highlights that the genetic architecture even of highly heritable traits is difficult to characterize in wild populations.     

Linkage analysis of quantitative traits in an interspecific cross of tomato (lycopersicon esculentum x lycopersicon pimpinellifolium) by means of genetic markers

Linkage relationships between loci affecting quantitative traits (QTL) and marker loci were examined in an interspecific cross between Lycopersicon esculentum and Lycopersicon pimpinellifolium. Parental lines differed for six morphological markers and for four electrophoretic markers. Almost 1700 F-2 plants were scored with respect to the genetic markers and also with respect to 18 quantitative traits. Major genes affecting the quantitative traits were not found, but out of 180 possible marker x trait combinations, 85 showed significant quantitative effects associated with the genetic markers. The average marker-associated main effect was on the order of 6% of the mean value of the trait. Most of the main effects were apparently due to linkage of QTL to the marker loci rather than to pleiotropy. Fourteen of the traits showed at least one highly significant effect of opposite sign to the overall difference between the parental lines, demonstrating the ability of this design to uncover cryptic genetic variation. Significant variance and skewness effects on the quantitative traits were found to be associated with the genetic markers, suggesting the possible presence of loci affecting the variance and shape of quantitative trait distribution in a population. Most marker-associated quantitative effects showed some degree of dominance, generally in the direction of the L. pimpinellifolium parent. When the significant marker-associated effects were examined in pairs, 12% showed significant interaction effects. The results of this study illustrate the potential usefulness of this type of analysis for the detailed genetic investigation of quantitative trait variation in suitably marked populations.