A quantitative trait locus for cold tolerance at the booting stage on rice chromosome 8

A quantitative trait locus (QTL) for cold tolerance at the booting stage of a cold-tolerant rice breeding line, Hokkai-PL9, was analyzed. A total of 487 simple sequence repeat (SSR) markers distributed throughout the genome were used to survey for polymorphism between Hokkai-PL9 and a cold-sensitive breeding line, Hokkai287, and 54 markers were polymorphic. Single marker analysis revealed that markers on chromosome 8 are associated with cold tolerance. By interval mapping using an F₂ population between Hokkai-PL9 and Hokkai287, a QTL for cold tolerance was detected on the short arm of chromosome 8. The QTL explains 26.6% of the phenotypic variance, and its additive effect is 11.4%. Substitution mapping suggested that the QTL is located in a 193-kb interval between SSR markers RM5647 and PLA61. We tentatively designated the QTL as qCTB8 (quantitative trait locus for cold tolerance at the booting stage on chromosome 8).     

Mapping quantitative trait loci using molecular marker linkage maps

Summary High-density restriction fragment length polymorphism (RFLP) and allozyme linkage maps have been developed in several plant species. These maps make it technically feasible to map quantitative trait loci (QTL) using methods based on flanking marker genetic models. In this paper, we describe flanking marker models for doubled haploid (DH), recombinant inbred (RI), backcross (BC), F₁ testcross (F₁TC), DH testcross (DHTC), recombinant inbred testcross (RITC), F₂, and F₃ progeny. These models are functions of the means of quantitative trait locus genotypes and recombination frequencies between marker and quantitative trait loci. In addition to the genetic models, we describe maximum likelihood methods for estimating these parameters using linear, nonlinear, and univariate or multivariate normal distribution mixture models. We defined recombination frequency estimators for backcross and F₂ progeny group genetic models using the parameters of linear models. In addition, we found a genetically unbiased estimator of the QTL heterozygote mean using a linear function of marker means. In nonlinear models, recombination frequencies are estimated less efficiently than the means of quantitative trait locus genotypes. Recombination frequency estimation efficiency decreases as the distance between markers decreases, because the number of progeny in recombinant marker classes decreases. Mean estimation efficiency is nearly equal for these methods.     

Correcting for bias in estimation of quantitative trait loci effects

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

A genome scan for quantitative trait loci influencing carcass,post‐natal growth and reproductive traits in commercial Angus cattle

To gain insight into the number of loci of large effect that underlie variation in cattle, a quantitative trait locus (QTL) scan for 14 economically important traits was performed in two commercial Angus populations using 390 microsatellites, 11 single nucleotide polymorphisms (SNPs) and one duplication loci. The first population comprised 1769 registered Angus bulls born between 1955 and 2003, with Expected Progeny Differences computed by the American Angus Association. The second comprised 38 half‐sib families containing 1622 steers with six post‐natal growth and carcass phenotypes. Linkage analysis was performed by half‐sib least squares regression with gridqtl or Bayesian Markov chain Monte Carlo analysis of complex pedigrees with loki . Of the 673 detected QTL, only 118 have previously been reported, reflecting both the conservative approach to QTL reporting in the literature, and the more liberal approach taken in this study. From 33 to 71% of the genetic variance and 35 to 56% of the phenotypic variance in each trait was explained by the detected QTL. To analyse the effects of 11 SNPs and one duplication locus within candidate genes on each trait, a single marker analysis was performed by fitting an additive allele substitution model in both mapping populations. There were 53 associations detected between the SNP/duplication loci and traits with ?log₁₀P_nominal≥ 4.0, where each association explained 0.92% to 4.4% of the genetic variance and 0.01% to 1.86% of the phenotypic variance. Of these associations, only six SNP/duplication loci were located within 8 cM of a QTL peak for the trait, with two being located at the QTL peak: SST_DG156121:c.362A>G for ribeye muscle area and TG_X05380:c.422C>T for calving ease. Strong associations between several SNP/duplication loci and trait variation were obtained in the absence of any detected linked QTL. However, we reject the causality of several commercialized DNA tests, including an association between TG_X05380:c.422C>T and marbling in Angus cattle.     

Estimating genetic variance contributed by a quantitative trait locus: A random model approach

Detecting quantitative trait loci (QTL) and estimating QTL variances (represented by the squared QTL effects) are two main goals of QTL mapping and genome-wide association studies (GWAS). However, there are issues associated with estimated QTL variances and such issues have not attracted much attention from the QTL mapping community. Estimated QTL variances are usually biased upwards due to estimation being associated with significance tests. The phenomenon is called the Beavis effect. However, estimated variances of QTL without significance tests can also be biased upwards, which cannot be explained by the Beavis effect; rather, this bias is due to the fact that QTL variances are often estimated as the squares of the estimated QTL effects. The parameters are the QTL effects and the estimated QTL variances are obtained by squaring the estimated QTL effects. This square transformation failed to incorporate the errors of estimated QTL effects into the transformation. The consequence is biases in estimated QTL variances. To correct the biases, we can either reformulate the QTL model by treating the QTL effect as random and directly estimate the QTL variance (as a variance component) or adjust the bias by taking into account the error of the estimated QTL effect. A moment method of estimation has been proposed to correct the bias. The method has been validated via Monte Carlo simulation studies. The method has been applied to QTL mapping for the 10-week-body-weight trait from an F₂ mouse population.     

Connected populations for detecting quantitative trait loci and testing for epistasis: an application in maize

Quantitative trait loci (QTL) detection experiments have often been restricted to large biallelic populations. Use of connected multiparental crosses has been proposed to increase the genetic variability addressed and to test for epistatic interactions between QTL and the genetic background. We present here the results of a QTL detection performed on six connected F₂ populations of 150 F_2:3 families each, derived from four maize inbreds and evaluated for three traits of agronomic interest. The QTL detection was carried out by composite interval mapping on each population separately, then on the global design either by taking into account the connections between populations or not. Epistatic interactions between loci and with the genetic background were tested. Taking into account the connections between populations increased the number of QTL detected and the accuracy of QTL position estimates. We detected many epistatic interactions, particularly for grain yield QTL (R ² increase of 9.6%). Use of connections for the QTL detection also allowed a global ranking of alleles at each QTL. Allelic relationships and epistasis both contribute to the lack of consistency for QTL positions observed among populations, in addition to the limited power of the tests. The potential benefit of assembling favorable alleles by marker-assisted selection are discussed.     

Mapping quantitative trait loci underlying the cooking and eating quality of rice using a DH population

The cooking and eating quality of rice has attracted more attention recently. In a comprehensive effort to unravel its genetic basis, we conducted a genome-wide analysis of six traits representing the cooking and eating quality of rice grain, namely, amylose content (AC), gel consistency (GC), gelatinization temperature (GT), water absorption (WA), cooked rice elongation (CRE) and volume expansion (VE) using a DH population derived from the anther culture of an F₁ hybrid between WYJ 2 (japonica) and Zhenshan 97B (indica). For each trait, one to three quantitative trait loci (QTL) were found, which were located on chromosomes 1, 2, 3, 6, 11. QTL analysis revealed a major QTL specifying GT, located at the interval RM276-RM121, which should be the same locus as the alkali degeneration gene (alk), while for each of the remaining five traits the QTL explaining the largest proportion of variance was located on the short arm of chromosome 6, centered at RM190 (found in the waxy gene). Our results, in combination with previous reports, further confirmed that either the waxy gene itself or a genomic region tightly linked to it plays a major role in determining the cooking and eating quality of rice.     

Detection and stability of quantitative trait loci (QTL) in Eucalyptus globulus

Eucalyptus globulus Labill. ssp. globulus is an important tree species for the pulp and paper industry, and several breeding programmes throughout the world are striving to improve key traits such as growth and wood density. This study aimed to detect quantitative trait loci (QTL) for growth, wood density, relative bark thickness and early flowering in a single full-sib E. globulus family grown across seven sites. Growth was measured a number of times over a 6-year period, enabling temporal stability of growth QTL to be studied. Ten putative QTL (LOD > 2.0) were detected in the single family, which was of moderate size. Based on permutations of the trait data, six of these QTL were significant at the experimentwise significance level of 0.1 for at least one of the four models implemented in analysis to remove site effects. For wood density, two putative QTL explained 20% of the variance for the trait, indicating that a small number of QTL might explain a reasonable proportion of the trait variance. One of these QTL was found to be independent of QTL for growth whereas the second QTL co-segregated with a QTL for relative incremental growth. The marker nearest to this QTL was associated with fast growth but low wood density. A putative growth QTL at year 6 was found to be relatively stable across ages. In addition, it was found that residuals from models based on measurements from across all families across all sites in the trial detected QTL with greater experimentwise significance.     

Derivation of the shrinkage estimates of quantitative trait locus effects

The shrinkage estimate of a quantitative trait locus (QTL) effect is the posterior mean of the QTL effect when a normal prior distribution is assigned to the QTL. This note gives the derivation of the shrinkage estimate under the multivariate linear model. An important lemma regarding the posterior mean of a normal likelihood combined with a normal prior is introduced. The lemma is then used to derive the Bayesian shrinkage estimates of the QTL effects.     

Identification of quantitative trait loci and associated candidate genes for low-temperature tolerance in cold-hardy winter wheat

Low-temperature (LT) tolerance is an important economic trait in winter wheat (Triticum aestivum L.) that determines the plants’ ability to cope with below freezing temperatures. Essential elements of the LT tolerance mechanism are associated with the winter growth habit controlled by the vernalization loci (Vrn-1) on the group 5 chromosomes. To identify genomic regions, which in addition to vrn-1 determine the level of LT tolerance in hexaploid wheat, two doubled haploid (DH) mapping populations were produced using parents with winter growth habit (vrn-A1, vrn-B1, and vrn-D1) but showing different LT tolerance levels. A total of 107 DH lines were analyzed by genetic mapping to produce a consensus map of 2,873 cM. The LT tolerance levels for the Norstar (LT₅₀=−20.7°C) × Winter Manitou (LT₅₀=−14.3°C) mapping population ranged from −12.0 to −22.0°C. Single marker analysis and interval mapping of phenotyped lines revealed a major quantitative trait locus (QTL) on chromosome 5A and a weaker QTL on chromosome 1D. The 5A QTL located 46 cM proximal to the vrn-A1 locus explained 40% of the LT tolerance variance. Two C-repeat Binding Factor (CBF) genes expressed during cold acclimation in Norstar were located at the peak of the 5A QTL.     

Identification and characterization of large-effect quantitative trait loci for grain yield under lowland drought stress in rice using bulk-segregant analysis

An F_4:5 population of 490 recombinant inbred lines (RILs) from the cross Apo/^2*Swarna was used to detect quantitative trait loci (QTL) with large effects on grain yield under drought stress using bulk-segregant analysis (BSA). Swarna is an important rainfed lowland rice variety grown on millions of hectares in Asia, but is highly susceptible to drought and aerobic soil conditions. Apo is an aerobic-adapted variety with moderate tolerance to drought. Two rice microsatellite (RM) markers, RM324, and RM416, located on chromosomes 2 and 3, respectively, were shown via BSA to be strongly associated with yield under lowland drought stress. The effects of these QTL were tested in a total of eight hydrological environments over a period of 3 years. The QTL linked to RM416 (DTY _3.1 ) had a large effect on grain yield under severe lowland drought stress, explaining about 31% of genetic variance for the trait (P < 0.0001). It also explained considerable variance for yield under mild stress in lowland conditions and aerobic environments. To our knowledge this is the first reported QTL that has a large effect on yield in both lowland drought and aerobic environments. The QTL linked to RM324 (DTY _2.1 ) had a highly significant effect on grain yield in lowland drought stress (R ² = 13–16%) and in two aerobic trials. The effect of these QTL on grain yield was verified to be not mainly due to phenology differences. Effects of DTY _3.1 on yield under stress have been observed in several other rice mapping populations studied at IRRI. Results of this study indicate that BSA is an effective method of identifying QTL alleles with large effects on rice yield under severe drought stress. The Apo alleles for these large-effect QTL for grain yield under drought and aerobic conditions may be immediately exploited in marker-assisted-breeding to improve the drought tolerance of Swarna.     

Marker-based mapping of quantitative trait loci using replicated progenies

Summary When heritability of the trait under investigation is low, replicated progenies can bring about a major reduction in the number of individuals that need to be scored for marker genotype in determining linkage between marker loci and quantitative trait loci (QTL). Savings are greatest when heritability of the trait is low, but are much reduced when heritability of the quantitative trait is moderate to high. Required numbers for recombinant inbred lines will be greater than those required for a simple F₂ population when heritabilities are moderate to high and the proportion of recombination between marker locus and quantitative trait locus is substantial.Contribution No. 2613-E of the Agricultural Research Organization, 1989 series     

Detection of quantitative trait loci controlling extremely early heading in rice

To clarify the genetic basis of extremely early heading in rice, we conducted quantitative trait locus (QTL) analyses using F₂ populations from two genetically wide cross combinations, Hayamasari/Kasalath (HaF₂) and Hoshinoyume/Kasalath (HoF₂). Hayamasari and Hoshinoyume are extremely early-heading japonica cultivars. Photoperiod sensitivity is completely lost in Hayamasari and weak in Hoshinoyume. Three QTLs, QTL(chr6), QTL(chr7), and QTL(chr8), for days-to-heading (DTH) in HaF₂ were detected on chromosomes 6, 7, and 8, respectively, and QTL(chr6) and QTL(chr7) were detected in HoF₂. On the basis of the chromosomal locations, QTL(chr6), QTL(chr7), and QTL(chr8) may be likely to be Hd1, Hd4, and Hd5, respectively, which had been detected previously as QTLs for DTH in an F₂ population of Nipponbare × Kasalath. Alleles of QTL(chr7) decreased DTH dramatically in both Hayamasari and Hoshinoyume, suggesting that QTL(chr7) has a major role in determining extremely early heading. In addition, allele-specific interactions were detected between QTL(chr6), QTL(chr7) and QTL(chr8). This result suggests that not only allelic differences but also epistatic interactions contribute to extremely early heading. QTL(chr8) was detected in HaF₂, but not in HoF₂, suggesting that it determines the difference in DTH between Hayamasari and Hoshinoyume. A major QTL was also detected in the region of QTL(chr8) in QTL analysis using an F₂ population of Hayamasari × Hoshinoyume. This result supports the idea that QTL(chr8) is a major factor that determines the difference in DTH between Hayamasari and Hoshinoyume, and is involved in photoperiod sensitivity.     

Statistical analysis of a linkage experiment in barley involving quantitative trait loci for height and ear-emergence time and two genetic markers on chromosome 4

Summary The quantitative traits height and ear-emergence date were analyzed in the F₂ progeny of a cross between a tall winter barley cultivar (Gerbel) and a short spring barley cultivar (Heriot). The trait distributions were found to be related to the genotypes at two biochemical loci, -amylase (Bmy1) and water-soluble protein (Wsp3), which are known to lie on the long arm of chromosome 4. Linkages between each trait and the markers were investigated using normal mixture models. The two parental phenotypes and the heterozygote phenotype of Bmy1 were distinguishable so the model could be used directly to estimate linkage between Bmy1 and a quantitative trait locus (QTL) for height (Height). The Gerbel homozygote and heterozygote phenotype of Wsp3 could not be distinguished and the model was adapted accordingly. The proportion of plants requiring vernalization was consistent with control by two independent genes acting epistatically, and a normal mixture model based on a two-gene hypothesis was fitted to the distribution of ear-emergence date to estimate linkage between the marker loci and a QTL for ear-emergence date (Vrn1). The parameters of each model were the recombination fraction between the marker locus and the QTL and the means and standard deviations associated with each QTL genotype; these were estimated by maximum likelihood. The fitted distributions correspond well to those observed and the order of the loci along the chromosome is inferred to be Height — Vrn1 — Bmy1 — Wsp3, with Wsp3 being the most distal.     

The distribution of the effects of genes affecting quantitative traits in livestock

Meta-analysis of information from quantitative trait loci (QTL) mapping experiments was used to derive distributions of the effects of genes affecting quantitative traits. The two limitations of such information, that QTL effects as reported include experimental error, and that mapping experiments can only detect QTL above a certain size, were accounted for. Data from pig and dairy mapping experiments were used. Gamma distributions of QTL effects were fitted with maximum likelihood. The derived distributions were moderately leptokurtic, consistent with many genes of small effect and few of large effect. Seventeen percent and 35% of the leading QTL explained 90% of the genetic variance for the dairy and pig distributions respectively. The number of segregating genes affecting a quantitative trait in dairy populations was predicted assuming genes affecting a quantitative trait were neutral with respect to fitness. Between 50 and 100 genes were predicted, depending on the effective population size assumed. As data for the analysis included no QTL of small effect, the ability to estimate the number of QTL of small effect must inevitably be weak. It may be that there are more QTL of small effect than predicted by our gamma distributions. Nevertheless, the distributions have important implications for QTL mapping experiments and Marker Assisted Selection (MAS). Powerful mapping experiments, able to detect QTL of 0.1σ_p, will be required to detect enough QTL to explain 90% the genetic variance for a quantitative trait.     

Validated quantitative trait loci for eggshell quality in experimental and commercial laying hens

Compromised eggshell quality causes considerable economic losses for the egg industry. Breeding for improved eggshell quality has been very challenging. Eggshell quality is a trait that would greatly benefit from marker‐assisted selection, which would allow the selection of sires for their direct contribution to the trait and would also allow implementation of measurements integrating a number of shell parameters that are difficult to measure. In this study, we selected the most promising autosomal quantitative trait loci (QTL) affecting eggshell quality on chromosomes 2, 3, 6 and 14 from earlier experiments and we extended the F₂ population to include 1599 F₂ females. The study was repeated on two commercial populations: Lohmann Tierzucht Rhode Island Red line (n = 692 females) and a Hy‐Line White Plymouth Rock line (n = 290 progeny tested males). We analyzed the selected autosomal QTL regions on the three populations with SNP markers at 4–13 SNPs/Mb density. QTL for eggshell quality were replicated on all studied regions in the F₂ population. New QTL were detected for eggshell color on chromosomes 3 and 6. Marker associations with eggshell quality traits were validated in the tested commercial lines on chromosomes 2, 3 and 6, thus paving the way for marker‐assisted selection for improved eggshell quality.     

The self-incompatibility locus (S) and quantitative trait loci for self-pollination and seed dormancy in sunflower

Wild populations of common sunflower (Helianthus annuus L.) are self-incompatible and have deep seed dormancy, whereas modern cultivars, inbreds, and hybrids are self-compatible and partially-to-strongly self-pollinated, and have shallow seed dormancy. Self-pollination (SP) and seed dormancy are genetically complex traits, the number of self-compatibility (S) loci has been disputed, and none of the putative S loci have been genetically mapped in sunflower. We genetically mapped quantitative trait loci (QTL) for self-incompatibility (SI), SP, and seed dormancy in a backcross population produced from a cross between an elite, self-pollinated, nondormant inbred line (NMS373) and a wild, self-incompatible, dormant population (ANN1811). A population consisting of 212 BC₁ progeny was subsequently produced by backcrossing a single hybrid individual to NMS373. BC₁ progeny produced 0–838 seeds per primary capitula when naturally selfed and 0–518 seeds per secondary capitula when manually selfed and segregated for a single S locus. The S locus mapped to linkage group 17 and was tightly linked to a cluster of previously identified QTL for several domestication and postdomestication traits. Two synergistically interacting QTL were identified for SP among self-compatible (ss) BC₁ progeny (R²=34.6%). NMS373 homozygotes produced 271.5 more seeds per secondary capitulum than heterozygotes. Germination percentages of seeds after-ripened for 4 weeks ranged from 0% to 100% among self-compatible BC₁S₁ families. Three QTL for seed dormancy were identified (R²=38.3%). QTL effects were in the predicted direction (wild alleles decreased self-pollination and seed germination). The present analysis differentiated between loci governing SI and SP and identified DNA markers for bypassing SI and seed dormancy in elite × wild crosses through marker-assisted selection.Electronic Supplementary Material Electronic supplementary material is available for this article at     

Estimation of genetic variance contributed by a quantitative trait locus: correcting the bias associated with significance tests

The Beavis effect in quantitative trait locus (QTL) mapping describes a phenomenon that the estimated effect size of a statistically significant QTL (measured by the QTL variance) is greater than the true effect size of the QTL if the sample size is not sufficiently large. This is a typical example of the Winners’ curse applied to molecular quantitative genetics. Theoretical evaluation and correction for the Winners’ curse have been studied for interval mapping. However, similar technologies have not been available for current models of QTL mapping and genome-wide association studies where a polygene is often included in the linear mixed models to control the genetic background effect. In this study, we developed the theory of the Beavis effect in a linear mixed model using a truncated noncentral Chi-square distribution. We equated the observed Wald test statistic of a significant QTL to the expectation of a truncated noncentral Chi-square distribution to obtain a bias-corrected estimate of the QTL variance. The results are validated from replicated Monte Carlo simulation experiments. We applied the new method to the grain width (GW) trait of a rice population consisting of 524 homozygous varieties with over 300 k single nucleotide polymorphism markers. Two loci were identified and the estimated QTL heritability were corrected for the Beavis effect. Bias correction for the larger QTL on chromosome 5 (GW5) with an estimated heritability of 12% did not change the QTL heritability due to the extremely large test score and estimated QTL effect. The smaller QTL on chromosome 9 (GW9) had an estimated QTL heritability of 9% reduced to 6% after the bias-correction.     

Replication and refinement of a quantitative trait locus influencing milk protein percentage on ovine chromosome 3

A previous genome scan that was conducted in Spanish Churra sheep identified a significant quantitative trait locus (QTL) for milk protein percentage (PP) on chromosome 3 (OAR3), between markers KD103 and OARVH34. The aim of this study was to replicate these results and to refine the mapped position of this QTL. To accomplish this goal, we analysed 14 new half‐sib families of Spanish Churra sheep including 1661 ewes from 29 different flocks. These animals were genotyped for 21 microsatellite markers mapping to OAR3. In addition to a classical linkage analysis (LA), a combined linkage disequilibrium and linkage analysis (LDLA) was performed with the aim of enhancing the resolution of the QTL mapping. The LA that was performed in this sheep population identified the presence of a highly significant QTL for PP near marker KD103 (P_c < 0.001; P_exp < 0.001). The phenotypic variance that was owing to the QTL was 2.74%. Two segregating families for the target QTL were identified in this population with QTL effect estimates of 0.47 and 0.95 SD. The LDLA identified the same QTL as the previous analyses with a high level of statistical significance (P = 9.184 E‐11) and narrowed the confidence interval (CI) to a 13 cM region. These results confirm the segregation of the previously identified OAR3 QTL that influences PP in Spanish Churra sheep. Future research will aim to increase the marker density across the refined CI and to analyse the corresponding candidate genes to identify the allelic variant or variants that underlie this genetic effect.     

Quantitative trait locus analysis of tuber dormancy in diploid potato (Solanum spp.)

Quantitative trait locus (QTL) analysis for tuber dormancy was performed in a diploid potato population (TRP133) consisting of 110 individuals. The female parent was a hybrid between haploid S. tuberosum (2x) and S. chacoense, while the male parent was a S. phureja clone. The population was characterized for ten isozyme loci, 44 restriction fragment length polymorphisms (RFLPs) and 63 random amplified polymorphic DNAs (RAPDs). Eighty-seven of these loci segregating from the female parent were utilized to develop a linkage map that comprised 10 of the 12 chromosomes in the genome. Dormancy, as measured by days-to-sprouting after harvest, ranged from 10 to 90 days, with a mean of 19 days. QTLs were mapped by conducting one-way analyses of variance for each marker locus by dormancy combination. Twenty-two markers had a significant association with dormancy, identifying six putative QTLs localized on each of chromosomes 2, 3, 4, 5, 7 and 8. The QTL with the strongest effect on dormancy was detected on chromosome 7. A multilocus model was developed using the locus with highest R² value in each QTL. This model explained 57.5% of the phenotypic variation for dormancy. Seven percent of possible epistatic interactions among significant markers were significant when tested through two-way analyses of variance. When these were included in the main-effects model, it explained 72.1% of the phenotypic variation for dormancy. QTL analysis in potato, the methodology to transfer traits and interactions into the 4x level, and QTLs of value for marker-assisted selection, are discussed.