Interactions between markers can be caused by the dominance effect of quantitative trait loci

F₂ populations are commonly used in genetic studies of animals and plants. For simplicity, most quantitative trait locus or loci (QTL) mapping methods have been developed on the basis of populations having two distinct genotypes at each polymorphic marker or gene locus. In this study, we demonstrate that dominance can cause the interactions between markers and propose an inclusive linear model that includes marker variables and marker interactions so as to completely control both additive and dominance effects of QTL. The proposed linear model is the theoretical basis for inclusive composite-interval QTL mapping (ICIM) for F₂ populations, which consists of two steps: first, the best regression model is selected by stepwise regression, which approximately identifies markers and marker interactions explaining both additive and dominance variations; second, the interval mapping approach is applied to the phenotypic values adjusted by the regression model selected in the first step. Due to the limited mapping population size, the large number of variables, and multicollinearity between variables, coefficients in the inclusive linear model cannot be accurately determined in the first step. Interval mapping is necessary in the second step to fine tune the QTL to their true positions. The efficiency of including marker interactions in mapping additive and dominance QTL was demonstrated by extensive simulations using three QTL distribution models with two population sizes and an actual rice F₂ population.     

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     

Relationship between heterosis and heterozygosity at marker loci: a theoretical computation

Summary In this paper we have studied the linear correlation between a genetic distance index between two parent lines (based on marker loci information) and the heterosis observed in the F₁ hybrid from the two lines, for a quantitative character (determined by several loci, or QTL). Theoretical computations of the correlation coefficient () between the distance index and the heterosis were made, assuming the biallelic model (defined by Fisher). When the alleles at both marker loci and QTL are equally distributed among the whole population of considered lines, the coefficient is a function of the squares of linkage disequilibria between alleles at marker loci and alleles at QTL. The QTL that are not marked by marker loci and marker loci that do not mark any QTL play symmetrical roles and can decrease greatly. We conclude that the prediction of F₁ hybrid heterosis based on marker loci would be more efficient if these markers were selected for their relationship to the alleles implicated in the heterotic traits considered.     

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.     

The genetic control of seven isozymic loci in Vicia faba L. Identification of lines and estimates of outcrossing rates between plants pollinated by bumble bees

A simplified and non-destructive method using starch gel electrophoresis has been developed on seeds to identify inbred lines of Vicia faba and assess outcrossing rates and gene dispersal in pollination experiments. Six enzyme systems (Alcohol dehydrogenase, Aspartate aminotransferase, Glucose-6-phosphate isomerase, Isocitrate dehydrogenase, Phosphogluconate dehydrogenase and Shikimate dehydrogenase) were analysed from parental lines, crosses performed between lines bearing dissimilar isozyme patterns in pollination cages with Bombus and F₂ progenies obtained from manual selfing of F₁ hybrids. The allozymes at each of the seven studied loci segregated in the expected Mendelian fashion and behaved in a co-dominant manner except for the Adh-2 locus where the only variant was a null allele. No evidence of genetic linkage was observed between at least 13 of the 15 pairs of the studied loci. Percentage of cross fertilisation by Bombus between seven pairs of inbred lines ranged between 1.7% and 28.3%. Pollen transfer between a donor line and a recipient line by two species of Bombus did not lead to differences in outcrossing rates (both about 8%). The new PGD marker with two loci at three alleles each is particularly discriminating and valuable in pollination studies and breeding of V. faba.     

Estimation of recombination parameters between a quantitative trait locus (QTL) and two marker gene loci

Summary A new method is described to obtain maximum likelihood estimates of recombination frequencies between quantitative trait loci (QTL) and marker gene loci; it is based on Fisher's method of scoring and numerical differentiation. The method is applied to data from chromosome-doubled monoploid lines of barley originating from the F₁ generation of a cross between two well-adapted barley varieties. The lines segregated for marker gene loci ddt (DDT resistance) and s (short rachilla hairs) on chromosome 7. The quantitative trait of single-kernel weight was found statistically significantly associated with locus s, but not with locus ddt. The association is ascribed to a QTL designated Kw1. It could not be ascribed to pleiotropism at locus s since the recombination frequency between s and Kw1 (0.26±0.09) differed significantly from zero. The recombination frequencies between Kw1 and ddt and between ddt and s were 0.42±0.07 and 0.31±0.03, respectively, suggesting the locus order ddt, s, Kw1. The segregation ratio for alleles in locus Kw1 was estimated to be 4357, which is not significantly different from a 11 ratio. Means and standard deviations of single-kernel weight for lines with either of the two Kw1 alleles were estimated; the Kw1 locus accounted for 25% of the variance of the single kernel weight.     

Quantitative trait loci affecting cotton fiber are linked to the t1 locus in upland cotton

Pilose (T ₁), a dominant marker in upland cotton, has been associated with coarse, short fibers. Pilose was, thereby, considered to be pleiotropic on fiber fineness and length. However, a pilose-expressing line with a fiber of average fineness was recently identified. This finding does not support pleiotropy between T ₁ and fiber traits, but is indicative of linkage between pilose and loci influencing fiber characteristics. To understand the relationship between T ₁ and fiber traits, a pilose line with short, coarse fiber was crossed to two t ₁ lines with standard fiber characteristics. One hundred and forty-nine F₂-derived F₃ lines were developed from one cross, and 60 F₂-derived F₃ lines from the other. Seven fiber traits (elongation, maturity, micronaire reading, perimeter, 2.5% span length, strength, and wall thickness) were measured. Segregation was normal, as indicated by allelic frequencies of 0.5 for T ₁ and t ₁, and segregation ratios of 121 for marker genotypes. The association of homozygous T ₁ lines with fibers of average fineness was again observed. Linkage between T ₁ and loci affecting micronaire, perimeter, 2.5% span length, strength, and wall thickness was found in both populations. Significant additive and non-additive gene effects for each of these traits at the marker locus were found as well. The pilose marker accounted for 10–75% of the phenotypic variation associated with each trait. In conclusion, the t ₁ locus is linked to numerous loci that influence fiber traits, and this linkage has previously been misinterpreted as pleiotropy.     

The effect of population structure on the relationship between heterosis and heterozygosity at marker loci

The relationship between heterozygosity at neutral marker loci and heterosis of F₁ hybrids is investigated using a theoretical model. Results emphasize that linkage disequilibrium between the markers and the loci implicated in heterosis [quantitative trait loci (QTLs) that exhibit dominance effects] is a necessary condition to finding a correlation ( _mh ) between heterozygosity at marker loci and the heterosis. The effect of population structure, in which the parental inbred lines of the hybrids belong to different heterotic groups, is considered. _mh is investigated for: (1) hybrids between lines that belong to the same heterotic group (within-group hybrids); (2) hybrids between lines that belong to different groups (between-group hybrids); and (3) all hybrids, both within and between-groups. Within a group, significant values of ( _mh ) may arise because of linkage disequilibrium generated by drift. At the between-group level, no correlation is expected since link-age disequilibrium should differ randomly from one group to the other, which is consistent with recent experimental results. Possible ways to achieve prediction of the heterosis in this situation are discussed. When all hybrids are considered simultaneously, divergence of allelic frequencies among groups for the markers and the QTLs produces a correlation between heterosis and heterozygosity at marker loci. This correlation increases with the number of markers that are considered.     

Genetic variation in pea (Pisum) dehydrins: sequence elements responsible for length differences between dehydrin alleles and between dehydrin loci in Pisum sativum L.

 The electrophoretic patterns of dehydrins extracted from mature seeds of a range of pea (Pisum) species revealed extensive variation in dehydrin polypeptide mobility. Variation was also observed among lines of P. sativum. Crosses between lines with different dehydrin electrophoretic patterns produced F₁ seeds with additive patterns, and segregation in the F₂ generation was consistent with a 1 : 2 : 1 ratio, indicating allelic variation at each of two dehydrin loci (Dhn2, Dhn3). Genetic linkage was observed between Dhn2 and Dhn3, and the segregation ratios indicated preferential transmission of one allele at the Dhn3 locus. Dehydrin cDNA clones were characterised that encoded the allelic variants at Dhn2 and Dhn3. Their deduced amino-acid sequences were very similar to each other as well as to the product of the Dhn1 locus reported previously. Comparisons were made between the sequences of allelic variants at a single locus, and between the products of different loci. Differences in the electrophoretic mobilities between allelic variants at Dhn2 and Dhn3 were associated with differences in polypeptide length resulting principally from tandem duplications of 21 (Dhn2) or 24 (Dhn3) amino-acid residues. These duplications accounted for much of the difference in length between dehydrins encoded by the different loci. The conserved core of one of the duplicated regions varied in copy number, and small insertions/deletions of amino acids near this core also contributed to length variation both between allelic forms and between loci. Dehydrins possess characteristic highly conserved amino-acid sequence motifs, yet vary considerably in length. Mechanisms involving sequence duplication appear to be responsible for generating the length differences observed between allelic variants as well as between the products of different loci. Received: 12 June 1997 / Accepted: 29 October 1997     

Comparison of genetic differentiation at marker loci and quantitative traits

The comparison of the degree of differentiation in neutral marker loci and genes coding quantitative traits with standardized and equivalent measures of genetic differentiation (F_ST and Q_ST, respectively) can provide insights into two important but seldom explored questions in evolutionary genetics: (i) what is the relative importance of random genetic drift and directional natural selection as causes of population differentiation in quantitative traits, and (ii) does the degree of divergence in neutral marker loci predict the degree of divergence in genes coding quantitative traits? Examination of data from 18 independent studies of plants and animals using both standard statistical and meta‐analytical methods revealed a number of interesting points. First, the degree of differentiation in quantitative traits (Q_ST) typically exceeds that observed in neutral marker genes (F_ST), suggesting a prominent role for natural selection in accounting for patterns of quantitative trait differentiation among contemporary populations. Second, the F_ST – Q_ST difference is more pronounced for allozyme markers and morphological traits, than for other kinds of molecular markers and life‐history traits. Third, very few studies reveal situations were Q_ST < F_ST, suggesting that selection pressures, and hence optimal phenotypes, in different populations of the same species are unlikely to be often similar. Fourth, there is a strong correlation between Q_ST and F_ST indices across the different studies for allozyme (r=0.81), microsatellite (r=0.87) and combined (r=0.75) marker data, suggesting that the degree of genetic differentiation in neutral marker loci is closely predictive of the degree of differentiation in loci coding quantitative traits. However, these interpretations are subject to a number of assumptions about the data and methods used to derive the estimates of population differentiation in the two sets of traits.     

Maximum likelihood techniques for the mapping and analysis of quantitative trait loci with the aid of genetic markers

A method is presented to estimate the biometric parameters of a quantitative trait locus linked to a genetic marker when both loci are segregating in the F-2 generation of a cross between two inbred lines. The method, which assumes underlying normal distributions, is a combination of maximum likelihood and moments methods and uses the statistics of the genetic marker genotype samples for the quantitative trait to estimate the recombination frequency between the two loci and the means and variances of the genotypes of the quantitative trait locus. With this method, the genetic parameters of a locus affecting plant height linked to an electrophoretic marker for esterase were accurately estimated from a sample of 1596 F-2 progeny of a cross between two species of Lycopersicon (tomato). Linkage distance between the two loci was 38 map units and the effect of the quantitative trait locus was 1.6 phenotypic standard deviation units. Accurate estimates of the genetic parameters and linkage distance for populations of 2000 individuals simulated with a segregating codominant locus with an effect of 1.63 standard deviations linked to a genetic marker with .2 recombination were also derived by this method. The method is not effective in distinguishing between complete and partial linkage in samples of only 500 individuals or for quantitative loci with effects less than a phenotypic standard deviation. The method is more effective for codominant than for dominant loci.     

Identification of two loci for resistance to clubroot (<Emphasis Type="Italic">Plasmodiophora brassicae</Emphasis> Woronin) in <Emphasis Type="Italic">Brassica rapa</Emphasis> L.

In an analysis of 114 F₂ individuals from a cross between clubroot-resistant and susceptible lines of Brassica rapa L., 'G004' and 'Hakusai Chukanbohon Nou 7' (A9709), respectively, we identified two loci, Crr1 and Crr2, for clubroot (caused by Plasmodiophora brassicae Woronin) resistance. Each locus segregated independently among the F₂ population, indicating that the loci reside on a different region of chromosomes or on different chromosomes. Genetic analysis showed that each locus had little effect on clubroot resistance by itself, indicating that these two loci are complementary for clubroot resistance. The resistance to clubroot was much stronger when both loci were homozygous for resistant alleles than when they were heterozygous. These results indicate that clubroot resistance in B. rapa is under oligogenic control and at least two loci are necessary for resistance.Communicated by H.C. Becker     

On the detection of imprinted quantitative trait loci in line crosses: effect of linkage disequilibrium

Imprinted quantitative trait loci (QTL) are commonly reported in studies using line-cross designs, especially in livestock species. It was previously shown that such parent-of-origin effects might result from the nonfixation of QTL alleles in one or both parental lines, rather than from genuine molecular parental imprinting. We herein demonstrate that if linkage disequilibrium exists between marker loci and nonfixed QTL, spurious detection of pseudo-imprinting is increased by an additional 40–80% in scenarios mimicking typical livestock situations. This is due to the fact that imprinting can be tested only in F₂ offspring whose sire and dam have distinct marker genotypes. In the case of linkage disequilibrium between markers and QTL, such parents have a higher chance to have distinct QTL genotypes as well, thus resulting in distinct padumnal and madumnal allele substitution effects, i.e., QTL pseudo-imprinting.     

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

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

Quantitative trait loci analysis of heat stress resistance of spermatocytes in the MRL/MpJ mouse

The MRL/MpJ mouse has previously been reported to possess an interesting phenotype in which spermatocytes are resistant to the abdominal temperature heat shock. In this study genetic analysis for it was performed. The phenotypes of F₂ progenies produced by mating MRL/MpJ and control strain C57BL/6 mice were not segregated into two types as parental phenotypes, suggesting that the phenotype is controlled by multiple genetic loci. Thus, quantitative trait loci (QTL) analysis was performed using 98 microsatellite markers. The weight ratio of the cryptorchid testis to the intact testis (testis weight ratio) and the Sertoli cell index were used for quantitative traits. QTL analysis revealed two significant QTLs located on Chrs 1 and 11 for testis weight ratio and one significant QTL located in the same region of Chr 1 for the Sertoli cell index. A microsatellite marker locus located in the peak of the QTL on Chr 1 did not recombine with the exonuclease 1 (Exo1) gene locus in 140 F₂ progenies. Mutation of the Exo1 gene was previously reported to be responsible for metaphase-specific apoptosis (MSA) of spermatocytes in the MRL/MpJ mouse. These results raise the possibility that mutation of the Exo1 gene is responsible for both MSA and heat stress resistance of spermatocytes in the MRL/MpJ mouse.     

Mapping the nucleolus organizer region,seed protein loci and isozyme loci on chromosome 1R in rye

Summary The nucleolus organizer region located on the short arm of chromosome 1R of rye consists of a large cluster of genes that code for ribosomal RNA (designated the Nor-R1 locus). The genes in the cluster are separated by spacer regions which can vary in length in different rye lines. Differences in the spacer regions were scored in two families of F₂ progeny. Segregation also occurred, in one or both of the families, at two seed protein loci and at two isozyme loci also located on chromosome 1R. The seed protein loci were identified as the Sec 1 locus controlling -secalins located on the short arm of chromosome 1R and the Sec 3 locus controlling high-molecular-weight secalins located on the long arm of 1R. The two isozyme loci were the Gpi-R1 locus controlling glucose-phosphate isomerase isozymes and the Pgd 2 locus controlling phosphogluconate dehydrogenase isozymes. The data indicated linkage between all five loci and map distances were calculated. The results indicate a gene order: Pgd 2 ... Sec 3 ... [centromere] ... Nor-R1 ... Gpi-R1 ... Sec 1. Evidence was obtained that rye possesses a minor 5S RNA locus (chromosome location unknown) in addition to the major 5S RNA locus previously shown to be located on the short arm of chromosome 1R.     

Linkage between loci of quantitative traits and marker loci: multi-trait analysis with a single marker

An efficient approach to increase the resolution power of linkage analysis between a quantitative trait locus (QTL) and a marker is described in this paper. It is based on a counting of the correlations between the QTs of interest. Such correlations may be caused by the segregation of other genes, environmental effects and physiological limitations. Let a QT locus A/a affect two correlated traits, x and y. Then, within the framework of mixture models, the accuracy of the parameter estimates may be seriously increased, if bivariate densities f _aa(x, y), f _Aa(x, y) and f _AA(x, y) rather than the marginals are considered as the basis for mixture decomposition. The efficiency of the proposed method was demonstrated employing Monte-Carlo simulations. Several types of progeny were considered, including backcross, F₂ and recombinant inbred lines. It was shown that provided the correlation between the traits involved was high enough, a good resolution to the problem is possible even if the QTL groups are strongly overlapping for their marginal densities.     

Mapping loci controlling vernalization requirement in Brassica rapa

Brassica cultivars are classified as biennial or annual based on their requirement for a period of cold treatment (vernalization) to induce flowering. Genes controlling the vernalization requirement were identified in a Brassica rapa F₂ population derived from a cross between an annual and a biennial oilseed cultivar by using an RFLP linkage map and quantitative trait locus (QTL) analysis of flowering time in F₃ lines. Two genomic regions were strongly associated with variation for flowering time of unvernalized plants and alleles from the biennial parent in these regions delayed flowering. These QTLs had no significant effect on flowering time after plants were vernalized for 6 weeks, suggesting that they control flowering time through the requirement for vernalization. The two B. rapa linkage groups containing these QTLs had RFLP loci in common with two B. napus linkage groups that were shown previously to contain QTLs for flowering time. An RFLP locus detected by the cold-induced gene COR6.6 cloned from Arabidopsis thaliana mapped very near to one of the B. rapa QTLs for flowering time.     

Identification of quantitative trait loci controlling sucrose content in soybean (Glycine max)

Sucrose is a primary constituent of soybean (Glycine max) seed; however, little information concerning the inheritance of seed sucrose in soybean is available. The objective of this research was to use molecular markers to identify genomic regions significantly associated with quantitative trait loci (QTL) controlling sucrose content in a segregating F₂ population. DNA samples from 149 F₂ individuals were analyzed with 178 polymorphic genetic markers, including RFLPs, SSRs, and RAPDs. Sucrose content was measured on seed harvested from each of 149 F_2:3 lines from replicated field experiments in 1993 and 1995. Seventeen marker loci, mapping to seven different genomic regions, were significantly associated with sucrose variation at P<0.01. Individually, these markers explained from 6.1% to 12.4% of the total phenotypic variation for sucrose content in this population. In a combined analysis these genomic regions; explained 53% of total variation for sucrose content. No significant evidence of epistasis among QTLs was observed. Comparison of our QTL mapping results for sucrose content and those previously reported for protein and oil content (the other major seed constituents in soybean), suggests that seed quality traits are inherited as clusters of linked loci or that `major' QTLs with pleiotropic effects may control all three traits. Of the seven genomic regions having significant effects on sucrose content, three were associated with significant variation for protein content and three were significantly associated with oil content.     

Mapping quantitative trait loci for binary trait in the F2:3 design

In the analysis of inheritance of quantitative traits with low heritability, an F_2:3 design that genotypes plants in F₂ and phenotypes plants in F_2:3 progeny is often used in plant genetics. Although statistical approaches for mapping quantitative trait loci (QTL) in the F_2:3 design have been well developed, those for binary traits of biological interest and economic importance are seldom addressed. In this study, an attempt was made to map binary trait loci (BTL) in the F_2:3 design. The fundamental idea was: the F₂ plants were genotyped, all phenotypic values of each F_2:3 progeny were measured for binary trait, and these binary trait values and the marker genotype informations were used to detect BTL under the penetrance and liability models. The proposed method was verified by a series of Monte-Carlo simulation experiments. These results showed that maximum likelihood approaches under the penetrance and liability models provide accurate estimates for the effects and the locations of BTL with high statistical power, even under of low heritability. Moreover, the penetrance model is as efficient as the liability model, and the F_2:3 design is more efficient than classical F₂ design, even though only a single progeny is collected from each F_2:3 family. With the maximum likelihood approaches under the penetrance and the liability models developed in this study, we can map binary traits as we can do for quantitative trait in the F_2:3 design.