Optimum spacing of genetic markers for determining linkage between marker loci and quantitative trait loci

The cost of experiments aimed at determining linkage between marker loci and quantitative trait loci (QTL) was investigated as a function of marker spacing and number of individuals scored. It was found that for a variety of experimental designs, fairly wide marker spacings (ca. 50 cM) are optimum or close to optimum for initial studies of marker-QTL linkage, in the sense of minimizing overall cost of the experiment. Thus, even when large numbers of more or less evenly spaced markers are available, it will not always be cost effective to make full utilization of this capacity. This is particularly true when costs of rearing and trait evaluation per individual scored are low, as when marker data are obtained on individuals raised and evaluated for quantitative traits as part of existing programs. When costs of rearing and trait evaluation per individual scored are high, however, as in human family data collection carried out primarily for subsequent marker — QTL analyses, or when plants or animals are raised specifically for purposes of marker — QTL linkage experiments, optimum spacing may be rather narrow. It is noteworthy that when marginal costs of additional markers or individuals are constant, total resources allocated to a given experiment will determine total number of individuals sampled, but not the optimal marker spacing.     

A general mixture model for mapping quantitative trait loci by using molecular markers

Summary In a segregating population a quantitative trait may be considered to follow a mixture of (normal) distributions, the mixing proportions being based on Mendelian segregation rules. A general and flexible mixture model is proposed for mapping quantitative trait loci (QTLs) by using molecular markers. A method is discribed to fit the model to data. The model makes it possible to (1) analyse non-normally distributed traits such as lifetimes, counts or percentages in addition to normally distributed traits, (2) reduce environmental variation by taking into account the effects of experimental design factors and interaction between genotype and environment, (3) reduce genotypic variation by taking into account the effects of two or more QTLs simultaneously, (4) carry out a (combined) analysis of different population types, (5) estimate recombination frequencies between markers or use known marker distances, (6) cope with missing marker observations, (7) use markers as covariables in detection and mapping of QTLs, and finally to (8) implement the mapping in standard statistical packages.     

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     

Sequential sampling in determining linkage between marker loci and quantitative trait loci

Summary As compared to classical, fixed sample size techniques, simulation studies showed that a proposed sequential sampling procedure can provide a substantial decrease (up to 50%, in some cases) in the mean sample size required for the detection of linkage between marker loci and quantitative trait loci. Sequential sampling with truncation set at the required sample size for the non-sequential test, produced a modest further decrease in mean sample size, accompanied by a modest increase in error probabilities. Sequential sampling with observations taken in groups produced a noticeable increase in mean sample size, with a considerable decrease in error probabilities, as compared to straightforward sequential sampling. It is concluded that sequential sampling has a particularly useful application to experiments aimed at investigating the genetics of differences between lines or strains that differ in some single outstanding trait.     

Trait-based analyses for the detection of linkage between marker loci and quantitative trait loci in crosses between inbred lines

Summary Methods are presented for determining linkage between a marker locus and a nearby locus affecting a quantitative trait (quantitative trait locus=QTL), based on changes in the marker allele frequencies in selection lines derived from the F-2 of a cross between inbred lines, or in the high and low phenotypic classes of an F-2 or BC population. The power of such trait-based (TB) analyses was evaluated and compared with that of methods for determining linkage based on the mean quantitative trait value of marker genotypes in F-2 or BC populations [marker-based (MB) analyses]. TB analyses can be utilized for marker-QTL linkage determination in situations where the MB analysis is not applicable, including analysis of polygenic resistance traits where only a part of the population survives exposure to the Stressor and analysis of marker-allele frequency changes in selection lines. TB analyses may be a useful alternative to MB analyses when interest is centered on a single quantitative trait only and costs of scoring for markers are high compared with costs of raising and obtaining quantitative trait information on F-2 or BC individuals. In this case, a TB analysis will enable equivalent power to be obtained with fewer individuals scored for the marker, but more individuals scored for the quantitative trait. MB analyses remain the method of choice when more than one quantitative trait is to be analyzed in a given population.Contribution from the ARO, Bet Dagan, Israel. No. 1698-E, 1986 series     

Constructing a new integrated genetic linkage map and mapping quantitative trait loci for vegetative mycelium growth rate in Lentinula edodes

The most saturated linkage map for Lentinula edodes to date was constructed based on a monokaryotic population of 146 single spore isolates (SSIs) using sequence-related amplified polymorphism (SRAP), target region amplification polymorphism (TRAP), insertion–deletion (InDel) markers, and the mating-type loci. Five hundred and twenty-four markers were located on 13 linkage groups (LGs). The map spanned a total length of 1006.1 cM, with an average marker spacing of 2.0 cM. Quantitative trait loci (QTLs) mapping was utilized to uncover the loci regulating and controlling the vegetative mycelium growth rate on various synthetic media, and complex medium for commercial cultivation of L. edodes. Two and 13 putative QTLs, identified respectively in the monokaryotic population and two testcross dikaryotic populations, were mapped on seven different LGs. Several vegetative mycelium growth rate-related QTLs uncovered here were clustered on LG4 (Qmgr1, Qdgr1, Qdgr2 and Qdgr9) and LG6 (Qdgr3, Qdgr4 and Qdgr5), implying the presence of main genomic areas responsible for growth rate regulation and control. The QTL hotspot region on LG4 was found to be in close proximity to the region containing the mating-type A (MAT-A) locus. Moreover, Qdgr2 on LG4 was detected on different media, contributing 8.07 %–23.71 % of the phenotypic variation. The present study provides essential information for QTL mapping and marker-assisted selection (MAS) in L. edodes.     

Estimation of the contribution of quantitative trait loci (QTL) to the variance of a quantitative trait by means of genetic markers

The estimation of the contribution of an individual quantitative trait locus (QTL) to the variance of a quantitative trait is considered in the framework of an analysis of variance (ANOVA). ANOVA mean squares expectations which are appropriate to the specific case of QTL mapping experiments are derived. These expectations allow the specificities associated with the limited number of genotypes at a given locus to be taken into account. Discrepancies with classical expectations are particularly important for two-class experiments (backcross, recombinant inbred lines, doubled haploid populations) and F₂ populations. The result allows us firstly to reconsider the power of experiments (i.e. the probability of detecting a QTL with a given contribution to the variance of the trait). It illustrates that the use of classical formulae for mean squares expectations leads to a strong underestimation of the power of the experiments. Secondly, from the observed mean squares it is possible to estimate directly the variance associated with a locus and the fraction of the total variance associated to this locus (r _l ² ). When compared to other methods, the values estimated using this method are unbiased. Considering unbiased estimators increases in importance when (1) the experimental size is limited; (2) the number of genotypes at the locus of interest is large; and (3) the fraction of the variation associated with this locus is small. Finally, specific mean squares expectations allows us to propose a simple analytical method by which to estimate the confidence interval of r _l ² . This point is particularly important since results indicate that 95% confidence intervals for r _l ² can be rather wide:2–23% for a 10% estimate and 8–34% for a 20% estimate if 100 individuals are considered.     

RiceQTLPro: an integrated database for quantitative trait loci marker mapping in rice plant

The National Agricultural Biotechnology Information Center (NABIC) in South Korea reconstructed a RiceQTLPro database for gene positional analysis and structure prediction of the chromosomes. This database is an integrated web-based system providing information about quantitative trait loci (QTL) markers in rice plant. The RiceQTLPro has the three main features namely, (1) QTL markers list, (2) searching of markers using keyword, and (3) searching of marker position on the rice chromosomes. This updated database provides 112 QTL markers information with 817 polymorphic markers on each of the 12 chromosomes in rice.

Availability

The database is available for free at http://nabic.rda.go.kr/gere/rice/geneticMap/     

Linkage disequilibrium fine mapping of quantitative trait loci: A simulation study

Recently, the use of linkage disequilibrium (LD) to locate genes which affect quantitative traits (QTL) has received an increasing interest, but the plausibility of fine mapping using linkage disequilibrium techniques for QTL has not been well studied. The main objectives of this work were to (1) measure the extent and pattern of LD between a putative QTL and nearby markers in finite populations and (2) investigate the usefulness of LD in fine mapping QTL in simulated populations using a dense map of multiallelic or biallelic marker loci. The test of association between a marker and QTL and the power of the test were calculated based on single-marker regression analysis. The results show the presence of substantial linkage disequilibrium with closely linked marker loci after 100 to 200 generations of random mating. Although the power to test the association with a frequent QTL of large effect was satisfactory, the power was low for the QTL with a small effect and/or low frequency. More powerful, multi-locus methods may be required to map low frequent QTL with small genetic effects, as well as combining both linkage and linkage disequilibrium information. The results also showed that multiallelic markers are more useful than biallelic markers to detect linkage disequilibrium and association at an equal distance.     

Joint mapping of quantitative trait loci using F2 populations

In this paper, the theory of joint mapping of quantitative trait loci is extended to F₂ populations. Two independent regression equations, related to the additive and dominance effects respectively, are derived. Therefore, there are three alternative strategies for mapping QTLs, called additive-based mapping (ABM), dominance-based mapping (DBM) and additive-dominance-based mapping (ADBM). Simulation results have shown that ADBM is the most appropriate in most situations.     

Lineage-specific mapping of quantitative trait loci

We present an approach for quantitative trait locus (QTL) mapping, termed as ‘lineage-specific QTL mapping'', for inferring allelic changes of QTL evolution along with branches in a phylogeny. We describe and analyze the simplest case: by adding a third taxon into the normal procedure of QTL mapping between pairs of taxa, such inferences can be made along lineages to a presumed common ancestor. Although comparisons of QTL maps among species can identify homology of QTLs by apparent co-location, lineage-specific mapping of QTL can classify homology into (1) orthology (shared origin of QTL) versus (2) paralogy (independent origin of QTL within resolution of map distance). In this light, we present a graphical method that identifies six modes of QTL evolution in a three taxon comparison. We then apply our model to map lineage-specific QTLs for inbreeding among three taxa of yellow monkey-flower: Mimulus guttatus and two inbreeders M. platycalyx and M. micranthus, but critically assuming outcrossing was the ancestral state. The two most common modes of homology across traits were orthologous (shared ancestry of mutation for QTL alleles). The outbreeder M. guttatus had the fewest lineage-specific QTL, in accordance with the presumed ancestry of outbreeding. Extensions of lineage-specific QTL mapping to other types of data and crosses, and to inference of ancestral QTL state, are discussed.     

Detection of linkage between marker loci and loci affecting quantitative traits in crosses between segregating populations

Summary By making use of pedigree information and information on marker-genotypes of the parent and F-1 individuals crossed to form an F-2 population, it is possible to carry out a linkage analysis between marker loci and loci affecting quantitative traits in a cross between segregating parent populations that are at fixation for alternative alleles at the QTL, but share the same alleles at the marker loci. For two-allele systems, depending on marker allele frequencies in the parent populations, 2–4 times as many F-2 offspring will have to be raised and scored for markers and quantitative traits in order to provide power equivalent to that obtained in a cross between fully inbred lines. Major savings in number of F-2 offspring raised can be achieved by scoring each parent pair for a large number of markers in each chromosomal region and scoring F-1 and F-2 offspring only for those markers for which the parents were homozygous for alternative alleles. For multiple allele systems, particularly when dealing with hypervariable loci, only 10%–20% additional F-2 offspring will have to be raised and scored to provide power equivalent to that obtained in a cross between inbred lines. When a resource population contains novel favorable alleles at quantitative trait loci that are not present (or rare) in a commercial population, analyses of this sort will enable the loci of interest to be identified, mapped and manipulated effectively in breeding programs.Contribution no. 2124-E, 1987 series from The Agricultural Research Organization, The Volcani Center, Bet Dagan, Israel     

Construction of a comprehensive PCR-based marker linkage map and QTL mapping for fiber quality traits in upland cotton (Gossypium hirsutum L.)

To facilitate marker assisted selection, there is an urgent need to construct a saturated genetic map of upland cotton (Gossypium hirsutum L.). Four types of markers including SSR, SRAP, morphological marker, and intron targeted intron–exon splice junction (IT-ISJ) marker were used to construct a linkage map with 270 F_2:7 recombinant inbred lines derived from an upland cotton cross (T586 × Yumian 1). A total of 7,508 SSR, 740 IT-ISJ and 384 SRAP primer pairs/combinations were used to screen for polymorphism between the two mapping parents, and the average polymorphisms of three types of molecular markers represented 6.8, 6.6 and 7.0%, respectively. The polymorphic primer pairs/combinations and morphological markers were used to genotype 270 recombinant inbred lines, and a map including 604 loci (509 SSR, 58 IT-ISJ, 29 SRAP and 8 morphological loci) and 60 linkage groups was constructed. The map spanned 3,140.9 cM with an average interval of 5.2 cM between two markers, approximately accounting for 70.6% of the cotton genome. Fifty-four of 60 linkage groups were ordered into 26 chromosomes. Multiple QTL mapping was used to identify QTL for fiber quality traits in five environments, and thirteen QTL were detected. These QTL included four for fiber length (FL), two for fiber strength (FS), two for fiber fineness (FF), three for fiber length uniformity (FU), and two for fiber elongation (FE), respectively. Each QTL explained between 7.4 and 43.1% of phenotypic variance. Five out of thirteen QTL (FL1 and FU1 on chromosome 6, FL2, FU2 and FF1 on chromosome7) were detected in five environments, and they explained more than 20% of the phenotypic variance. Eleven QTL were distributed on A genome, while the other two on D genome.     

Mapping quantitative trait loci for seedling vigor in rice using RFLPs

Improving seedling vigor is an important objective of modern rice (Oryza saliva L.) breeding programs. The purpose of this study was to identify and map quantitative trait loci (QTL) underlying seedling vigor-related traits using restriction fragment length polymorphisms (RFLPs). An F₂ population of 204 plants was developed from a cross between a low-vigor japonica cultivar Labelle (LBL) and a high-vigor indica cultivar Black Gora (BG). A linkage map was constructed of 117 markers spanning 1496 Haldane cM and encompassing the 12 rice chromosomes with an average marker spacing of 14 cM. The length of the shoots, roots, coleoptile and mesocotyl were measured on F₃ families in slantboard tests conducted at two temperatures (18° and 25°C). By means of interval analysis, 13 QTLs, each accounting for 7% to 38% of the phenotypic variance, were identified and mapped in the two temperature regimes at a log-likelihood (LOD) threshold of 2.5. Four QTLs controlled shoot length, 2 each controlled root and coleoptile lengths and 5 influenced mesocotyl length. Single-point analysis confirmed the presence of these QTLs and detected additional loci for shoot, root and coleoptile lengths, these latter usually accounting for less than 5% of the phenotypic variation. Only 3 QTLs detected both by interval and singlepoint analyses were expressed under both temperature regimes. Additive, dominant and overdominant modes of gene action were observed. Contrary to what was predicted from parental phenotype, the low-vigor LBL contributed 46% of the positive alleles for shoot, root and coleoptile lengths. Positive alleles from the high-vigor parent BG were identified for increased root, coleoptile and mesocotyl lengths. However, BG contributed alleles with only minor effects for shoot length, the most important determinant of seedling vigor in water-seeded rice, suggesting that it would not be an ideal donor parent for introducing faster shoot growth alleles into temperate japonica cultivars.     

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

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

Model fitting and model testing in the method of joint mapping of quantitative trait loci

A previous paper proposed a new method of QTL mapping called joint mapping (JM). Some problems have been found in model fitting and model testing due to the neglect of the correlations among different observations of the dependent variable in this model. The present paper reports a method of solving the problems. The coefficient of correlation between two observations of the dependent variable is derived. A generalized least square (GLS) approach is developed for model fitting and a strategy and procedure of model testing based on a chi-square test is suggested. A simulated example is given. The example shows that the JM method is quite efficient in mapping multiple linked QTLs.     

Theobroma cacao L.: a genetic linkage map and quantitative trait loci analysis

A genetic linkage map of Theobroma cacao (cocoa) has been constructed from 131 backcross trees derived from a cross between a single tree of the variety Catongo and an F1 tree from the cross of Catongo by Pound 12. The map comprises 138 markers: 104 RAPD loci, 32 RFLP loci and two morphologic loci. Ten linkage groups were found which cover 1068 centimorgans (cM). Only six (4%) molecular-marker loci show a significant deviation from the expected 11 segregation ratio.The average distance between two adjacent markers is 8.3 cM. The final genome-size estimates based on two-point linkage data ranged from 1078 to 1112 cM for the cocoa genome. This backcross progeny segregates for two apparently single gene loci controlling (1) anthocyanidin synthesis (Anth) in seeds, leaves and flowers and (2) self-compatibility (Autoc). The Anth locus was found to be 25 cM from Autoc and two molecular markers co-segregate with Anth. The genetic linkage map was used to localize QTLs for early flowering, trunk diameter, jorquette height and ovule number in the BC₁ generation using both single-point ANOVA and interval mapping. A minimum number of 2–4 QTLs (P<0.01) involved in the genetic expression of the traits studied was detected. Coincident map locations of a QTL for jorquette height and trunk diameter suggests the possibility of pleiotropic effects in cocoa for these traits. The combined estimated effects of the different mapped QTLs explained between 11.2% and 25.8% of the phenotypic variance observed in the BC₁ population.     

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.     

Model selection for quantitative trait loci mapping in a full-sib family

Statistical methods for mapping quantitative trait loci (QTLs) in full-sib forest trees, in which the number of alleles and linkage phase can vary from locus to locus, are still not well established. Previous studies assumed that the QTL segregation pattern was fixed throughout the genome in a full-sib family, despite the fact that this pattern can vary among regions of the genome. In this paper, we propose a method for selecting the appropriate model for QTL mapping based on the segregation of different types of markers and QTLs in a full-sib family. The QTL segregation patterns were classified into three types: test cross (1:1 segregation), F₂ cross (1:2:1 segregation) and full cross (1:1:1:1 segregation). Akaike’s information criterion (AIC), the Bayesian information criterion (BIC) and the Laplace-empirical criterion (LEC) were used to select the most likely QTL segregation pattern. Simulations were used to evaluate the power of these criteria and the precision of parameter estimates. A Windows-based software was developed to run the selected QTL mapping method. A real example is presented to illustrate QTL mapping in forest trees based on an integrated linkage map with various segregation markers. The implications of this method for accurate QTL mapping in outbred species are discussed.     

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

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