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.     

Quantitative trait loci controlling phenotypes related to the perennial versus annual habit in wild relatives of maize

We used quantitative trait locus/loci (QTL) mapping to study the inheritance of traits associated with perennialism in a cross between an annual (Zea mays ssp. parviglumis) and a perennial (Z. diploperennis) species of teosinte. The most striking difference between these species is that Z. diploperennis forms rhizomes, whereas Z. mays ssp. parviglumis lacks these over-wintering underground stems. An F₂ population of 425 individuals was genotyped at 95 restriction fragment length polymorphism marker loci and the association between phenotype and genotype was analyzed by composite interval mapping. We detected a total of 38 QTL for eight traits. The number of QTL found for each trait ranged from two for rhizome formation to nine for tillering. QTL for six of the traits mapped near each other on chromosome 2, and QTL for four traits mapped near each other on chromosome 6, suggesting that these regions play an important role in the evolution of the perennial habit in teosinte. Most of the 38 QTL had small effects, and no single QTL showed a strikingly large effect. The map positions that we determined for rhizome formation and other traits in teosinte may help to locate corresponding QTL in pasture and turf grasses used as forage for cattle and for erosion control in agro-ecosystems.     

Linkage between quantitative trait loci and marker loci: resolution power of three statistical approaches in single marker analysis

This paper presents a comparison of three methods of parameter estimation in analysis of linkage between a quantitative trait locus (QTL) and a marker locus: maximum likelihood, mean square for trait cumulative distribution function, and method of moments, employing simulated backcross data. The sensitivity of estimates to violation of assumptions of normality and equal variances were also studied. Some measures of discrepancy between the trait distributions in the QTL groups are considered to evaluate the potential dependence of the resolution capacity of the QTL substitution effect with respect to trait mean value and variance.     

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.     

Quantitative trait loci for inflorescence development in Arabidopsis thaliana

Variation in inflorescence development patterns is a central factor in the evolutionary ecology of plants. The genetic architectures of 13 traits associated with inflorescence developmental timing, architecture, rosette morphology, and fitness were investigated in Arabidopsis thaliana, a model plant system. There is substantial naturally occurring genetic variation for inflorescence development traits, with broad sense heritabilities computed from 21 Arabidopsis ecotypes ranging from 0.134 to 0.772. Genetic correlations are significant for most (64/78) pairs of traits, suggesting either pleiotropy or tight linkage among loci. Quantitative trait locus (QTL) mapping indicates 47 and 63 QTL for inflorescence developmental traits in Ler x Col and Cvi x Ler recombinant inbred mapping populations, respectively. Several QTL associated with different developmental traits map to the same Arabidopsis chromosomal regions, in agreement with the strong genetic correlations observed. Epistasis among QTL was observed only in the Cvi x Ler population, and only between regions on chromosomes 1 and 5. Examination of the completed Arabidopsis genome sequence in three QTL regions revealed between 375 and 783 genes per region. Previously identified flowering time, inflorescence architecture, floral meristem identity, and hormone signaling genes represent some of the many candidate genes in these regions.     

Mapping quantitative trait loci for yield components and morphological traits in an advanced backcross population between Oryza grandiglumis and the O. sativa japonica cultivar Hwaseongbyeo

Introgression has been achieved from wild species Oryza grandiglumis (2n=48, CCDD, Acc. No. 101154) into O. sativa subsp. japonica cv. Hwaseongbyeo as a recurrent parent. An advanced introgression (backcross) line, HG101, produced from a single plant from BC₅F₃ families resembled Hwaseongbyeo, but it showed differences from Hwaseongbyeo in several traits, including days to heading and culm length. To detect the introgressions, 450 microsatellite markers of known chromosomal position were used for the parental survey. Of the 450 markers, 51 (11.3%) detected O. grandiglumis segments in HG101. To characterize the effects of alien genes introgressed into HG101, an F_2:3 population (150 families) from the cross Hwaseongbyeo/HG101 was developed and evaluated for 13 agronomic traits. Several lines outperformed Hwaseongbyeo in several traits, including days to heading. Genotypes were determined for 150 F₂ plants using simple sequence repeat markers. Qualitative trait locus (QTL) analysis was carried out to determine the relationship between marker genotype and the traits evaluated. A total of 39 QTL and 1 gene conferring resistance to blast isolate were identified using single-point analysis. Phenotypic variation associated with each QTL ranged from 4.2 to 30.5%. For 18 (46.2%) of the QTL identified in this study, the O. grandiglumis-derived alleles contributed a desirable agronomic effect despite the overall undesirable characteristics of the wild phenotype. Favorable wild alleles were detected for days to heading, spikelets per panicle, and grain shape traits. Grain shape QTL for grain weight, thickness, and width identified in the F_2:3 lines were further confirmed based on the F₄ progeny test. The confirmed locus, tgw2 for grain weight is of particular interest because of its independence from undesirable height and maturity. Several QTL controlling amylose content and grain traits have not been detected in the previous QTL studies between Oryza cultivars, indicating potentially novel alleles from O. grandiglumis. The QTL detected in this study could be a rich source of natural genetic variation underlying the evolution and breeding of rice.     

Quantitative trait loci that modify the sootiness of yellow pigmentation in KK-A y /a mice

Compared with C57BL/6J-A ^y /a, KK-A ^y /a mice have yellow fur that is markedly darker. Furthermore, there is a considerable variation in the tone of color with a continuous range in F₂ progeny produced from C57BL/6J females and KK-A ^y /a males. The aims of this study are to reveal the phenotypic differences between the two A ^y congenic strains and to elucidate the genetic factors responsible for the sooty yellow pigmentation in the KK background. On the basis of a chemical analysis, the sootiness in KK-A ^y /a was the result of increased eumelanin (PTCA) and decreased pheomelanin (AHP). A statistically significant QTL was identified on Chromosome (Chr) 15, responsible for the AHP content. No significant loci responsible for PTCA were identified. On the other hand, on the basis of an optical analysis for color difference and overall sootiness, significant evidence of linkage was identified on the proximal part of Chr 15, in the region similar to AHP QTL. The overall sootiness is thus controlled solely by the locus on Chr 15 in F₂ progeny; however, the KK allele at this locus significantly increased the AHP content. Received: 8 September 1999 / Accepted: 18 April 2000     

Quantitative trait loci for flowering time and inflorescence architecture in rose

The pattern of development of the inflorescence is an important characteristic in ornamental plants, where the economic value is in the flower. The genetic determinism of inflorescence architecture is poorly understood, especially in woody perennial plants with long life cycles. Our objective was to study the genetic determinism of this characteristic in rose. The genetic architectures of 10 traits associated with the developmental timing and architecture of the inflorescence, and with flower production were investigated in a F ₁ diploid garden rose population, based on intensive measurements of phenological and morphological traits in a field. There were substantial genetic variations in inflorescence development traits, with broad-sense heritabilities ranging from 0.82 to 0.93. Genotypic correlations were significant for most (87%) pairs of traits, suggesting either pleiotropy or tight linkage among loci. However, non-significant and low correlations between some pairs of traits revealed two independent developmental pathways controlling inflorescence architecture: (1) the production of inflorescence nodes increased the number of branches and the production of flowers; (2) internode elongation connected with frequent branching increased the number of branches and the production of flowers. QTL mapping identified six common QTL regions (cQTL) for inflorescence developmental traits. A QTL for flowering time and many inflorescence traits were mapped to the same cQTL. Several candidate genes that are known to control inflorescence developmental traits and gibberellin signaling in Arabidopsis thaliana were mapped in rose. Rose orthologues of FLOWERING LOCUS T (RoFT), TERMINAL FLOWER 1 (RoKSN), SPINDLY (RoSPINDLY), DELLA (RoDELLA), and SLEEPY (RoSLEEPY) co-localized with cQTL for relevant traits. This is the first report on the genetic basis of complex inflorescence developmental traits in rose.     

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.     

Quantitative trait loci for baseline erythroid traits

A substantial genetic contribution underlies variation in baseline peripheral blood counts. We performed quantitative trait locus/loci (QTL) analyses to identify chromosome (Chr) regions harboring genes influencing the baseline erythroid parameters in F₂ intercrosses between NZW/LacJ, SM/J, and C57BLKS/J inbred mice. We identified multiple significant QTL for red blood cell (RBC) count, hemoglobin (Hgb) and hematocrit (Hct) levels, mean corpuscular volume (MCV), mean corpuscular hemoglobin (MCH), and mean cell hemoglobin concentration (CHCM). We identified four RBC count QTL: Rbcq1 (Chr 1, peak LOD score at 62 cM,), Rbcq2 (Chr 4, 60 cM), Rbcq3 (Chr 11, 34 cM), and Rbcq4 (Chr 10, 60 cM). Three MCV QTL were identified: Mcvq1 (Chr 7, 30 cM), Mvcq2 (Chr 11, 6 cM), and Mcvq3 (Chr 10, 60 cM). Single significant loci for Hgb (Hgbq1, Chr 16, 32 cM), Hct (Hctq1, Chr 3, 42 cM), and MCH (Mchq1, Chr 10, 60 cM) were identified. The data support the existence of a common RBC/MCH/MCV locus on Chr 10. Two QTL for CHCM (Chcmq1, Chr 2, 48 cM; Chcmq2, Chr 9, 44 cM) and an interaction between Chcmq2 with a locus on Chr 19 were identified. These analyses emphasize the genetic complexity underlying the regulation of erythroid peripheral blood traits in normal populations and suggest that genes not previously recognized as significantly impacting normal erythropoiesis exist.     

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     

Quantitative trait loci analysis of nitrogen use efficiency in Arabidopsis

Improving plant nitrogen (N) use efficiency or controlling soil N requires a better knowledge of the regulation of plant N metabolism. This could be achieved using Arabidopsis as a model genetic system, taking advantage of the natural variation available among ecotypes. Here, we describe an extensive study of N metabolism variation in the Bay-0 x Shahdara recombinant inbred line population, using quantitative trait locus (QTL) mapping. We mapped QTL for traits such as shoot growth, total N, nitrate, and free-amino acid contents, measured in two contrasting N environments (contrasting nitrate availability in the soil), in controlled conditions. Genetic variation and transgression were observed for all traits, and most of the genetic variation was identified through QTL and QTL x QTL epistatic interactions. The 48 significant QTL represent at least 18 loci that are polymorphic between parents; some may correspond to known genes from the N metabolic pathway, but others represent new genes controlling or interacting with N physiology. The correlations between traits are dissected through QTL colocalizations: The identification of the individual factors contributing to the regulation of different traits sheds new light on the relations among these characters. We also point out that the regulation of our traits is mostly specific to the N environment (N availability). Finally, we describe four interesting loci at which positional cloning is feasible.     

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.     

Theory for identification of marker locus-QTL associations in population by line crosses

The objective of this paper is to present genetic theory demonstrating the conditions under which it should be possible to identify molecular marker-quantitative trait locus (QTL) associations in crosses of random-mating populations to inbreds. Using as an example the cross of a corn (Zea mays L.) population to an inbred, the expected disequilibrium for testcross and per se performance of F₂, F₃, BC₁ (to the inbred) and recombinant inbred generations was derived for cases where a marker allele is linked to an unfavorable QTL allele in the inbred and where the marker allele is linked to a favorable QTL allele in the inbred. Disequilibrium in segregating generations was shown to be a function of disequilibrium in the parent population, the frequency of marker and QTL alleles in the parent population, and the recombination distance between the marker and the QTL. To maximize the opportunity to identify a favorable QTL the following procedures are suggested:

Identification of quantitative trait loci associated with self-compatibility in a Prunus species

Self-compatibility in Rosaceous fruit species is based on a single-locus qualitative trait. However, the evidence observed in different species has indicated the presence of modifier genes outside the S locus affecting the expression of self-compatibility/self-incompatibility. The study of a progeny obtained from the cross of the almond genotypes ‘Vivot’× ‘Blanquerna’ has allowed the construction of a genetic map based on microsatellite markers and the identification for the first time in the Rosaceae family of two additional loci located outside the S locus and affecting the expression of self-compatibility/self-incompatibility. A quantitative trait locus (QTL) was located relatively close to the S locus, on linkage group 6 (G6), whereas the second one was located on G8. These QTLs appear to be involved in conferring self-compatibility to genotypes not possessing the S _f allele. These results are consistent with almond being a self-incompatible species with a genetic background of pseudo-self-compatibility controlled by modifier genes. The effect of the S _f allele and the two QTLs may contribute to explain the wide range of fruit sets observed when self-pollinating different almond genotypes.     

Pleiotropy of the branching locus (B) masks linked and unlinked quantitative trait loci affecting seed traits in sunflower

The discovery of unbranched, monocephalic natural variants was pivotal for the domestication of sunflower (Helianthus annuus L.). The branching locus (B), one of several loci apparently targeted by aboriginal selection for monocephaly, pleiotropically affects plant, seed and capitula morphology and, when segregating, confounds the discovery of favorable alleles for seed yield and other traits. The present study was undertaken to gain deeper insights into the genetics of branching and seed traits affected by branching. We produced an unbranched hybrid testcross recombinant inbred line (TC-RIL) population by crossing branched (bb) and unbranched (BB) RILs to an unbranched (BB) tester. The elimination of branching concomitantly eliminated a cluster of B-linked seed trait quantitative trait loci (QTL) identified by RIL per se testing. We identified a seed oil content QTL linked in repulsion and a 100-seed weight QTL linked in coupling to the B locus and additional unlinked QTL, previously masked by B-locus pleiotropy. Genomic segments flanking the B locus harbor multiple loci for domestication and post-domestication traits, the effects of which are masked by B-locus pleiotropy in populations segregating for branching and can only be disentangled by genetic analyses in unbranched populations. QTL analyses of NILs carrying wild B alleles substantiated the pleiotropic effects of the B locus. The effect of the B locus on branching was masked by the effects of wild alleles at independent branching loci in hybrids between monocephalic domesticated lines and polycephalic wild ecotypes; hence, the B locus appears to be necessary, but not sufficient, for monocephaly in domesticated sunflower.     

Quantitative trait locus effects and environmental interaction in a sample of North American barley germ plasm

Quantitative trait locus (QTL) and QTL x environment (E) interaction effects for agronomic and malting quality traits were measured using a 123-point linkage map and multi-environment phenotype data from an F₁-derived doubled haploid population of barley (Hordeum vulgare). The QTL × E interactions were due to differences in magnitude of QTL effects. Highly significant QTL effects were found for all traits at multiple sites in the genome. Yield QTL peaks and support intervals often coincided with plant height and lodging QTL peaks and support intervals. QTL were detected in the vicinity of a previously mapped Mendelian maturity locus and known function probes for- and-amylase genes. The average map density (9.6 cM) should be adequate for molecular marker-assisted selection, particularly since there were few cases of alternative favorable alleles for different traits mapping to the same or adjacent intervals.Oreg Agric Exp Stn J No. 10150     

Restriction fragment length polymorphism analysis of loci associated with disease resistance genes and developmental traits in Pisum sativum L.

An F₂ population of pea (Pisum sativum L.) consisting of 174 plants was analysed by restriction fragment length polymorphism (RFLP) and random amplified polymorphic DNA (RAPD) techniques. Ascochyta pisi race C resistance, plant height, flowering earliness and number of nodes were measured in order to map the genes responsible for their variation. We have constructed a partial linkage map including 3 morphological character genes, 4 disease resistance genes, 56 RFLP loci, 4 microsatellite loci and 2 RAPD loci. Molecular markers linked to each resistance gene were found: Fusarium wilt (6 cM from Fw), powdery mildew (11 cM from er) and pea common Mosaic virus (15 cM from mo). QTLs (quantitative traits loci) for Ascochyta pisi race C resistance were mapped, with most of the variation explained by only three chromosomal regions. The QTL with the largest effect, on chromosome 4, was also mapped using a qualitative, Mendelian approach. Another QTL displayed a transgressive segregation, i.e. the parental line that was susceptible to Ascochyta blight had a resistance allele at this QTL. Analysis of correlations between developmental traits in terms of QTL effects and positions suggested a common genetic control of the number of nodes and earliness, and a loose relationship between these traits and height.     

Identification of quantitative trait loci controlling developmental characteristics of Brassica oleracea L

A segregating population of F₁-derived doubled haploid (DH) lines of Brassica oleracea was used to detect and locate QTLs controlling 27 morphological and developmental traits, including leaf, flowering, axillary bud and stem characters. The population resulted from a cross between two very different B. oleracea crop types, an annual cauliflower and a biennial Brussels sprout. A principal component analysis (PCA), based on line means, allowed all the traits to be grouped into distinct categories according to the first five Principal Components. These were: leaf traits (PC1), flowering traits (PC2), axillary bud traits (PC3 and 5) and stem traits (PC4). Between zero and four putative QTL were located per trait, which individually explained between 6% and 43% of the additive genetic variation, using the multiple-marker regression approach to QTL mapping. For lamina width, bare petiole length and stem length two QTL with opposite effects were detected on the same linkage groups. Intra- and inter-specific comparative mapping using RFLP markers identified a QTL on linkage group O8 accounting for variation in vernalisation, which is probably synonymous with a QTL detected on linkage group N19 of Brassica napus. In addition, a QTL for petiole length detected on O3 of this study appeared to be homologous to a QTL detected on another B. oleracea genetic map (Camargo et al. 1995). Received: 28 March 2001 / Accepted: 25 June 2001     

Optimal Fixing of the Bandwidth-Parameter for the Empirical Regression1,2

The estimator ?₀(x) of the regression r(x) = E (Y | × = x) from measured points (x_i, y_i), i = 1(1) n, of a continuous two-dimensional random variable (X, Y) with unknown continuous density function f(x, y) and with moments up to the second order can be made with the help of a density estimation f?₀(x, y) (see e.g. SCHMERLING and PEIL, 1980). Here f?₀(x, y) still contains free parameters (so-called band-width-parameters), the values of which have to be optimally fixed in the concrete case. This fixing can be done by using a modification of the maximum-likelihood principle including jackknife techniques. The parameter values can be also found from the estimators for r(x). Here the cross-validation principle can be applied. Some numerical aspects of these possibilities for optimally fixing the bandwidth-parameter are discussed by means of examples. If ?₀(x) is used as a smoothing operator for time series the optimal choice of the parameter values is dependent on the purpose of application of the smoothed time series. The fixing will then be done by considering the so-called filter-characteristic of ?C₀(x).