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.     

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.     

QTL analysis of horticultural traits differentiating the cultivated tomato from the closely related species Lycopersicon pimpinellifolium

Molecular markers were used to map and characterize quantitative trait loci (QTLs) for several characters of agronomic and biological importance in an interspecific backcross of tomato. The parents of the cross were an elite processing inbred Lycopersicon esculentum cv M82-1-7 and the closely related red-fruited wild species L. pimpinellifolium (LA1589). A total of 257 BC₁ plants were grown under field conditions in Ithaca, New York and scored for 19 quantitative traits. A genetic linkage map was constructed for the same population using 115 RFLP, 3 RAPD and 2 morphological markers that spanned 1,279 cM of the tomato genome with an average interval length of 10.7 cM. A minimum of 54 putatively significant QTLs (P<0.001; LOD> 2.4) were detected for all characters with a range of 1–7 QTLs detected per character. Of the total 54 QTLs 11% had alleles with effects opposite to those predicted by the parental phenotypes. The percentage of phenotypic variation associated with single QTLs ranged from 4% to 47%. Multilocus analysis showed that the cumulative action of all QTLs detected for each trait accounted for 12–59% of the phenotypic variation. The difference in fruit weight was controlled largely by a single major QTL (fw2.2). Digenic epistasis was not evident. Several regions of the genome (including the region near sp on chromosome 6) showed effects on more than one trait. Implications for variety improvement and inferences about the domestication of the cultivated tomato are discussed.     

EFFECTS OF WATER VELOCITY ON THE ARCHITECTURE AND EPIPHYTES OF CLADOPHORA GLOMERATA (CHLOROPHYTA)1

The architecture of the filamentous green alga Cladophora glomerata (L.) Kütz. and the composition of this alga's epiphytes [primarily the diatoms Epithemia turgida (Ehrenb.) Kütz., Epithemia sorex Kütz., and Cocconeis pediculus Ehrenb.] were examined in different velocity regimes. After transferring algal-bearing cobbles among velocities, the effects of changes in velocity were also examined. Cladophora branching pattern did not initially differ among slow, medium, and fast velocities, indicating that stable water velocities did not affect branching pattern. Two weeks after cobble transfer, Cladophora in fast velocity had fragmented more (i.e. had fewer filaments and fewer branch points per length of filament and had a higher percentage of unbranched filaments) than Cladophora in slow velocity. Fragmentation was greatest in tufts moved from slow velocity, suggesting velocity-associated differences in susceptibility to breakage. Epiphytic assemblage composition differed among slow, medium, and fast velocities and between locations on the filament (base and apex). Cocconeis pediculus dominated where exposure to high velocity was greater (filament apices in medium and fast velocities), whereas the Epithemia spp. dominated where lower velocities occurred (filament bases in all velocities and apices in slow velocity). Two weeks after the cobble transfer, the translocated diatom assemblages had changed and the original pattern of diatom distribution was restored.     

QTL analysis of flowering time inArabidopsis thaliana

Quantitative trait loci (QTL) analyses based on restriction fragment length polymorphism maps have been used to resolve the genetic control of flowering time in a cross between twoArabidopsis thaliana ecotypes H51 and Landsbergerecta, differing widely in flowering time. Five quantitative trait loci affecting flowering time were identified in this cross (RLN1-5), four of which are located in regions containing mutations or loci previously identified as conferring a late-flowering phenotype. One of these loci is coincident with theFRI locus identified as the major determinant for late flowering and vernalization responsiveness in theArabidopsis ecotype Stockholm.RLN5, which maps to the lower half of chromosome five (between markers mi69 and m233), only affected flowering time significantly under short day conditions following a vernalization period. The late-flowering phenotype of H51 compared to Landsbergerecta was due to alleles conferring late flowering at only two of the five loci. At the three other loci, H51 possessed alleles conferring early flowering in comparison to those of Landsbergerecta. Combinations of alleles conferring early and late flowering from both parents accounted for the transgressive segregation of flowering time observed within the F₂ population. Three QTL,RLN1,RLN2 andRLN3 displayed significant genotype-by-environment interactions for flowering time. A significant interaction between alleles atRLN3 andRLN4 was detected.     

Mapping the genome of rapeseed (Brassica napus L.). I. Construction of an RFLP linkage map and localization of QTLs for seed glucosinolate content

A linkage map of the rapeseed genome comprising 204 RFLP markers, 2 RAPD markers, and 1 phenotypic marker was constructed using a F₁ derived doubled haploid population obtained from a cross between the winter rapeseed varieties Mansholt's Hamburger Raps and Samourai. The mapped markers were distributed on 19 linkage groups covering 1441 cM. About 43% of these markers proved to be of dominant nature; 36% of the mapped marker loci were duplicated, and conserved linkage arrangements indicated duplicated regions in the rapeseed genome. Deviation from Mendelian segregation ratios was observed for 27.8% of the markers. Most of these markers were clustered in 7 large blocks on 7 linkage groups, indicating an equal number of effective factors responsible for the skewed segregations. Using cDNA probes for the genes of acyl-carrier-protein (ACP) and -ketoacyl-ACP-synthase I (KASI) we were able to map three and two loci, respectively, for these genes. The linkage map was used to localize QTLs for seed glucosinolate content by interval mapping. Four QTLs could be mapped on four linkage groups, giving a minimum number of factors involved in the genetic control of this trait. The estimated effects of the mapped QTLs explain about 74% of the difference between both parental lines and about 61.7 % of the phenotypic variance observed in the doubled haploid mapping population.     

RFLP mapping of resistance to the blackleg disease [causal agent,Leptosphaeria maculans (Desm.) Ces. et de Not.] in canola (Brassica napus L.)

We report the tagging of genes involved in blackleg resistance, present in the French cultivar Crésor of B. napus, with RFLP markers. A total of 218 cDNA probes were tested on the parental cultivars Crésor (resistant) and Westar (susceptible), and 141 polymorphic markers were used in a segregating population composed of 98 doubled-haploid lines (DH). A genetic map from this cross was constructed with 175 RFLP markers and allowed us to scan for specific chromosomal associations between response to blackleg infection and RFLP markers. Canola residues infested with virulent strains of Leptosphaeria maculans were used as inoculum and a suspension of pycnidiospores from cultures of L. maculans, including the highly virulent isolate Leroy, was sprayed to increase disease pressure. QTL mapping suggested that a single chromosomal region was responsible for resistance in each of the four environments tested. This QTL accounted for a high proportion of the variation of blackleg reaction in each of the assays. A second QTL, responsible for a small proportion of the variation of blackleg reaction, was present in one of four year-site assays. A Mendelian approach, using blackleg disease ratings for classifying DH lines as resistant or susceptible, also allowed us to map resistance in the region of the highly significant LOD scores observed in each environment by interval mapping. Results strongly support the presence of a single major gene, named LmFr ₁ controlling adult plant resistance to blackleg in spring oil-seed rape cultivar Crésor. Several RFLP markers were found associated with LmFr ₁.     

Infrared microspectroscopy: Sampling heterogeneity in plant cell wall composition and architecture

The use of probes such as monoclonal and polyclonal antibodies to specific cell wall components, at both the light and electron microscope levels, has demonstrated the diversity in cell wall composition between species, between tissues, between different regions of the cell surface, and even within a single wall. Traditional methods of cell wall analysis have provided valuable information on wall composition and architecture, but, by having to rely on the use of bulk samples, have averaged out this intrinsic heterogeneity. Fourier Transform Infrared (FTIR) microspectroscopy addresses this problem by providing chemical information from an area as small as 10×10 μm of a single cell wall fragment or area of a tissue section that has been imaged with a microscope accessory.
We have used FTIR microspectroscopy as a powerful and extremely rapid assay for wall components and putative cross-links in muro. The spectra are sensitive to polymer conformation, and the use of polarisers in the microscope accessory allows the orientation of particular functional groups to be determined, with respect to the long axis of elongating cells. The spectra constitute species and tissue-specific 'fingerprints', and the use of classical discriminant analysis may provide the opportunity for correlating spectral features with chemical, architectural or rheological wall properties. Spectral mapping of an area of a specimen allows the morphological features resulting from cell growth and differentiation to be characterised chemically at the single cell level.     

Fractal geometry of bean root systems: correlations between spatial and fractal dimension

An obstacle to the study of root architecture is the difficulty of measuring and quantifying the three-dimensional configuration of roots in soil. The objective of this work was to determine if fractal geometry might be useful in estimating the three-dimensional complexity of root architecture from more accessible measurements. A set of results called projection theorems predict that the fractal dimension (FD) of a projection of a root system should be identical to the FD of roots in three-dimensional space (three-dimensional FD). To test this prediction we employed SimRoot, an explicit geometric simulation model of root growth derived from empirical measurements of common bean (Phaseolus vulgaris L.). We computed the three-dimensional FD, FD of horizontal plane intercepts (planar FD), FD of vertical line intercepts (linear FD), and FD of orthogonal projections onto planes (projected FD). Three-dimensional FD was found to differ from corresponding projected FD, suggesting that the analysis of roots grown in a narrow space or excavated and flattened prior to analysis is problematic. A log-linear relationship was found between FD of roots and spatial dimension. This log-linear relationship suggests that the three-dimensional FD of root systems may be accurately estimated from excavations and tracing of root intersections on exposed planes.     

Mapping quantitative trait loci with dominant and missing markers in various crosses from two inbred lines

Dominant phenotype of a genetic marker provides incomplete information about the marker genotype of an individual. A consequence of using this incomplete information for mapping quantitative trait loci (QTL) is that the inference of the genotype of a putative QTL flanked by a marker with dominant phenotype will depend on the genotype or phenotype of the next marker. This dependence can be extended further until a marker genotype is fully observed. A general algorithm is derived to calculate the probability distribution of the genotype of a putative QTL at a given genomic position, conditional on all observed marker phenotypes in the region with dominant and missing marker information for an individual. The algorithm is implemented for various populations stemming from two inbred lines in the context of mapping QTL. Simulation results show that if only a proportion of markers contain missing or dominant phenotypes, QTL mapping can be almost as efficient as if there were no missing information in the data. The efficiency of the analysis, however, may decrease substantially when a very large proportion of markers contain missing or dominant phenotypes and a genetic map has to be reconstructed first on the same data as well. So it is important to combine dominant markers with codominant markers in a QTL mapping study. This revised version was published online in July 2006 with corrections to the Cover Date.