Brian S. Yandell and Jaya M. Satagopan
University of Wisconsin-Madison
Some agronomic traits seem to behave like genetic markers presented earlier in this book, displaying simple Mendelian inheritance. However, many traits exhibit more complex inheritance, requiring a more careful examination of relationships. These complex traits [\protect\citeauthoryearLander and SchorkLander and Schork1994] may be subject to large variation which might be attributed to a combination of environmental factors and one or more genes, or polygenes [\protect\citeauthoryearTanksleyTanksley1993]. Many papers in the literature refer to such traits as quantitative traits, and the gene positions as quantitative trait loci, or QTLs. A modern treatment of this subject can be found in the forthcoming book by lync:wals:1995.
For convenience, a particular experiment is considered involving a cross of Major (A) and Stellar (B) varieties of oilseed Brassica napus [\protect\citeauthoryearFerreira, Satagopan, Yandell, Williams, and OsbornFerreira et al.1995]. The phenotypic trait considered here is days to flower after eight weeks of vernalization.
The Brassica genus has been widely studied for disease resistance, freezing tolerance, flowering time and seed oil content, among various other traits of economic importance. Here we analyze double haploid (DH) progeny from Brassica napus to detect QTLs for flowering time. A double haploid line from the Brassica napus cv. Stellar (an annual canola cultivar) was crossed to a single plant of cv. Major (a biennial rapeseed cultivar) which was used as a female. Microspore culture of a single F1 hybrid plant was used to obtain a segregating population. One hundred and five DH lines, the F1 hybrid and progeny from self-pollination of the parents Major and Stellar were evaluated in the field for flower initiation. The plants were divided into 3 groups and each group was exposed to one of the 3 treatments - no vernalization, 4 weeks vernalization and 8 weeks vernalization. The treatments were at 4C and were used to induce or accelerate flowering. The experimental design used was a split-plot with two replications. The treatments were main plots and the subplots consisted of a single row of 10 plants of a DH or parental line, or the F1 hybrid. Further details about the materials and methods, and preliminary analysis of the split-plot experiment can be found in Ferreira et al. (1995).
For each subplot, the number of days to flowering was recorded as the first day when at least 50% of the plants in that subplot had flowered. The preliminary analysis showed no significant difference between replicates for each treatment. Hence the number of days to flowering were averaged over the two replicates for each treatment. However, there was a significant difference between the treatments, as expected. DNA was extracted from all the progeny and linkage map obtained [\protect\citeauthoryearFerreira, Williams, and OsbornFerreira et al.1994] using Mapmaker (Lander et al. 1987).
The first section considers the problem of assessing gene effects for a trait controlled by one or more QTLs of known genotypes. Analysis for a trait influenced by only one gene involves one-factor analysis of variance. Multiple loci, with possible epistasis, require more complicated models with several factors. Issues of model selection arise even if the genotypes are known at all putatitive QTL. Section two considers ``point analysis,'' using the markers of a linkage map as surrogates for genes controlling a trait. However, this method has low power if markers are not close to the actual genes. Section three develops ``interval analysis,'' which uses a linkage map to estimate gene location between markers. This method is very powerfull, but relies on some theoretical assumptions which may not be appropriate for modest sample sizes. Finally, recent ideas on ``Monte Carlo analysis'' illuminate a data-driven approach to infer the loci and effects for genes controlling a quantitative trait. The last section reviews assumptions inherent in these analyses, indicating some quick, informal checks, transformations and cautions, as well as raising some issues about experimental design.