A statistical framework for the detection of quantitative trait loci in plant multi-parent populations composed of crosses

Since Mendel and the birth of (plant) genetic as a science, the use of controlled plant populations is central in plant science. Different plant populations have been developed to investigate biological questions like the detection of quantitative trait loci (QTLs). Historically, QTL detection has been performed in bi-parental crosses and association panels but these populations are limited by their reduced genetic diversity or their unknown population structure. Multi-parent populations (MPPs) composed of crosses are structured populations using genotypes coming from several crosses between a set of parents. Therefore, MPPs address the limitations of both bi-parental crosses and association panels. Populations like the nested association mapping, the diallels, and the factorial designs used in breeding programs are important examples of MPPs composed of crosses. An important element for QTL detection is the necessity to reflect the biological properties of the studied population in the statistical model. Thus, the central question of this thesis was to develop a statistical QTL detection methodology adapted to the MPPs composed of crosses. In the second chapter, we presented a collection of QTL detection models for MPPs with different biological assumptions about the type of QTL effect. We defined models where the QTL effects could be: a) specific to a particular cross (cross-specific), b) where the effects of a common parent or ancestor were consistently defined in the whole MPP (parental and ancestral), and c) with QTL allelic effects attached to the SNP alleles (bi-allelic). We also let the error term variance of our models being cross-specific to reflect differences of residual polygenic effect between crosses. In the third chapter, we tested our methodology on real data and we evaluated some biological assumptions behind our models. We were not able to verify the assumption that models with a reduced number of QTL terms perform better in MPPs with a narrow genetic basis. We could also not verify the usefulness of cross-specific error term variances to handle the heterogeneity of the genetic distance between the MPPs parents. However, we showed that models with QTLs described by different type of effects could improve the modelling of the phenotypic variation. In chapter four, we evaluated our methodology by simulation. We simulated traits with a genetic architecture composed of QTLs showing more or less allelic diversity to investigate the effect of genetic diversity on the QTL detection power. We also tried to determine some guidelines to build MPPs maximizing the QTL detection power. We noticed that MPPs with large cross sizes were the most powerful designs. Increasing the number of parents was only useful to detect QTLs with a reduced allele frequency. In the fifth chapter, we extended our methodology to analyze QTL experiments made on MPPs characterized in multiple environments (MPP-ME). We analyzed jointly MPP-ME data taking into consideration the correlation due to the same genotype measured in different environments. We showed that our method could estimate the QTL by environment (QTLxE) effects, which was not the case for methods generally used to analyze MPP-ME data. We also showed that our models could integrate environmental information to get more insight about the underlying mechanisms behind the QTLxE effects. To conclude, we would like to emphasize that the methodology we developed in this thesis allows to exploit the full potential of MPP-ME QTL experiments. Our models allow to estimate QTL variations: a) within the MPP between different cross genetic backgrounds, and b) between the environments. Therefore, our models can detect QTLs that potentially have a consistent effect within the population and between the environments. Such QTLs are certainly the most valuable for marker assisted selection.