Mixed model methods for quantitative trait loci estimation in crosses between outbred lines

Methodology is developed for Quantitative Trait Loci (QTL) analysis in F₂ and backcross designed experiments between outbred lines using a mixed model framework through the modification of segment mapping techniques. Alleles are modelled in the F₁ and parental generations allowing the estimation of individual additive allele effects while accounting for QTL segregation within lines as well as differences in mean QTL effects between lines.

Initially the theory, called F₁ origin mapping, is developed for a single trait scenario involving possible multiple QTL and polygenic variation. Additive genetic variances are estimated via Restricted Maximum Likelihood (REML) and allele effects are modelled using Best Linear Unbiased Prediction (BLUP). Simulation studies are carried out comparing F₁ origin mapping with existing segment mapping methods in a number of genetic scenarios. While there was no significant difference in the estimation of effects between the two methods the average CPU time of one hundred replicates was 0.26 seconds for F₁ origin mapping and 3.77 seconds for the segment mapping method. This improvement in computation efficiency is due to the restructuring of IBD matrices which result in the inversion and REML iteration over much smaller matrices.

Further theory is developed which extends F₁ origin mapping from single to multiple trait scenarios for F₂ crosses between outbred lines. A bivariate trait is simulated using a single QTL with and without a polygenic component. A single trait and bivariate trait analysis are performed to compare the two approaches. There was no significant difference in the estimation of QTL effects between the two approaches. However, there was a slight improvement in the accuracy of QTL position estimates in the multiple trait approach. The advantage of F₁ origin mapping with regard to computational efficiency becomes even more important with multiple trait analysis and allows the investigation of interesting biological models of gene expression.

F₁ origin mapping is developed further to model the correlation structure inherent in repeated measures data collected on F₂ crosses between outbred lines. A study was conducted to show that repeated measures F₁ origin mapping and multiple trait F₁ origin mapping give similar results in certain circumstances. Another simulation study was also conducted in which five regular repeated measures where simulated with allele breed difference effects and allele variances increasing linearly over time. Various polynomial orders of fit where investigated with the linear order of fit most parsimoniously modelling the data. The linear order of fit correctly identified the increasing trend in both the additive allele difference and allele variance. Repeated measures F₁ origin mapping possesses the benefits of using the correlated nature of repeated measures while increasing the efficiency of QTL parameter estimation. Hence, it would be useful for QTL studies on measurements such as milk yield or live weights when collected at irregular intervals.

Theory is developed to combine the data from QTL studies involving F₂ and backcross designed experiments. Genetic covariance matrices are developed for random QTL effects by modelling allele variation in the parental generation instead of the offspring generation for an F₂ and backcross between outbred lines. The result is a general QTL estimation method called parental origin mapping. Phenotypes and genotypes from such a study involving Romney and Merino sheep are analysed providing evidence for a QTL affecting adult and hogget fibre diameter.

By coupling these new methods with computer software programs such as ASREML, F₁ origin mapping and parental origin mapping provide powerful and flexible tools for QTL studies with the ability to efficiently handle single traits, multiple traits and repeated measures.