The power of QTL detection was studied both empirically and deterministically for several methods. TDT was more powerful than a linkage test, but less powerful than a pure association test. There were no great differences in power between TDTs. One of the TDTs was implemented in BLUP (Best Linear Unbiased Prediction) to study the effect of a candidate gene, the melanocortin 4- receptor (MC4R), on growth, appetite and fatness in pigs. We found significant effects on growth and fatness but not on appetite. TDT uses within families genetic variation. A novel parameter to estimate gene effects using between families genetic variation was also included. If there is no spurious disequilibrium both estimates should be identical, otherwise only the within-families estimator is unbiased. It was more powerful to simulate missing parental genotypes with Gibbs Sampling than analysing data with sib-ship TDTs disregarding parental information. TDT was also used in a genome-wide search for markers associated with bovine spongiform encaphalopathy (BSE). TDT was implemented using logistic regressions, more amenable to statistical modelling than the original form. Maker loci near the Prion Protein gene did not show any associations with BSE, however, markers located on chromosomes 5, 10 and 20, did. A second study that focused on these three chromosomal regions confirmed the association for the marker on chromosome 5. TDT has shown reasonable power and exceptional robustness when mapping QTL in structured populations. Therefore TDT should be part of the gene cartographers’ continuously evolving arsenal of tools for gene mapping. However, previously published TDTs were developed for analysing human populations, whereas domestic/wild populations have different structures and histories that may require alternative statistical analyses. Linked gene flow (LGF) theory can be used for predicting identity-by-descent (IBD) probabilities between individuals. IBD probabilities are at the core of mixed model equations for mapping QTL in outbred populations via variance components estimation. In this thesis, LGF theory was used for determining inbreeding within each individual and chromosomal location using multi-marker information, hence paving the way for further developments.