Interactions in complex traits

The availability of cheap genotyping technologies has enabled to collection of very large samples with both genetic and phenotypic information, enabling the interrogation of the genetic architecture of complex traits in humans and other organisms. The role of interactions between genetic variants and between genetic variants and environmental factors in complex traits is not well characterised, especially in humans. This is in part due to a lack of theory and methods designed for powerful investigation of interactions in complex traits in large-scale datasets. This thesis develops both theory and methods relating to interactions between genetic variants and between genetic and environmental factors, complemented by empirical analyses aimed at discovering the influence of interactions on complex traits. The effect of genetic variation on trait variation can be decomposed into components reflecting interactions involving different numbers of genetic variants. The first part of this thesis generalises classical theory on the decomposition of the genetic variance into components arising from different types of interaction to finite populations, where the influence of interactions is more easily detected. The theory is applied to determine the proportion of growth variance from pairwise and third and higher order interactions in a yeast cross. The subsequent parts of the thesis are more directly concerned with interactions between genetic variants and environmental factors. It is first demonstrated that multiple lifestyle factors modify the effect of variants in the FTO gene on body mass index (BMI). This motivates the development of the heteroskedastic linear mixed model (HLMM), which exploits changes in variability with genotype to aid discovery of genetic variants involved in interactions. An efficient algorithm for application of the HLMM to large scale datasets is developed and applied to discover genetic variants likely to be involved in interactions on BMI