Dissecting genetic interactions in complex traits

Of central importance in the dissection of the components that govern complex traits is understanding the architecture of natural genetic variation. Genetic interaction, or epistasis, constitutes one aspect of this, but epistatic analysis has been largely avoided in genome wide association studies because of statistical and computational difficulties. This thesis explores both issues in the context of two-locus interactions. Initially, through simulation and deterministic calculations it was demonstrated that not only can epistasis maintain deleterious mutations at intermediate frequencies when under selection, but that it may also have a role in the maintenance of additive variance. Based on the epistatic patterns that are evolutionarily persistent, and the frequencies at which they are maintained, it was shown that exhaustive two dimensional search strategies are the most powerful approaches for uncovering both additive variance and the other genetic variance components that are co-precipitated. However, while these simulations demonstrate encouraging statistical benefits, two dimensional searches are often computationally prohibitive, particularly with the marker densities and sample sizes that are typical of genome wide association studies. To address this issue different software implementations were developed to parallelise the two dimensional triangular search grid across various types of high performance computing hardware. Of these, particularly effective was using the massively-multi-core architecture of consumer level graphics cards. While the performance will continue to improve as hardware improves, at the time of testing the speed was 2-3 orders of magnitude faster than CPU based software solutions that are in current use. Not only does this software enable epistatic scans to be performed routinely at minimal cost, but it is now feasible to empirically explore the false discovery rates introduced by the high dimensionality of multiple testing. Through permutation analysis it was shown that the significance threshold for epistatic searches is a function of both marker density and population sample size, and that because of the correlation structure that exists between tests the threshold estimates currently used are overly stringent. Although the relaxed threshold estimates constitute an improvement in the power of two dimensional searches, detection is still most likely limited to relatively large genetic effects. Through direct calculation it was shown that, in contrast to the additive case where the decay of estimated genetic variance was proportional to falling linkage disequilibrium between causal variants and observed markers, for epistasis this decay was exponential. One way to rescue poorly captured causal variants is to parameterise association tests using haplotypes rather than single markers. A novel statistical method that uses a regularised parameter selection procedure on two locus haplotypes was developed, and through extensive simulations it can be shown that it delivers a substantial gain in power over single marker based tests. Ultimately, this thesis seeks to demonstrate that many of the obstacles in epistatic analysis can be ameliorated, and with the current abundance of genomic data gathered by the scientific community direct search may be a viable method to qualify the importance of epistasis

An Evolutionary Perspective on Epistasis and the Missing Heritability

<div><p>The relative importance between additive and non-additive genetic variance has been widely argued in quantitative genetics. By approaching this question from an evolutionary perspective we show that, while additive variance can be maintained under selection at a low level for some patterns of epistasis, the majority of the genetic variance that will persist is actually non-additive. We propose that one reason that the problem of the “missing heritability” arises is because the additive genetic variation that is estimated to be contributing to the variance of a trait will most likely be an artefact of the non-additive variance that can be maintained over evolutionary time. In addition, it can be shown that even a small reduction in linkage disequilibrium between causal variants and observed SNPs rapidly erodes estimates of epistatic variance, leading to an inflation in the perceived importance of additive effects. We demonstrate that the perception of independent additive effects comprising the majority of the genetic architecture of complex traits is biased upwards and that the search for causal variants in complex traits under selection is potentially underpowered by parameterising for additive effects alone. Given dense SNP panels the detection of causal variants through genome-wide association studies may be improved by searching for epistatic effects explicitly.</p> </div

Statistical inference in two-sample summary-data Mendelian randomization using robust adjusted profile score

Mendelian randomization (MR) is a method of exploiting genetic variation to unbiasedly estimate a causal effect in presence of unmeasured confounding. MR is being widely used in epidemiology and other related areas of population science. In this paper, we study statistical inference in the increasingly popular two-sample summary-data MR design. We show a linear model for the observed associations approximately holds in a wide variety of settings when all the genetic variants satisfy the exclusion restriction assumption, or in genetic terms, when there is no pleiotropy. In this scenario, we derive a maximum profile likelihood estimator with provable consistency and asymptotic normality. However, through analyzing real datasets, we find strong evidence of both systematic and idiosyncratic pleiotropy in MR, echoing the omnigenic model of complex traits that is recently proposed in genetics. We model the systematic pleiotropy by a random effects model, where no genetic variant satisfies the exclusion restriction condition exactly. In this case we propose a consistent and asymptotically normal estimator by adjusting the profile score. We then tackle the idiosyncratic pleiotropy by robustifying the adjusted profile score. We demonstrate the robustness and efficiency of the proposed methods using several simulated and real datasets.Comment: 59 pages, 5 figures, 6 table

Population phenomena inflate genetic associations of complex social traits

Heritability, genetic correlation, and genetic associations estimated from samples of unrelated individuals are often perceived as confirmation that genotype causes the phenotype(s). However, these estimates can arise from indirect mechanisms due to population phenomena including population stratification, dynastic effects, and assortative mating. We introduce these, describe how they can bias or inflate genotype-phenotype associations, and demonstrate methods that can be used to assess their presence. Using data on educational achievement and parental socioeconomic position as an exemplar, we demonstrate that both heritability and genetic correlation may be biased estimates of the causal contribution of genotype. These results highlight the limitations of genotype-phenotype estimates obtained from samples of unrelated individuals. Use of these methods in combination with family-based designs may offer researchers greater opportunities to explore the mechanisms driving genotype-phenotype associations and identify factors underlying bias in estimates