Performance of epistasis detection methods in semi-simulated GWAS.

BACKGROUND: Part of the missing heritability in Genome Wide Association Studies (GWAS) is expected to be explained by interactions between genetic variants, also called epistasis. Various statistical methods have been developed to detect epistasis in case-control GWAS. These methods face major statistical challenges due to the number of tests required, the complexity of the Linkage Disequilibrium (LD) structure, and the lack of consensus regarding the definition of epistasis. Their limited impact in terms of uncovering new biological knowledge might be explained in part by the limited amount of experimental data available to validate their statistical performances in a realistic GWAS context. In this paper, we introduce a simulation pipeline for generating real scale GWAS data, including epistasis and realistic LD structure. We evaluate five exhaustive bivariate interaction methods, fastepi, GBOOST, SHEsisEpi, DSS, and IndOR. Two hundred thirty four different disease scenarios are considered in extensive simulations. We report the performances of each method in terms of false positive rate control, power, area under the ROC curve (AUC), and computation time using a GPU. Finally we compare the result of each methods on a real GWAS of type 2 diabetes from the Welcome Trust Case Control Consortium. RESULTS: GBOOST, SHEsisEpi and DSS allow a satisfactory control of the false positive rate. fastepi and IndOR present an increase in false positive rate in presence of LD between causal SNPs, with our definition of epistasis. DSS performs best in terms of power and AUC in most scenarios with no or weak LD between causal SNPs. All methods can exhaustively analyze a GWAS with 6.105 SNPs and 15,000 samples in a couple of hours using a GPU. CONCLUSION: This study confirms that computation time is no longer a limiting factor for performing an exhaustive search of epistasis in large GWAS. For this task, using DSS on SNP pairs with limited LD seems to be a good strategy to achieve the best statistical performance. A combination approach using both DSS and GBOOST is supported by the simulation results and the analysis of the WTCCC dataset demonstrated that this approach can detect distinct genes in epistasis. Finally, weak epistasis between common variants will be detectable with existing methods when GWAS of a few tens of thousands cases and controls are available.

Fixation probability in a two-locus intersexual selection model.

We study a two-locus model of intersexual selection in a finite haploid population reproducing according to a discrete-time Moran model with a trait locus expressed in males and a preference locus expressed in females. We show that the probability of ultimate fixation of a single mutant allele for a male ornament introduced at random at the trait locus given any initial frequency state at the preference locus is increased by weak intersexual selection and recombination, weak or strong. Moreover, this probability exceeds the initial frequency of the mutant allele even in the case of a costly male ornament if intersexual selection is not too weak. On the other hand, the probability of ultimate fixation of a single mutant allele for a female preference towards a male ornament introduced at random at the preference locus is increased by weak intersexual selection and weak recombination if the female preference is not costly, and is strong enough in the case of a costly male ornament. The analysis relies on an extension of the ancestral recombination-selection graph for samples of haplotypes to take into account events of intersexual selection, while the symbolic calculation of the fixation probabilities is made possible in a reasonable time by an optimizing algorithm.