Figure 1.
Power to Detect Association for 1,500 Individuals where Both Loci Are Responsible for 5% of the Trait Variance
Power is displayed on the vertical axis, allele frequencies at both loci on the horizontal axes. Results are shown for an (A) additive model where there is no epistasis (MA), (B) a simple looking epistatic model (M27) in which an individual requires at least one copy of the increaser allele at both loci in order to increase the quantitative phenotype above baseline levels, and (C) a more exotic model where an individual has to be heterozygous at both loci in order to have a trait mean above baseline (M16).
Figure 2.
Partitioning of the Variance for Four Quantitative Trait Models
(A) Expected variance components at locus 1, locus 2, and the epistatic variance component for model M27 in which an individual requires at least one copy of the increaser allele at both loci in order to increase the quantitative phenotype above baseline levels. Note in particular that when alleles “A” and “B” are common at both loci, the majority of genetic variance resides in the epistatic component.
(B) The proportion of the total genetic variance which is due to statistical epistasis for three simple models. The vertical axis denotes the proportion of variance, whereas the horizontal axes denote allele frequencies at each locus. For each model, the epistatic variance component is appreciable for a sizeable portion of the space of possible allele frequencies.
Figure 3.
Power Associated with the Two-Stage Strategies in the Case of Two Loci Responsible for 5% of the Trait Variance Generated under Model M27 in which an Individual Requires at Least One Copy of the Increaser Allele at Both Loci in Order to Increase the Quantitative Phenotype above Baseline Levels as Applied to 1,000 Individuals
Five different first-stage thresholds are shown. In the case of the Both Significant Two-Stage Strategy, there is a rapid decrease in power with increasingly stringent first-stage thresholds, except for a small proportion of the space of possible allele frequencies where there is a small gain in power. In the case of the Either Significant Strategy, power declines more slowly as the first-stage threshold becomes increasingly stringent.
Figure 4.
Fifty-One Biallelic Two-locus Models Incorporating Varying Degrees of Epistasis
Each row indexes the genotype at the first locus and each column refers to the genotype at the second locus. The number in each cell is the trait mean for that genotype. Models range from the very simple (e.g., M1) to the more exotic (e.g., M170).
Table 1.
Genotypic Means and Frequencies for a Biallelic Two-Locus Model