An evolutionary perspective on epistasis and the missing heritability

Abstract

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.

Figure 1. Allele frequency trajectories under selection.

Top row: G-P maps. 1. Independent additive effects at locus A and B; 2. Dominant pattern of canalisation; 3. Recessive pattern of canalisation; 4–6. Patterns generated by a genetic algorithm optimising for maximised additive variance and long-term survival at intermediate frequency. Middle row: Expected allele frequency trajectories for G-P maps under selection, as derived deterministically, with initial frequencies of 0.1, 0.3, 0.5, 0.7, and 0.9 enumerated over both loci. Frequencies on the -axis correspond to alleles a/b. Only one colour appears for patterns 1–3 because the trajectories of both alleles are identical. Bottom row: The path of allele frequencies as observed through stochastic simulations of populations comprising 1000 individuals and at generation 0, with initial allele frequencies at both loci of 0.5.

Figure 2. Deterministic change in variance components of G-P maps under selection.

For (a) Genetic variance and (b) Additive variance as a proportion of genetic variation, with initial frequencies of 0.1, 0.3, 0.5, 0.7 and 0.9 enumerated over both loci. The variance decomposition was performed at the causal locus (), and at SNP pairs that were in incomplete LD with the causal loci. Boxes represent the different G-P maps from Figure 1.

Figure 3. Effect of LD on G-P map estimation.

Different G-P maps of causal variants (rows of graphs) deterministically calculated from neighbouring SNPs in different levels of linkage disequilibrium (columns of graphs). All SNP and causal variant frequencies are set to 0.5. Rows 1–2: Canalisation; 3: ; 4: ; 5: .

Figure 4. The percentage of total additive variance detected by each of 5 different methods.

Columns of graphs refer to G-P maps (Figure 1), rows refer to between causal variants and observed SNPs. (a) Deterministic calculations were performed 25 times, each with different initial allele frequencies. The percentage of additive variance explained is summed across all runs and generations. (b) The summed detected at each generation as a percentage of the summed simultaneously present in 50 populations. For clarity, only the most powerful 1D test (A+D) is compared against the most powerful 2D test (full parameterisation). A Bonferroni threshold was used, for 1D strategies and for 2D strategies.