Introduction

The contribution of non-additive genetic variation in human traits is nil for dominance, small for epistasis and, theory suggests, minimal for gene-environment interaction. Evidence from large-scale behavioral and molecular genetics studies, on the other hand, indicate genetic interactions play a nontrivial role in complex traits. We propose an analytic approach that concurrently estimates SNPs’ within individual effects on trait level (additive) and variability (non-additive). We fit a SNP-by-time model to our data. Since time broadly represents an individual’s changing external and internal environment during development, we hypothesize that the SNP-by-time parameter in this model recapitulates gene-environment and epistatic interactions.

Methods

Two-level within individual mixed effects model:

\[Y_{ij} = \textbf{X}_{ij} \beta + SNP_{j} \beta_{snp} + \mu_{j} + \delta_{j} + \epsilon_{ij}\] where \(i\) indexes time whereas \(j\) the person, \(\textbf{X}_{ij}\) is a matrix of covariates (i.e., time, sex, batch, 10 PCs) including the intercept with \(\beta\) as their respective effect size with \(\mu_{j}\) as the random intercept of individual, \(\delta_{j}\) is the genetic relatedness matrix (GRM) and \[\epsilon_{ij} \sim N (0, exp(\alpha + \color{violet}{\tau} SNP_j))\]

We assume uncorrelated variance components: \(\mu_{j} \sim N(0, \sigma^2_{\mu j})\), \(\delta_{j} \sim N(0, \sigma^2_{F}\Phi)\), \(\epsilon_{ij} \sim N (0, exp(\alpha + \tau SNP_j ))\) and \(\Phi\) is \(2\times\) the kinship matrix.

Simulating additive versus non-additive effect

Results

Variants with non-additive effect for height:

Variants with non-additive effect for BMI:

Variants with non-additive effect for math:

Variants with non-additive effect for reading: