A quantitative genetic model for indirect genetic effects and genomic imprinting under random and assortative mating

An individual's phenotype reflects a complex interplay of the direct effects of their DNA, epigenetic modifications of their DNA induced by their parents, and indirect effects of their parents' DNA. Here, we derive how the genetic variance within a population is changed under the influence of indirect maternal, paternal and parent-of-origin effects under random mating. We also consider indirect effects of a sibling, in particular how the genetic variance is altered when looking at the phenotypic difference between two siblings. The calculations are then extended to include assortative mating (AM), which alters the variance by inducing increased homozygosity and correlations within and across loci. AM likely leads to covariance of parental genetic effects, a measure of the similarity of parents in the indirect effects they have on their children. We propose that this assortment for parental characteristics, where biological parents create similar environments for their children, can create shared parental effects across traits and the appearance of cross-trait AM. Our theory shows how the resemblance among relatives increases under both AM, indirect and parent-of-origin effects. When our model is used to predict correlations among relatives in human height, we find that explaining the patterns observed in real data requires both indirect genetic effects and assortative mating. The degree to which direct, indirect and epigenetic effects shape the phenotypic variance of complex traits remains an open question that requires large-scale family data to be resolved.