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

An individuals 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. Interestingly, the genetic variances is increased under AM for the childmother-father design, while it is decreased for the sibling difference. Our results demonstrate that it is not possible to get unbiased estimates of direct genetic effects without controlling for parental and parent-of-origin effects.