Simulation of functional additive and non-additive genetic effects using statistical estimates from quantitative genetic models

Stochastic simulation software is commonly used to aid breeders designing cost-effective breeding programs and to validate statistical models used in genetic evaluation. An essential feature of the software is the ability to simulate populations with desired genetic and non-genetic parameters. However, this feature often fails when non-additive effects due to dominance or epistasis are modeled, as the desired properties of simulated populations are estimated from classical quantitative genetic statistical models formulated at the population level. The software simulates underlying functional effects for genotypic values at the individual level, which are not necessarily the same as effects from statistical models in which dominance and epistasis are included. This paper provides the theoretical basis and mathematical formulas for the transformation between functional and statistical effects in such simulations. The transformation is demonstrated with two statistical models analyzing individual phenotypes in a single population (common in animal breeding) and plot phenotypes of three-way hybrids involving two inbred populations (observed in some crop breeding programs). We also describe different methods for the simulation of functional effects for additive genetics, dominance, and epistasis to achieve the desired levels of variance components in classical statistical models used in quantitative genetics.