QUANTITATIVE GENETIC MODELS FOR DEVELOPMENT, EPIGENETIC SELECTION, AND PHENOTYPIC EVOLUTION.

Herein we describe a general multivariate quantitative genetic model that incorporates two potentially important developmental phenomena, maternal effects and epigenetic effects. Maternal and epigenetic effects are defined as partial regression coefficients and phenotypic variances are derived in terms of age-specific genetic and environmental variances. As a starting point, the traditional quantitative genetic model of additive gene effects and random environmental effects is cast in a developmental time framework. From this framework, we first extend a maternal effects model to include multiple developmental ages for the occurrence of maternal effects. An example of maternal effects occurring at multiple developmental ages is prenatal and postnatal maternal effects in mammals. Subsequently, a model of intrinsic and epigenetic effects in the absence of maternal effects is described. It is shown that genetic correlations can arise through epigenetic effects, and in the absence of other developmental effects, epigenetic effects are in general confounded with age-specific intrinsic genetic effects. Finally, the two effects are incorporated into the basic quantitative genetic model. For this more biologically realistic model combining maternal and epigenetic effects, it is shown that the phenotypic regressions of offspring on mother and offspring on father can be used in some cases to estimate simultaneously maternal effects and epigenetic effects.