Let say I have large phenotypic data, spanning many parents, children and environments. I estimated the broad sense Heritability from siblings ANOVA, the narrow sense heritability from parent-offs. regression (~σ2A). and the environment effect from comparing individuals across environments. So now, given a random parent values, The predicted children mean will be the parent mean + some X value, associated with the dominance effect, and variance coming from the enviro. effect. how to calculate this "X" factor ? This what puzzles me. - what will be the mean and var. of the population?

I see, so what you are actually asking is about reprogramming cells to become eggs?

I would like to simulate a population in which I know the real heritability, dominance effects and environment effect, estimated from sibling ANOVA, parent-offspring regression and comparing different environments. Although I can understand the role of these effects on a large population, I am not sure how to apply this to the predicted parameters of each individual offspring of two individual parents. What will be the right formula to estimate the phenotype of each offspring in the simulation?

I see, but how the dominance effect changes the mean? and what will be the variance of the offspring population - is it just the environmental related variance?

Thank you very much, it was very helpful. I went on trying with the REML/MCMC methods, and will check how it goes.