Survival rates of mutant genes under artificial selection using individual and family information

We have used diffusion and branching process methods to investigate fixation rates, probabilities of survival per generation, and times to fixation of mutant genes under different selection methods incorporating individual and family information. Diffusion approximations fit well to simulated results even for large selection coefficients. Methods that give much weight to family information, such as BLUP evaluation which is widely used in animal breeding, reduce fixation rates of mutant genes because of the reduced effective population sizes. In general, it is observed that even mutants with relatively small heterozygous effects (say 0.1 phenotypic standard deviation) are practically 'safe' (i.e. their probability of loss from one generation to the next is smaller than, say, 10%) after just a few generations, typically less than 10. For methods of selection with larger effective size, such as within-family selection, the mutant is 'safe' in the population somewhat earlier but eventual fixation takes a longer time. Finally we evaluate the amount by which the use of marker assisted selection reduces the fixation probability of newly arisen mutants.