A theory of limits in artificial selection

Abstract (1) The paper presents a theory of selection limits in artificial selection. It is, however, developed primarily in terms of single genes. (2) For a single gene with selective advantage s, the chance of fixation (the expected gene frequency at the limit) is a function only of Ns, where N is the effective population size. In artificial selection based on individual measurements, where the selection differential is ī standard deviations, the expected Limit of individual selection in any population is a function only of Nī. (3) For low values of Nī, the total advance by selection is, for additive genes, 2N times the gain in the first generation but may be much greater than this for recessives, particularly if their initial frequency is low. (4) The half-life of any selection process will, for additive genes, not be greater than 1.4 N generations but may for rare recessives equal 2N. (5) The effect of an initial period of selection or inbreeding or of both together on the limits in further selection is discussed. It appears that the effects of restrictions in population size on the selection limit may be a useful diagnostic tool in the laboratory. (6) The treatment can be extended to deal with the limits of further selection after the crossing of replicate lines from the same population when the initial response has ceased. (7) In a selection programme of individual selection of equal intensity in both sexes, the furthest limit should be attained when half the population is selected from each generation. (8) The treatment can also be extended to include selection based on progeny or family records. Consideration of the optimum structure, as far as the limit is concerned, shows that the use of the information on relatives is always a sacrifice on the eventual limit for the sake of immediate gain in the early generations. The loss may, however, be small in large populations.