Long-term response to selection I. Relation to breeding population size, intensity, and accuracy with additive gene action.

Dual CDC-6500 computers were used to simulate the probabilistic aspects of genetic selection and reproduction in random mating populations with additive gene action. These simulations involved either 10 or 20 replicates of 200 consecutive nonoverlapping generations for 72 combinations of breeding population sizes, mating ratios, selection intensities, and accuracies of genetic determination of quantitative phenotypes. The results demonstrate that at least some long-term responses can be characterized by modified exponential functions that, with increasing generations, approach asymptotically to limits whose expectations increase linearly with the inverse tangent of multiples of the expected initial responses. The multiplicative constants are greater for populations with large effective breeding population size than for those of smaller size. Agreement with and discrepancies from past theoretical results are discussed. The supposition is made that the general form of these equations will be retained for broader situations than those simulated, but probably not for nonadditive gene action.