Maximising a function of the selection differential

Summary It is shown that some problems of optimising selection response can be solved without assuming a specific form of distribution for the trait of interest. To maximise the selection limit using selection among a fixed number every generation, all above the mean should retained. If a fraction of a population is set aside as a sire breeding nucleus, and selection is at one stage, maximum response per generation occurs when the nucleus as a fraction of the whole population is the square root of the sires: dams ratio. When a trait has an optimum, but declines in value at different rates A above and B below the optimum, the population mean should be chosen so that a fraction B/(A + B) are above the optimum.