Implications of non-linear economic weights for breeding.

Relationships were studied theoretically between phenotypic values of selection candidates ('parents') and economic worth of the 'offspring' that would belong to production populations. The candidates could include individuals, crosses or clones, and the offspring could be produced either sexually or vegetatively. Cases considered included: three systems for generating production populations [clonal propagation, pair(full-sib)crosses and half-sib crosses]; three economic-worth (profit) functions for individual offspring (linear, intermediate optimum, acceptable versus cull); and independently varying heritabilities for both parents and offspring. The heritabilities were varied in the model against a background of fixed genetic variance. Parental values were considered in terms of phenotypic standard deviations from the population mean, assuming normality. Lower heritabilities and, to a lesser extent, genetic segregation severely damped down the non-linearities of economic worth in relation to measured parental values, such that the linear weightings for traits in a selection index should usually be a good approximation, provided the profit function for individual offspring is monotonic. The economic advantages of corrective mating within a select population may be minimal if both heritabilities are low and the profit functions apply to individual offspring. The economic advantages accruing from genetic uniformity of clones (or crosses between inbreds) in conjunction with non-linear profit functions are strongly dependent on achieving high broad-sense heritabilites, particularly in the offspring (production population).