“A Discriminant Function For Plant Selection”, 1936-11 (; similar):
The characters with which a plant breeder is principally concerned are those known as “quantitative characters”. They present particular difficulty because heritable variations are masked by larger non-heritable variations which make it difficult to determine the genotypic values of individual plants or lines unless we have sufficient seed and facilities to grow replicated plots of each line. In the earlier stages of selection breeders try to select plants in the field on the basis of observable characters which they believe may be associated with the desired character or quality (for example, grain and ear sizes as indices to yielding ability, or flintiness of grain as an index of protein content), but the actual worth to be attributed to each character is usually unknown. The problem may be approached by seeking to determine what “discriminant function” (1936) of the observable characters may best indicate the “genetic value” of a plant or line.
…The object of this paper is to suggest how a method for selecting plant lines may be worked out in a logical and systematic manner. The value of a plant may be expressed as a linear function of its characters, then, using Fisher’s concept of “discriminant functions”, we may derive that linear function of observable characters which will be the best available guide to the genetic value of each line.
The expectation of “genetic advance” over the mean of the unselected population for any given selection intensity may also be estimated and used to compare the relative efficiencies of various breeding programmes.
It is shown further that arbitrary ratios, such as the “migration coefficient” or the “tiller survival rate”, are likely to be inefficient as indices to the genetic value of either of the characters whose ratio is observed.