## Determining Gene Number for a Polygenic Characteristic

When two individuals homozygous for different alleles at a single locus are crossed (A1A1 X A2A2) and the resulting F1 are interbred (A1A2 X A1A2), one-fourth of the F2 should be homozygous like each of the original parents. If the original parents are homozygous for different alleles at two loci, as are those in Nilsson-Ehle's crosses, then 1/4 X 1/4 = 1/16 of the F2 should resemble one of the original homozygous parents. Generally, (1/4)" will be the number of individuals in the F2 progeny that should resemble each of the original homozy-gous parents, where n equals the number of loci with a segregating pair of alleles that affects the characteristic. This equation provides us with a possible means of determining the number of loci influencing a quantitative characteristic.

To illustrate the use of this equation, assume that we cross two different homozygous varieties of pea plants that differ in height by 16 cm, interbreed the F1, and find that approximately 1/256 of the F2 are similar to one of the original homozygous parental varieties. This outcome would suggest that 4 loci with segregating pairs of alleles (1/256 = 1/44) are responsible for the height difference between the two varieties. Because the two homozygous strains differ in height by 16 cm and there are 4 loci each with two alleles (8 alleles in all), each of the alleles contributes 16 cm/8 = 2 cm in height.

This method for determining the number of loci affecting phenotypic differences requires the use of homozygous strains, which may be difficult to obtain in some organisms. It also assumes that all the genes influencing the characteristic have equal effects, that their effects are additive, and that the loci are unlinked. For many polygenic characteristics, these assumptions are not valid, so this method of determining the number of genes affecting a characteristic has limited application.

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