## Info

Purple

Dark red

Dark red

Light red

Light red

White

Combine common phenotypes

F2 ratio Number of ^ Frequency pigment genes

4l6 3

616 2

4l6 1

Phenotype

Purple Dark red Red

Light red White

Purple Dark red Red

Light red White

Conclusion: Polygenic characteristics are inherited according to Mendel's principles.

To obtain the probability of combinations of genes at both loci, we must use the multiplication rule of probability (p. 000 in Chapter 3), which is based on Mendel's principle of independent assortment. The expected proportion of F2 progeny with genotype A+A+B+B+ is the product of the probability of obtaining genotype A+A+ (1/4) and the probability of obtaining genotype B+B+ (1/4), or 1/4 X 1/4 = 1/16 (I Figure 22.4). The probabilities of each of the phenotypes can then be obtained by adding the probabilities of all the genotypes that produce that phenotype. For example, the red phenotype is produced by three genotypes:

Genotype

Probability

Thus, the overall probability of obtaining red kernels in the F2 progeny is 1/16 + 1/16 + 1/4 = 6/16. Figure 22.4 shows that the phenotypic ratio expected in the F2 is 1/16 purple, 4/16 dark red, 6/16 red, 4/16 light red, and 1/16 white. This pheno-typic ratio is precisely what Nilsson-Ehle observed in his F2 progeny, demonstrating that the inheritance of a continuously varying characteristic such as kernel color is indeed according to Mendel's basic principles.

Nilsson-Ehle's crosses demonstrated that the difference between the inheritance of genes influencing quantitative characteristics and the inheritance of genes influencing discontinuous characteristics is in the number of loci that determine the characteristic. When multiple loci affect a character, more genotypes are possible; so the relation between the genotype and the phenotype is less obvious. As the number of loci affecting a character increases, the number of phenotypic classes in the F2 increases (I Figure 22.5).

Several conditions of Nilsson-Ehle's crosses greatly simplified the polygenic inheritance of kernel color and made it possible for him to recognize the Mendelian nature of the characteristic. First, genes affecting color segregated at only two or three loci. If genes at many loci had been segregating, he would have had difficulty in distinguishing the phenotypic classes. Second, the genes affecting kernel color had strictly additive effects, making the relation between genotype and phenotype simple. Third, environment played almost no role in the phenotype; had environmental factors

22.4 Nilsson-Ehle demonstrated that kernel color in wheat is inherited according to Mendelian principles. He crossed two varieties of wheat that differed in pairs of alleles at two loci affecting kernel color. A purple strain (A+A+B+B+) was crossed with a white strain (A-A-B-B-), and the F1 was intercrossed to produce F2 progeny. The ratio of phenotypes in the F2 can be determined by breaking the dihybrid cross into two simple single-locus crosses and combining the results with the multiplication rule.

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