Mendelian Genetics

Mendel began a numerical evaluation of, respectively, two and three traits simultaneously, because he also wanted to know how different traits sorted themselves during gamete formation. He began a numerical evaluation of how two and then three traits were inherited simultaneously. The dihybrid cross involved two traits: the form of the plant's ripe seeds and the color of its interior seeds. He crossed one true-breeding variety that had wrinkled seeds and a green interior, with another that had round seeds and a yellow interior. The dihybrid cross generated offspring that all had round, yellow seeds, but the seeds' outward appearance, or phenotype, hid the offspring's heterozygous nature. The offspring contained recessive alleles for making wrinkled, green seeds, as well as the dominant alleles that generated the seeds' round and yellow appearance.

The round, yellow seeds, which were the seeds of the first filial generation, or F1, were planted, raised, and made to self-pollinate. Their progeny, the second filial generation, or F2, had four phenotypes for seed form and color, in a ratio of 9:3:3:1 (nine round and yellow, to three wrinkled and yellow, to three round and green, to one wrinkled and green).

To unmask the F2 genotypes, the next generation's wrinkled, round, yellow, or green seeds were collected. The seeds showed that there were nine different genotypes among the F2 plants. If Y represents yellow, y represents green, R represents round, and r represents wrinkled, the nine geno-types were: YyRr, YyRR, Yyrr, YYRr, YYRR, YYrr, yyRr, yyRR, and yyrr. Four of the genotypes were homozygous for both traits, four were homozygous for one trait and heterozygous for the other, and one was heterozygous for both traits.

Mendel's trihybrid cross included the trait for the color of the seed coats, which could be white or non-white, in addition to the same two traits used in the dihybrid cross. In this cross, the F2 generation had eight different combinations of seed shape, seed coat color, and interior seed color and twenty-seven different genotypes.

The existence of all these allelic combinations revealed that chance had a lot to do with what ended up in the same gamete. The chance of a descendent getting a specific seed shape and color depended on straight math, not on interaction between shape and color or another unknown influence. A ratio of three dominant to one recessive phenotype appeared for each trait, as if the other traits' alleles did not exist. The arrival of one allele inside a gamete was unaffected by the entry of another trait's allele. Mendel described this formally as "each pair of different characters in hybrid union is independent of the other differences."

The chance of a descendant getting a specific trait depends on probability, not on the interaction between traits. This is formally stated as Mendel's Second Law, or the Principle of Independent Assortment: Different traits assort (i.e. are included in gametes) independently of one another.

A Punnett square, designed by English geneticist Reginald Punnett (1875-1967) and shown in Figure 1, shows the outcomes of crosses that follow Mendel's laws. The capital letters A and B represent dominant alleles, and the lowercase letters a and b represents recessive alleles. A genotype that is heterozygous for both traits in a dihybrid cross is represented as AaBb.