In this case, 25 percent of the F₂ offspring will be AA, 50 percent will be Aa, and 25 percent will be aa. Both AA and Aa will have the dominant phenotype, giving the 3:1 ratio (75 percent to 25 percent) of dominant to recessive phenotypes that Mendel observed.

 

    For the SAT II Biology, if you are given the genotypes of two parents, you should be able to predict the genotypes and phenotypes of their offspring by using a Punnett square.

 

 

    After finishing his monohybrid crosses, Mendel moved on to dihybrid crosses, in which he bred pure, parental varieties that had two traits distinguishing them from each other. He wanted to determine whether the inheritance of one trait was connected in any way to the inheritance of the other.

 

    The color and shape of the pea seeds provided two convenient traits to study. The seeds were either yellow or green, with yellow dominant; in shape, they were either round or wrinkled, with round dominant. Mendel crossed double dominant (phenotype yellow and round, genotype RRYY) plants with double recessive (phenotype green and wrinkled, genotype rryy) plants. As expected, the F₁ generation consisted of hybrid offspring all with the double dominant (round yellow) phenotype and a heterozygous genotype (RrYy). The key test came in the proportions of different phenotypes in the F₂ generation. If the inheritance of one trait did not influence the inheritance of the other, then each parent should make equal numbers of the four possible gametes, and sixteen different genotypes would be equally represented in the offspring. As seen in the Punnett square below, there should be four different phenotypes (yellow and round, green and round, yellow and wrinkled, green and wrinkled) occurring in the proportions 9:3:3:1.

    Mendel’s phenotype counts of F₂ seeds did indeed show the 9:3:3:1 proportions anticipated in the Punnett square for the dihybrid cross. From these results, he concluded that the inheritance of one trait was unrelated to the inheritance of a second trait. The units from any one hereditary pair segregate into the gametes independently of the segregation of the units from any other pair. This principle is known as the law of independent assortment.

 

 

    Drawing Punnett squares is a helpful way to visualize simple genetics problems, but with problems involving several different genes, it is often easier to use the rules of probability. (A Punnett square for a three-gene hybrid cross would have 64 squares!) There are two rules of probability that you will need to solve genetics problems. First, the probability of an outcome that depends on the occurrence of two or more independent events is obtained by multiplying together the probability of each necessary independent event. This is the and rule of probability: