### Punnet squares

Now, let’s get back to the results of Mendel’s experiment. Why does self-fertilization of hybrid round peas (Rr x Rr) result in a ratio of 1 RR : 2 Rr : 1 rr? Well, when an individual produces sperm or eggs, each gamete contains only one of the two alleles (i.e. either R or r). Each allele is equally likely to be included in a gamete, so half of the pollen grains from an Rr plant will be R and half will be r. Likewise, half of the ovules will be R and half will be r. During fertilization, a pollen grain and ovule fuse to create an embryo with two allele copies. Fertilization is random, so all combinations of pollen and ovules are possible.

We can represent all possible combinations for a cross with a Punnett square (named after British geneticist Reginald Punnett). First, choose one of the parents, and write each possible gamete from that parent in the first row. Then write each possible gamete from the other parent in the first column. Next, fill in the progeny genotypes by combining the gamete in the first row with the gamete in the first column. Click on the checkbox in the upper left corner to see correct answers.

Since fertilization is random, each of the four boxes is equally likely. By counting the boxes with each genotype, we obtain the progeny ratio of 1 RR : 2 Rr : 1 rr. There are twice as many Rr progeny because two different combinations give that result (R pollen + r ovule, or r pollen + R ovule). In contrast, only one combination gives RR progeny (R sperm + R ovule) and only one combination that gives rr progeny (r sperm + r ovule). Since we know that the R round allele is dominant to the r wrinkled allele, we can also obtain the phenotypic ratio of 3 round : 1 wrinkled (3 R- : 1 rr) from the Punnett square.