Question

In pea plants, the allele for round seeds is dominant to the allele for wrinkled seeds. At another gene locus, the allele for yellow seeds is dominant to the allele for green seeds. These two allele pairs assort independently. If a plant breeder crosses two plants that are both heterozygous at both gene loci, what percentage of the plants that produce round seeds will also produce yellow seeds?

Answer 1

When crossing two heterozygous pea plants (RrYy), there is a 56.25% chance that the progeny producing round seeds will also produce yellow seeds, due to the application of the product rule for two independent events.

Step-by-step explanation:

In pea plants, round seeds (R) are dominant to wrinkled seeds (r), and the allele for yellow seeds is dominant to the allele for green seeds. Each trait is inherited independently due to Mendel's law of independent assortment. When crossing two plants heterozygous for both traits (RrYy), we can use a Punnett square to predict the offspring's phenotype ratios. For the seed shape, heterozygous plants will produce round seeds (R) 75% of the time (RR, Rr, and Rr) and wrinkled seeds (rr) 25% of the time. For the seed color, heterozygous yellow plants will also show the dominant phenotype 75% of the time (YY, Yy, and Yy) and the recessive green 25% of the time (yy).

Combining these independent probabilities, the chance of producing offspring with both round and yellow seeds is the product of both 3:1 ratios: 0.75 (for round) × 0.75 (for yellow) = 0.5625 or 56.25%. Consequently, if a plant produces round seeds, there is a 56.25% probability that these seeds will also be yellow. This calculation is based on the product rule in genetics, which allows us to calculate the likelihood of two independent events occurring together.