Question

1. in pea plants, two traits are being studied: seed shape and seed color. the allele for round seeds (r) is dominant over the allele for wrinkled seeds (r), and the allele for yellow seeds (y) is dominant over the allele for green seeds (y).

complete the dihybrid square for two heterozygous pea plants.
what are the possible phenotypes of the offspring, and what is the probability of each?
phenotypes
what is the ratio among the following (hint: numbers should add up to 16; count 1/16 as 1, 2/16 as 2, 4/16 as 4, etc)?

Explanation:

Step1: Determine the gametes

Heterozygous pea plants have the genotype \(RrYy\). Using the law of independent assortment, the gametes produced are \(RY\), \(Ry\), \(rY\), \(r y\).

Step2: Set up the dihybrid cross

When we cross \(RrYy\times RrYy\), we use a Punnett - square. The possible phenotypes are determined by the combination of alleles for seed shape (\(R\) (round) dominant over \(r\) (wrinkled)) and seed color (\(Y\) (yellow) dominant over \(y\) (green)).
The four phenotypes are:

• Round yellow (\(R - Y-\)): \(R\) can be \(RR\) or \(Rr\), and \(Y\) can be \(YY\) or \(Yy\). The number of genotypes for round yellow is \(RRYY\), \(RRYy\), \(RrYY\), \(RrYy\). The probability is \(\frac{9}{16}\) (because \(3/4\) chance for round (\(RR + Rr\)) and \(3/4\) chance for yellow (\(YY+Yy\)), and \(\frac{3}{4}\times\frac{3}{4}=\frac{9}{16}\)).
• Round green (\(R - yy\)): Genotypes are \(RRyy\), \(Rryy\). The probability is \(\frac{3}{16}\) (\(3/4\) chance for round and \(1/4\) chance for green (\(yy\)), \(\frac{3}{4}\times\frac{1}{4}=\frac{3}{16}\)).
• Wrinkled yellow (\(rrY-\)): Genotypes are \(rrYY\), \(rrYy\). The probability is \(\frac{3}{16}\) (\(1/4\) chance for wrinkled (\(rr\)) and \(3/4\) chance for yellow, \(\frac{1}{4}\times\frac{3}{4}=\frac{3}{16}\)).
• Wrinkled green (\(rryy\)): Probability is \(\frac{1}{16}\) (\(1/4\) chance for wrinkled and \(1/4\) chance for green, \(\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}\)).

Answer:

The possible phenotypes of the offspring are round yellow, round green, wrinkled yellow, and wrinkled green. The probabilities are \(\frac{9}{16}\) (round yellow), \(\frac{3}{16}\) (round green), \(\frac{3}{16}\) (wrinkled yellow), and \(\frac{1}{16}\) (wrinkled green). The phenotypic ratio is \(9:3:3:1\).