Solutions For An Introduction to Genetic Analysis Chapter 3 Problem 46P

In tomatoes, two pure lines are present. One is a red, two-loculed fruit in a dwarf plant and the other a yellow, multi-loculed fruit in a tall plant. The red allele is dominant over the yellow allele, while the two-loculed nature is dominant over the multi-loculed nature. The tall vine is dominant over the dwarf plant.

The breeder wants a vine to be tall and produce yellow, two loculed fruits - r/r; L/L; H/H

We give genetic symbols for the different characters under study:

• Color: Red – R, yellow – r

• Locules: two locules – L, multi-loculed – l

• Height: tall – H, dwarf – h

The details of parental cross are as follows:

• R/R; L/L; h/h

• r/r; l/l; H/H

The F₁ progeny is: R/r; L/l; H/h

When the F₁ is selfed, only 1/64 will have the desired genotype of r/r; L/L; H/H.

Tall plants giving yellow, two-loculed fruits are chosen from progeny. The genotype of such plants will be r/r; L/- ; H/-. To select the number of plants required for further testing we need to find the probability of a plant being homozygous dominant for both the L and H genes.

The probability of being homozygous dominant for each gene:

The probability of being heterozygous dominant for each gene would be: 8/9. This probability value should be less than 0.05.

This indicates that at least 27 plants need to be test crossed to a homozygous recessive plant. After the testcross, all heterozygous plants are discarded. If no recessive allele is seen in the progeny and all plants are homozygous, then we need to test using this formula:

This formula gives 95% surety that the plants are homozygous, while it also takes into consideration the 5% of not being homozygous.

Hence, the number of phenotypically dominant plants, which need to be taken from each testcross to be confident that the plant is homozygous, is 5.