Question

In a series of crosses between two true-breeding strains of peaches, the \(F_{1}\) generation was uniform, producing 30 -g peaches. The \(\mathrm{F}_{2}\) fruit mass ranges from 38 to \(22 \mathrm{g}\) at intervals of \(2 \mathrm{g}\) (a) Using these data, determine the number of polygenic loci involved in the inheritance of peach mass. (b) Using gene symbols of your choice, give the genotypes of the parents and the \(\mathrm{F}_{1}\).

Short answer

Answer: There are 2 polygenic loci involved in the inheritance of peach mass. The parent genotypes are AABB (with alleles contributing to the larger phenotype) and aabb (with alleles contributing to the smaller phenotype). In the F1 generation, all individuals have the genotype AaBb.

Step-by-step solution

Identify the phenotypic range of F2 generation

In the exercise, we are given that the F2 fruit mass ranges from 38 g to 22 g at intervals of 2 g. We would use this information to identify the number of distinct phenotypes within the range.

Calculate the number of polygenic loci

To determine the number of polygenic loci involved in the inheritance of peach mass, count the number of distinct phenotypes within the F2 range (subtract the lowest mass from the highest mass, divide by the interval, and add one). Then take the square root of this number and compare it to the standard 1:2:1 ratio for a single polygenic locus. Based on the calculated ratio, we can then identify the number of polygenic loci involved in the inheritance of peach mass.

Calculate the genotypes of the parents and F1 generation

After identifying the number of polygenic loci involved in the inheritance of peach mass, we can determine the genotypes of the parents and F1 generation by giving gene symbols of our choice.

Identify the phenotypic range of F2 generation

The F2 fruit mass ranges from 38 g to 22 g at intervals of 2 g. Subtract the lowest mass from the highest mass and divide by the interval: (38-22)/2 = 16/2 = 8. Add one to the result, and we have a total of 9 distinct phenotypes in the F2 generation.

Calculate the number of polygenic loci

Now, we need to compare the number of distinct phenotypes in the F2 generation to the standard 1:2:1 ratio for a single polygenic locus. The ratio 1:2:1 has three distinct phenotypes: 3^n, where n is the number of polygenic loci. We take the square root of the number of distinct phenotypes (9) to calculate the number of loci: n = \(\sqrt{9} = 3\). Therefore, there are 2 polygenic loci involved in the inheritance of peach mass.

Calculate the genotypes of the parents and F1 generation

We choose two gene symbols, A and B, to represent the two polygenic loci involved in the inheritance of peach mass. Since both parent strains are true-breeding, one parent strain would be AABB (with alleles contributing to the larger phenotype) and the other parent strain would be aabb (with alleles contributing to the smaller phenotype). In the F1 generation, all individuals are heterozygotes and will have the genotype AaBb.