Question

Two different crosses were set up between carrots (Daucus carota \()\) of different colors and carotenoid content (Santos, Carlos A. F. and Simon, Philipp W. 2002. Horticultura Brasileira 20). Analyses of the \(\mathrm{F}_{2}\) generations showed that four loci are associated with the \(\alpha\) carotene content of carrots, with a broad-sense heritability of \(90 \% .\) How many distinct phenotypic categories and genotypes would be seen in each \(\mathrm{F}_{2}\) generation, and what does a broad-sense heritability of \(90 \%\) mean for carrot horticulture?

Short answer

Answer: There are 5 distinct phenotypic categories in this carrot population. A broad-sense heritability of 90% means that 90% of the observed variation in alpha carotene content is due to genetic factors, indicating that selective breeding would be effective in increasing the carotene content of the carrots.

Step-by-step solution

Calculate the distinct genotypic categories

To calculate the distinct genotypic categories, we have to consider that each locus can be homozygous dominant (AA), heterozygous (Aa), or homozygous recessive (aa). Since there are 4 loci associated with the trait, the total number of distinct genotypic categories can be calculated using the formula \(3^n\), where n is the number of loci. Hence, the total number of genotypic categories is \(3^4\).

Calculate the phenotypic categories

Here we have 4 loci associated with the carotene content, and each locus may have dominant (A) and recessive (a) alleles. The phenotypes depend on these alleles as dominant alleles (A) would lead to higher carotene content, while recessive alleles (a) would lead to lower carotene content. Since we have 4 loci, there could be a phenotypic range from 0 (all recessive alleles) to 4 (all dominant alleles) in steps of 1. Therefore, there are a total of 5 distinct phenotypic categories.

Calculate the number of genotypes in each F2 generation

Given that we've found a total of 81 genotypic categories (\((3^4)=81)\), then each F2 generation will have 81 distinct genotypes.

Explain the meaning of the broad-sense heritability of 90%

Broad-sense heritability (H2) is a measure of the proportion of phenotypic variance that can be attributed to genetic factors. In this case, the broad-sense heritability of 90% means that 90% of the observed variation in alpha carotene content in the carrot population can be explained by the genetic differences among the carrots. The remaining 10% of the variation is due to environmental factors or interactions between genes and the environment. For carrot horticulture, this high heritability implies that selective breeding will be effective in increasing the carotene content of the carrots, as the majority of the variations are determined by the carrots' genetic constitution.