In humans the presence of chin and cheek dimples is dominant to the absence of dimples, and the ability to taste the compound PTC is dominant to the inability to taste the compound. Both traits are autosomal, and they are unlinked. The frequencies of alleles for dimples are D = 0.62 and d = 0.38. For tasting, the allele frequencies are T = 0.76 and t = 0.24.
What are the expected frequencies of the four possible phenotype combinations: dimpled tasters, undimpled tasters, dimpled nontasters, and undimpled nontasters?

Verified step by step guidance

1. Step 1: Understand the problem. The question asks for the expected frequencies of four phenotype combinations based on the allele frequencies provided. The traits (dimples and PTC tasting) are autosomal and unlinked, meaning their inheritance is independent of each other. The phenotype combinations are: dimpled tasters, undimpled tasters, dimpled nontasters, and undimpled nontasters.
2. Step 2: Calculate the genotype frequencies for each trait using the Hardy-Weinberg principle. For dimples, the allele frequencies are D = 0.62 and d = 0.38. The genotype frequencies are: P(DD) = (0.62)^2, P(Dd) = 2(0.62)(0.38), and P(dd) = (0.38)^2. Similarly, for PTC tasting, the allele frequencies are T = 0.76 and t = 0.24. The genotype frequencies are: P(TT) = (0.76)^2, P(Tt) = 2(0.76)(0.24), and P(tt) = (0.24)^2.
3. Step 3: Determine the phenotype frequencies for each trait. For dimples, the dominant phenotype (presence of dimples) is expressed by genotypes DD and Dd, so P(dimpled) = P(DD) + P(Dd). The recessive phenotype (absence of dimples) is expressed by genotype dd, so P(undimpled) = P(dd). For PTC tasting, the dominant phenotype (taster) is expressed by genotypes TT and Tt, so P(taster) = P(TT) + P(Tt). The recessive phenotype (nontaster) is expressed by genotype tt, so P(nontaster) = P(tt).
4. Step 4: Use the principle of independent assortment to calculate the frequencies of the four phenotype combinations. Multiply the phenotype probabilities for dimples and PTC tasting to find the joint probabilities: P(dimpled tasters) = P(dimpled) × P(taster), P(undimpled tasters) = P(undimpled) × P(taster), P(dimpled nontasters) = P(dimpled) × P(nontaster), and P(undimpled nontasters) = P(undimpled) × P(nontaster).
5. Step 5: Summarize the results. The expected frequencies of the four phenotype combinations are the values calculated in Step 4. These frequencies represent the proportion of individuals in the population expected to exhibit each phenotype combination.

Key Concepts

Mendelian Genetics

Mendelian genetics is the study of how traits are inherited through generations based on the principles established by Gregor Mendel. It involves understanding dominant and recessive alleles, where dominant traits mask the expression of recessive ones. In this context, the presence of dimples and the ability to taste PTC are both dominant traits, which means individuals with at least one dominant allele will express these traits.

Hardy-Weinberg Principle

The Hardy-Weinberg principle provides a mathematical framework for understanding allele frequencies in a population at equilibrium. It states that allele and genotype frequencies will remain constant from generation to generation in the absence of evolutionary influences. This principle is essential for calculating expected genotype frequencies based on known allele frequencies, which is necessary for determining the phenotype combinations in the given question.

Phenotype and Genotype Frequencies

Phenotype frequencies refer to the observable traits of individuals in a population, while genotype frequencies refer to the genetic makeup that determines these traits. In this scenario, the expected phenotype combinations (dimpled tasters, undimpled tasters, dimpled nontasters, and undimpled nontasters) can be calculated using the allele frequencies provided. By applying the principles of Mendelian inheritance and the Hardy-Weinberg equation, one can derive the expected frequencies of these phenotypes.