Blue moon beans produce beans that are either the dominant color blue or the recessive color white. The bean pods for this species always contain four seeds each. If two heterozygous plants that each have the Bb genotype are crossed, what are the predicted frequencies of each of the five outcome classes for combinations of blue and white seeds in pods?

Verified step by step guidance

1. Determine the genotypic ratio of offspring from the cross of two heterozygous plants (Bb x Bb) using a Punnett square. The possible genotypes are BB, Bb, and bb, with a ratio of 1:2:1.
2. Identify the phenotypes associated with each genotype. BB and Bb produce blue seeds (dominant phenotype), while bb produces white seeds (recessive phenotype). This results in a phenotypic ratio of 3 blue:1 white.
3. Calculate the probability of each seed being blue or white. The probability of a seed being blue is 3/4, and the probability of a seed being white is 1/4.
4. Use the binomial probability formula to calculate the frequencies of each outcome class (0, 1, 2, 3, or 4 blue seeds in a pod). The formula is P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k)), where n = 4 (number of seeds per pod), k = number of blue seeds, p = probability of a blue seed (3/4), and (1-p) = probability of a white seed (1/4).
5. Compute the frequencies for each outcome class: 0 blue seeds (all white), 1 blue seed, 2 blue seeds, 3 blue seeds, and 4 blue seeds. Substitute k = 0, 1, 2, 3, and 4 into the binomial formula to find the predicted frequencies for each class.

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 alleles mask the expression of recessive ones. In this case, the blue color (B) is dominant over the white color (b), which is crucial for predicting the offspring's phenotypes.

Punnett Square

A Punnett square is a diagram used to predict the genotypic and phenotypic outcomes of a genetic cross. By arranging the alleles of the parents along the top and side of a grid, one can visualize all possible combinations of alleles in the offspring. For the Bb x Bb cross, the Punnett square helps determine the expected ratios of blue and white seeds in the resulting pods.

Genotypic and Phenotypic Ratios

Genotypic ratios refer to the relative frequencies of different genotypes in the offspring, while phenotypic ratios refer to the observable traits. In the case of the Bb x Bb cross, the genotypic ratio is 1 BB : 2 Bb : 1 bb, leading to a phenotypic ratio of 3 blue (BB and Bb) to 1 white (bb). Understanding these ratios is essential for predicting the outcomes of genetic crosses.