In a cross between a strain of large guinea pigs and a strain of small guinea pigs, the F₁ are phenotypically uniform, with an average size about intermediate between that of the two parental strains. Among 1014 F₂ individuals, 3 are about the same size as the small parental strain and 5 are about the same size as the large parental strain. How many gene pairs are involved in the inheritance of size in these strains of guinea pigs?

Verified step by step guidance

1. span>Step 1: Understand the problem context. We are dealing with a quantitative trait, guinea pig size, which shows continuous variation and is likely controlled by multiple genes (polygenic inheritance).</span
2. span>Step 2: Recognize that the F₁ generation being intermediate suggests incomplete dominance or additive effects of alleles from multiple genes.</span
3. span>Step 3: Use the formula for polygenic inheritance: \( (1/4)^n \), where \( n \) is the number of gene pairs, to determine the proportion of F₂ individuals that resemble the parental strains.</span
4. span>Step 4: Calculate the observed proportion of F₂ individuals resembling each parental strain: \( \frac{3 + 5}{1014} \).</span
5. span>Step 5: Set the observed proportion equal to \( 2 \times (1/4)^n \) (since both extremes are considered) and solve for \( n \) to find the number of gene pairs involved.</span

Key Concepts

Mendelian Inheritance

Mendelian inheritance refers to the principles of heredity established by Gregor Mendel, which include the concepts of dominant and recessive traits. In this case, the size of guinea pigs is likely influenced by alleles that follow Mendelian ratios, where dominant alleles mask the expression of recessive ones. Understanding these principles helps in predicting the phenotypic ratios in offspring based on parental genotypes.

Phenotypic Ratio

The phenotypic ratio is the ratio of different phenotypes in the offspring resulting from a genetic cross. In this scenario, the F₁ generation shows an intermediate phenotype, suggesting incomplete dominance. The F₂ generation's phenotypic distribution can be analyzed to determine the number of gene pairs involved, as the observed ratios can indicate whether one or multiple gene pairs contribute to the trait.

Gene Pairs and Polygenic Inheritance

Polygenic inheritance involves multiple gene pairs contributing to a single trait, resulting in a continuous range of phenotypes. In the case of the guinea pigs, the presence of both small and large individuals in the F₂ generation suggests that more than one gene pair is influencing size. By analyzing the phenotypic ratios, one can infer the number of gene pairs involved in the inheritance of size, which is crucial for understanding complex traits.