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. Recognize that the problem describes incomplete dominance or additive gene action, where the F₁ phenotype is intermediate between the two parental phenotypes, and the F₂ shows a range of phenotypes including parental types and intermediates.
2. Identify that the number of gene pairs (n) involved can be estimated by analyzing the proportion of F₂ individuals that resemble the parental phenotypes, which correspond to the homozygous genotypes at all loci.
3. Recall that for n gene pairs with additive effects, the proportion of F₂ individuals showing the parental phenotype is given by the formula \(\left(\frac{1}{4}\right)^n\) for each parental type, because each gene pair segregates independently and the parental phenotype requires homozygosity at all loci.
4. Calculate the observed frequency of each parental phenotype in the F₂ generation by dividing the number of individuals with that phenotype by the total number of F₂ individuals (e.g., for the small phenotype, frequency = \(\frac{3}{1014}\)).
5. Set up the equation \(\left(\frac{1}{4}\right)^n = \text{observed frequency}\) and solve for n by taking the logarithm of both sides: \(n = \frac{\log(\text{observed frequency})}{\log(\frac{1}{4})}\). This will give the number of gene pairs involved.

Key Concepts

Incomplete Dominance and Intermediate Phenotypes

Incomplete dominance occurs when the heterozygote phenotype is intermediate between the two homozygotes, as seen in the F₁ guinea pigs with sizes between large and small parents. This suggests that neither allele is completely dominant, resulting in blending traits rather than a dominant-recessive pattern.

Polygenic Inheritance

Polygenic inheritance involves multiple gene pairs contributing additively to a single trait, such as size. The continuous variation and intermediate phenotypes in the F₂ generation indicate that size is controlled by several genes, each with small effects, rather than a single gene.

Segregation Ratios and Estimating Number of Gene Pairs

The number of gene pairs can be estimated by analyzing the frequency of parental phenotypes in the F₂ generation. The proportion of individuals resembling parental extremes follows a (1/4)^n pattern, where n is the number of gene pairs, allowing calculation of n from observed counts of extreme phenotypes.