In 1988, Horst Wilkens investigated blind cavefish, comparing them with members of a sibling species with normal vision that are found in a lake [Wilkens, H. (1988). Evol. Biol. 25:271–367]. We will call them cavefish and lakefish. Wilkens found that cavefish eyes are about seven times smaller than lakefish eyes. F₁ hybrids have eyes of intermediate size. These data, as well as the F₁ × F₁ cross and those from backcrosses (F₁ × cavefish and F₁ × lakefish), are depicted below. Examine Wilkens's results and respond to the following questions:
Wilkens examined about 1000 F₂ progeny and estimated that 6–7 genes are involved in determining eye size. Is the sample size adequate to justify this conclusion? Propose an experimental protocol to test the hypothesis.

Verified step by step guidance

1. Step 1: Understand the problem. The question is asking whether the sample size of 1000 F₂ progeny is adequate to justify the conclusion that 6–7 genes are involved in determining eye size in cavefish. Additionally, it asks for an experimental protocol to test this hypothesis.
2. Step 2: Recall the concept of polygenic inheritance. Traits controlled by multiple genes, such as eye size, often show continuous variation. The number of genes involved can be estimated using statistical methods, such as the number of phenotypic classes observed in the F₂ generation. The sample size must be large enough to detect these classes reliably.
3. Step 3: Evaluate the adequacy of the sample size. To justify the conclusion that 6–7 genes are involved, the sample size must be sufficient to distinguish between phenotypic classes. The formula for estimating the number of phenotypic classes is 2ⁿ, where n is the number of genes. For 6–7 genes, this would result in 64–128 phenotypic classes. A sample size of 1000 may be adequate if the phenotypic differences are distinct and measurable.
4. Step 4: Propose an experimental protocol. To test the hypothesis, perform a controlled cross between cavefish and lakefish to produce F₁ hybrids. Then, cross F₁ hybrids to produce F₂ progeny. Measure eye size in the F₂ generation and analyze the distribution of phenotypes. Use statistical methods, such as chi-square tests, to determine if the observed phenotypic distribution matches the expected distribution for 6–7 genes.
5. Step 5: Include additional controls and replicates. To ensure reliability, repeat the experiment with multiple independent crosses and measure eye size using standardized methods. Consider environmental factors that might influence eye size and control for these variables in the experimental design.

Key Concepts

Genetic Variation

Genetic variation refers to the differences in DNA sequences among individuals within a population. In the context of Wilkens's study, the variation in eye size between cavefish and lakefish suggests that multiple genes contribute to this trait. Understanding genetic variation is crucial for analyzing how traits are inherited and expressed, particularly in hybrid offspring.

Quantitative Trait Loci (QTL)

Quantitative Trait Loci (QTL) are regions of the genome that are associated with a quantitative trait, such as eye size. The identification of 6-7 genes influencing eye size in Wilkens's study implies that these genes may be located in specific QTLs. QTL mapping is a common method used to determine the genetic basis of complex traits, which is essential for validating the hypothesis regarding eye size inheritance.

Sample Size and Statistical Power

Sample size and statistical power are critical in experimental design, as they determine the reliability of the results. A larger sample size increases the likelihood of detecting true effects and reduces the impact of random variation. In Wilkens's study, examining about 1000 F₂ progeny provides a substantial sample size, which is generally adequate for estimating the number of genes involved in a trait, thus supporting the conclusion drawn from the data.