Final answer:
The expected proportion of offspring with the dominant phenotype at all four loci in a tetrahybrid cross is 81/256. This result is calculated using the product rule, with the individual probability of each genotype (homozygous dominant or heterozygous) being 3/4. The ratios are derived from the laws of segregation and independent assortment.
Step-by-step explanation:
Calculating the Proportion of Dominant Phenotypes in a Tetrahybrid Cross
To determine the expected proportion of offspring with the dominant phenotype at all four loci in a tetrahybrid cross, we utilize genotypic proportions rather than phenotypic proportions. For each genotype, the probability of being homozygous dominant or heterozygous is 3/4, as both contribute to a dominant phenotype. Applying the product rule, the proportion of offspring that show the dominant phenotype at all loci (A, B, C, and D) is calculated as the product of their individual probabilities: 3/4 × 3/4 × 3/4 × 3/4, which equals 81/256. This demonstrates how the law of segregation and the law of independent assortment influence the genotypic makeup of offspring from a cross between two heterozygotes.
Understanding Genotypic and Phenotypic Ratios
A typical dihybrid cross will exhibit a phenotypic ratio of 9:3:3:1. This means, out of 16 potential combinations in the offspring, there would be 9 with the dominant phenotype for both traits, 3 with the dominant phenotype for one trait and the recessive for the other, and 1 with the recessive phenotype for both traits. When calculating the expected ratios using a Punnett square or the forked-line method, the genotypic ratios align with the expected phenotypic ratio, assuming a large enough sample size, which is essential to minimize experimental error and ensure repeatability.