Final answer:
A three-factor cross in Drosophila genetics starts with crossing true-breeding lines differing in three gene loci. The F2 generation's genotype ratios are examined using a linkage map, and a forked-line diagram can be constructed to visualize and calculate the probabilities of different genotypic combinations based on the principle of independent assortment.
Step-by-step explanation:
The first step in using a three-factor cross to map genes is to cross two true-breeding lines of flies that differ with regard to alleles at three gene loci. For example, a cross might be made with true-breeding AABB flies and true-breeding aabb flies. The resulting F1 generation would then be crossed again, perhaps with true-breeding aabb flies, to examine the F2 generation genotype ratios based on the linkage map.
When constructing a forked-line diagram for a cross between F1 heterozygotes resulting from a cross between true-breeding AABBCC and aabbcc parents, we create rows equal to the number of genes being considered. Alleles are segregated in each row on forked lines according to the probabilities for individual monohybrid crosses. The probabilities along each forked path are multiplied to obtain the F2 offspring probabilities, following the product rule for independent assortment. For a trihybrid cross, the F2 phenotypic ratio is 27:9:9:9:3:3:3:1.
In the context of Drosophila melanogaster, when a true-breeding wild-type male is crossed with a true-breeding female with black body and cinnabar eyes, and all of the F1 progeny display a wild-type phenotype, we infer that the wild-type alleles are dominant over those for black body and cinnabar eyes.
If we consider another example where Drosophila are true-breeding for straight wings (S) and red eyes (R) and are crossed with flies true-breeding for curved wings (s) and brown eyes (r), a test cross could be performed between the F1 offspring and the true-breeding ssrr flies to further investigate genetic relationships.