In the fruit fly Drosophila melanogaster a spineless no wing

In the fruit fly, Drosophila melanogaster, a spineless (no wing bristles) female fly is mated to a male that is claret(dark eyes) and hairless (no thoracic bristles). Phenotypically wild-type F_1 female progeny were mate to fully homozygous (mutant) males, and the following progeny (1000 total) were observed: Which gene is in the middle?

Solution

Assuming genes for the phenotype spineless, claret, and hairless are linked and in a chromosome the middle gene will show strong linkage with both first and third gene and the linkage between the first and third gene will be in second order.

Clarlet, hairless frequency was highest (309) i.e. output of highest linkage/ closest in position/ they are consecutive. Clarlet, and spineless frequency is second highest (130) which also implies their strong linkage and consecutiveness. Hairless and spineless linkage is week as the frequency was observed at less frequency (12) than hairless, claret and spineless (32). Hence the order of genes is Hairless-Clarlet-Spineless or reverse and the gene in the middle is Clarlet.