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Answer:
Parents: pr vg x pr+ vg+
pr vg pr+ vg+
F1: pr vg
pr+ vg+
F1 backcross: pr vg male x pr vg female
pr+ vg+ pr vg
Expect in F2: male gametes:
pr vg pr vg+ pr+ vg pr+ vg+
_________________________________________
female gametes pr vg | pr pr vgvg pr pr vg+vg pr+pr vgvg pr+pr vg+vg
This predicts four different phenotypes, purple vestigial, purple long-winged, red-eyed vestigial, and red-eyed long-winged, in equal numbers (each comprising 0.25 of the progeny).
b) The actual results were markedly different. In fact none of the recombinant phenotypes, purple long-winged and red-eyed vestigial, were observed. This indicates that the purple and vestigial genes are linked. Subsequent mapping showed that they are both in the second linkage group (Drosophila has four linkage groups, corresponding to three autosomes and one pair of sex chromosomes). Note that no measurable recombination occurred between the purple and vestigial genes in this backcross; this is a peculiarity of male Drosophila and the heterogametic sex in some other species. Other experiments with heterozygous F1 females do show recombination (see part 1c).
Let's re-examine the predictions of the matings, now that it is clear that the genes are linked. In the notation below, a horizontal line with more than one gene above and below it means that the genes are linked. Again, alleles for one homologous chromosome are above the line, and those for the other chromosome are below it.
Parents: pr vg x pr+ vg+
pr vg pr+ vg+
F1: pr vg
pr+ vg+
F1 backcross: pr vg male x pr vg female
pr+ vg+ pr vg
Expect in F2: male gametes:
pr vg pr+ vg+
_____________________
female gametes pr vg | pr vg pr+ vg+
pr vg pr vg
Thus in the absence of recombination, one obtains equal numbers of purple vestigial and red-eyed long-winged flies in the progeny.
c) In this case, the mating is
F1 backcross: pr vg female x pr vg male
pr+ vg+ pr vg
and recombination does occur (as mentioned in 1.1b, the absence of recombination is peculiar to male Drosophila). Note that the frequency of recombinant types is much less than the 50% predicted for no linkage (see 1.1a). The purple long-winged flies have the genotype
pr vg+
pr vg
and red-eyed vestigial flies have the genotype
pr + vg
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