In Drosophila melanogaster, short wings are caused by an allele (Xs ) that is X linked and recessive to an allele for normal wings (X+ ). White eyes are caused by an allele (w) that is autosomal and recessive to an allele for gray eyes (w + ). A female fly that is homozygous for normal wings and gray eyes mates with a male fly that has short wings and white eyes. The F1 are intercrossed to produce the F2. What will the phenotypes and proportions of the F2 flies be from the cross?

([tex]X^+X^+w^+w^+[/tex], [tex]X^+X^+w^+w[/tex], [tex]X^+X^sw^+w^+[/tex], [tex]X^+X^sw^+w[/tex] , [tex]X^+X^+w^+w[/tex], [tex]X^+X^sw^+w[/tex] ) = female with normal wings and gray eyes = [tex]\frac{6}{16}[/tex]

([tex]X^+X^+ww[/tex] , [tex]X^+X^sww[/tex]) = female with normal wings and white eyes = [tex]\frac{2}{16}[/tex]

([tex]X^+Yw^+w^+[/tex], [tex]X^+Yw^+w[/tex] , [tex]X^+Yw^+w[/tex] ) = male with normal wings and gray eyes = [tex]\frac{3}{16}[/tex]

([tex]X^sYw^+w^+[/tex] , [tex]X^sYw^+w[/tex], [tex]X^sYw^+w[/tex] ) = male with short wings and gray eyes

= [tex]\frac{3}{16}[/tex]

([tex]X^+Yww[/tex] ) = male with normal wings and white eyes = [tex]\frac{1}{16}[/tex]

([tex]X^sYww[/tex]) = male with short wings and white eyes = [tex]\frac{1}{16}[/tex]

Explanation:

Let the allele for short wings = [tex]X^s[/tex]

Let the allele for normal wings = [tex]X^+[/tex]

Let the allele for white eye = [tex]w[/tex]

Let the allele for gray eye = [tex]w^+[/tex]

A female fly that is homozygous for normal wings and gray eyes mates with a male fly that has short wings and white eyes.

i.e

[tex]X^+X^+[/tex][tex]w^+w^+[/tex] [tex]*[/tex] [tex]X^sY[/tex][tex]ww[/tex]

[tex]X^+w^+[/tex] [tex]X^+w^+[/tex]

[tex]X^sw[/tex] [tex]X^+X^sw^+w[/tex] [tex]X^+X^sw^+w[/tex]

[tex]Yw[/tex] [tex]X^+Y w^+w[/tex] [tex]X^+Y w^+w[/tex]

The [tex]F_1[/tex] offspring are : [tex]X^+X^sw^+w[/tex] & [tex]X^+Y w^+w[/tex]

Now: if [tex]X^+X^sw^+w[/tex] self-crossed; we have the following gametes for the [tex]F_2[/tex] cross.

[tex]X^+w^+[/tex], [tex]X^+w[/tex], [tex]X^sw^+[/tex], [tex]X^sw[/tex]

On the other hand; if [tex]X^+Y w^+w[/tex] self-crossed; we have the following.

[tex]X^+w^+[/tex], [tex]X^+w[/tex], [tex]Yw^+[/tex] , [tex]Yw[/tex]

So the [tex]F_2[/tex] is shown below as follows:

[tex]X^+w^+[/tex] [tex]X^+w[/tex] [tex]X^sw^+[/tex] [tex]X^sw[/tex]

[tex]X^+w^+[/tex] [tex]X^+X^+w^+w^+[/tex] [tex]X^+X^+w^+w[/tex] [tex]X^+X^sw^+w^+[/tex] [tex]X^+X^sw^+w[/tex]

[tex]X^+w[/tex] [tex]X^+X^+w^+w[/tex] [tex]X^+X^+ww[/tex] [tex]X^+X^sw^+w[/tex] [tex]X^+X^sww[/tex]

[tex]Yw^+[/tex] [tex]X^+Yw^+w^+[/tex] [tex]X^+Yw^+w[/tex] [tex]X^sYw^+w^+[/tex] [tex]X^sYw^+w[/tex]

[tex]Yw[/tex] [tex]X^+Yw^+w[/tex] [tex]X^+Yww[/tex] [tex]X^sYw^+w[/tex] [tex]X^sYww[/tex]

The phenotypes and their proportions are: