In Drosophila pseudoobscura the alleles P and p determine re

In Drosophila pseudoobscura, the alleles P and p determine red versus pink eyes, and Na and na determine wide (wildtype) versus narrow wings. A dihybrid cross was carried out to produce flies homozygous for both p and na. The following phenotypes were obtained in the F_2 generation: red eyes, wide wings 583 red eyes, narrow wings 193 pink eyes, wide wings 168 pink eyes, narrow wings 56 Test these data for agreement with the 9: 3: 3: 1 ratio expected under the hypothesis that the two pairs of alleles undergo independent assortment.

Solution

To test these data we have to use Chi-square test.

Total number of progeny = 583+193+168+50 = 994

Expected number of progeny will be

Red wide = 9/16* 994 = 559

Red narrow 3/16*994 = 186

Pink Wide   3/16*994 = 186

Pink Narrow 1/16*994 = 62

Chi square = Summation of (observed -Expected)²/Expected

(583-559)²/559 + (193-186)²/186 + (168-186)²/168 + (50-62)²/62

(24)²/559 + (7)²/186 + (18)²/168 + (12)²/62

= 576/559 + 49/186 + 324/168 + 144/62

= 1.03 + 0.26 + 1.74 + 2.32

=5.35

We have four phenotypic class so degree of freedom will be 4-1 = 3

For 3 degree of freedom 5% critical value is 7.815

Our chi square value is less than the critical value so ou rhypothesis is correct