A collector of fancy mice develops a new variety with a spotted coat, and wishes

Question

A collector of fancy mice develops a new variety with a spotted coat, and wishes to determine the genetics of this new phenotype. Initial experiments show that the spotted coat phenotype is recessive to a solid coat. The collector tests the hypothesis that this phenotype is caused by a single gene. They perform a series of crosses between two fully heterozygous parents, and count 56 solid mice and 4 spotted mice. On a separate page, show the 2 analysis of this hypothesis. Also, come up with another hypothesis that better explains this data.

Explanation / Answer

Solid coat = Dominant = SS or Ss
Spotted coat = Recessive = ss

Parental cross = Ss X Ss
Progeny = SS Ss Ss ss
Expected frequency of ss progeny = 1/4

Total progeny = 60
Observed ss progeny = 4
Expected progeny = 60/4 = 15

Chi2 = (O-E)^2/E
= (4-15)^2/15
= 8.06

Degrees of freedom = 2-1 = 1
Since the chi2 value is beyond significant. So, the given hypothesis that it is a monogenic trait is wrong.

Alternative hypothesis:
Coat color could be due to two genes.
In such cases, 1 out of 16 individuals shows recessive phenotype.

Observed ss progeny = 4
Expected progeny = 60/16 = 3.75

Chi2 = (O-E)^2/E
= (4-3.75)^2/3.75
= 0.016

Degrees of freedom = 2-1 = 1
Since the chi2 value is highly significant. So, the given hypothesis that the given trait is governed by two different genes is correct.

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