Question #108918

using true-breeding dogs, the Lansing Lab breeders have produced 922 black (B) long haired Labrador retrievers and 282 white (b) long-haired labs. Is the coat color inherited in a Mendelian fashion? Support your answer with chi-square analysis by filing out a table

Expert's answer

True-breeding is observed when parents pass certain phenotypic traits to offspring and are homozygous for every trait. As *B* is black and *b* is white, the genotypes of parental dogs should be *BB* and *bb*. According to Mendelian laws, the possible offspring are:

Parents: *BB* (black) × *bb* (white)--> offspring: *BB* (black), *2Bb* (black) and *bb* (white).

In this case, the expected phenotypic ratio of the offspring is:

3 black : 1 white.

As the total number of produced dogs is 1204, the expected phenotypic ratio is:

903 black : 301 white

In the breedin example, the observed phenotypic ratio of the offspring:

922 black : 282 white

According to chi-square equation:

*X*^{2} = (observed_{black} - expected_{black})^{2} / expected_{black} + (observed_{white} - expected_{white})^{2} / expected_{white} = (922 - 903)^{2} / 903 + (282 - 301)^{2} / 301 = 0.4 + 1.2 = 1.6

As there are two phenotypic classes, the number of degrees of freedom (df) equals 2 -1 = 1.

As *X*^{2} = 1.6 and df = 1, *p*-value = 0.2

As 0.2 > 0.05, the null hypothesis is accepted. As a result, there is no difference between the expected and observed numbers of produced dogs. Therefore, the coat color in long-haired labs is inherited in a Mendelian fashion.

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