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# Answer to Question #108940 in Genetics for Lannah

Question #108940
using true breeding dogs the lansing lab breeders have produced 922 black.long bair labradors and 282 white long haired labs is the coat color inherited in a mendelian fashion
1
2020-04-22T07:44:26-0400

Chi-square equation can be used to estimate if the color is inherited with a Mendelian fashion:

X2 = [(Oblack - Eblack)2 / Eblack]+ [(Owhite - Ewhite)2 / Ewhite]

where O - number of observed phenotypes, E - number of expected phenotypes.

For the calculation, the number of offspring with specific phenotypes must be evaluated.

Assuming that B is a black allele and W is a white allele, the genotypes of parental dogs used for true breeding are BB (black) and WW(white).

The possible offspring are:

parents: BB (black) × WW (white)

offspring: BB (black), 2BW (black) and WW (white).

The expected phenotypic ratio of the offspring is:

3 black : 1 white.

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

903 black : 301 white

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

922 black : 282 white

Using chi-square equation, X2 is calculated:

X2 = [(922 - 903)2 / 903] + [(282 - 301)2 / 301] = 0.4 + 1.2 = 1.6

The number of degrees of freedom (df) equals 2 -1 = 1, due to the presence of two phenotypic classes.

From the X2 table, p-value = 0.2.

As 0.2 > 0.05, there is no difference between the expected and observed numbers of dogs. As a result, the coat color is inherited in a Mendelian fashion.

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