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

Expert's answer

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

*X*^{2} = [(O_{black} - E_{black})^{2} / E_{black}]+ [(O_{white} - E_{white})^{2} / E_{white}]

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, *X*^{2} is calculated:

*X*^{2} = [(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 *X*^{2} 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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