Answer to Question #108940 in Genetics for Lannah

Question

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

Answer 1

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

X² = [(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, 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.