Answer to Question #108918 in Genetics for David

Question

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

Answer 1

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:

X² = (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 X² = 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.