Question

Wild populations of mice typically have gray-brown (agouti) fur and some laboratory strains have yellow fur. A single yellow male mated to several wild type (agouti) females. Altogether, the mating produced 40 progeny, 22 with agouti fur and 18 with yellow fur. The agouti F1 mice were intercrossed with each other and produced all agouti mice in the F2. Similarly, the yellow F1 animals were intercrossed with each other, but their F2 progeny segregated into two classes: 30 were agouti and 54 were yellow. What is the inheritance pattern of coat color in these mice? Use χ2 to test if the phenotypes in the F2 fit the expected Mendelian ratio.

Answer 1

Inheritance pattern in organisms follow mostly Mendelian principles. The three Mendelian principles are Law of Dominance, Law of Segregation and Law of Independent Assortment.

Law of Dominance states that out of a pair of contrasting characters only one can express itself and the other remans suppressed.

Law of Segregation: The two members out of a pair of factors separate during the formation of gametes.

Law of Independent Assortment: In case of two pairs of characters, the distribution of alleles in one character into the gametes is independent of the distribution of the allele of the other character of the gametes.

Let the wild type gray brown (agouti) fur be yy.

In the F1 generation, the offspring are almost 50% yellow and 50% agouti. This means that there is a presence of heterozygous genotype in the parent. Since, wild type is homozygous, therefore, the laboratory strain will be heterozygous.

Therefore, the genotype for yellow fur is Yy.

In the F2 generation, agouti F1 mice were intercrossed with each other and produced all agouti mice.

Again, F1 yellow mice were intercrossed and give the following results in the F2 generation.

Here, the number of progenies were segregated as 30 agouti and 54 yellow.

We expected that the ratio of the F2 generation would be 3:1. But as the results, the observed ratio is not aligned with expected ratio. This is because the inheritance pattern of this kind is due to the presence of lethal allele. Here, Y when present in homozygous condition promotes the synthesis of a protein that is lethal for the organism and it disappears the progeny from the population, which is why we get only 2:1 ratio in F2 generation.

Observed Ratio:

Yellow =

=

Agouti =

=

Expected Ratio:

Yellow =

=

Agouti =

= 21

χ² =

χ² for yellow =

χ² for agouti =

χ² = = 5.13

Degree of freedom is the number of ways in which the observed classes are free to vary i.e. the number of phenotypes minus unity.

Degree of freedom = 2-1=1

Now, looking at the values in the chart for χ² we get,

6.635 > χ² > 5.024

Which corresponds to 0.025> χ² >0.01

This means, there is less than 2.5% probability that the given deviation in observation and expectation is by chance.

Therefore, there is a significant difference between observed and expected values and this deviation is not by chance.