Question

In the California poppy, an allele for yellow flowers (C) is dominant over an allele for white flowers (c).At an independently assorting locus, an allele for entire petals (F) is dominant over an allele for fringed petals (f). A plant that is homozygous for yellow and entire petals is crossed with a plant that is white and fringed. The F1 progeny were then testcrossed and the following progeny were produced: 54 yellow and entire, 58 yellow and fringed, 53 white and entire, and 10 white and fringed. Use a chi-square test to compare the observed numbers with those expected for the cross. Please feel free to use the chi-squared equation and the chi-squared distribution table.

What is the p-value for this cross?

What are the degrees of freedom for this cross?

Answer 1

In the question it is mentioned that C allele coding for Yellow colour is dominant over c allele coding for purple colour of the California poppy. Also F allele coding for entire petals is dominant over f allele coding for fringed petals.

In the first cross, a plant homozygous for yellow and entire petals is crossed with a plant that is white and fringed.

Homozygous means the genotype of the individual is composed of the same alleles. So homozygous for yellow and entire petals means the genotype must be CCFF. Similarly the genotype of the other homozygous parent must be ccff. (Please refer the first image below)

When the above parents are crossed, they produce all heterozygous CcFf F1 offspring. Heterozygous means the genotype consists of more than one allele and is a mixture of alleles.

In the second cross, the  F1 offspring is test- crossed. Test cross refers to a type of cross where an individual is crossed with a homozygous recessive individual. Homozgyous recessive means that the genotype of the individual is composed of only recessive alleles of the genes. Here the recessive allele for colour is c and recessive allele for petal type is f. So the homozgyous recessive individual has the genotype ccff. Now the CcFf  F1​​​​​​​ offspring is crossed with this ccff individual to obtain F2 offspring. (Please refer the First image below).

Chi-square test is a statistical test for independence which checks if the two variables are related to each other or not. Here Chi-square test is used to see if the alleles assort independently or are linked to each other. (Please refer images 2 and 3)

Degree of freedom is the number of factors which can affect the Chi-square value. Here the number of phenotypic classes i.e. 4 can affect the Chi-square value. Thus the degree of freedom = 4 - 1 = 3 (Refer 4th image for explanation).

After calculating the Chi-square value we compare it with the value given in the Chi-square table to see if the difference between observed and expected numbers is significant at 0.05 level of significance.

Here we observe that the calculated Chi-square value of 35.03 is very higher than the value of Chi-square at degree of freedom = 3 , at 0.05 level of significance i.e. 7.815.

Since the calculated value is higher, we can say that the difference in the observed and expected numbers is stastically significant. Thus the alleles are not independently assorting according to Law of Independent Assortment which states the alleles of two or more genes segregate independent of each other and assort in gametes independently.