Question

In flower beetles, pygmy (py) is recessive to normal size (py+), and red color (r) is recessive to brown (r+). A beetle heterozygous for these characteristics was test crossed to a beetle homozygous for pygmy and red. The following are progeny phenotypes from this testcross: py+ r+ 180 py+ r 22 py r+ 19 py r 191 Total 412.

Carry out a series of chi-square tests to determine if there is equal segregation of alleles at the py locus. What is the CORRECT chi-square value and how many degree(s) of freedom should be used in its interpretation?
a) Chi-square value = 3.84, degrees of freedom = 1
b) Chi-square value = 7.81, degrees of freedom = 3
c) Chi-square value = 5.99, degrees of freedom = 2
d) Chi-square value = 9.21, degrees of freedom = 4

Answer 1

The chi-square test is used to determine if there is equal segregation of alleles at the py locus. The calculated value is not among the provided options, which suggests a potential error not reflected in the options given. For the test cross data provided, the degrees of freedom should be 3.

Step-by-step explanation:

To determine if there is equal segregation of alleles at the py locus for the flower beetles described, a chi-square test is necessary. The observed progeny phenotypes from the testcross are 180 normal brown (py+ r+), 22 normal red (py+ r), 19 pygmy brown (py r+), and 191 pygmy red (py r) for a total of 412 progeny.

Under the hypothesis of equal segregation, we expect a 1:1:1:1 ratio among the progeny. This is because a beetle heterozygous for both traits (py+/py r+/r) is crossed with one that is homozygous recessive for both traits (py/py r/r). Each class, therefore, should have about 103 progeny (412/4). Using the chi-square formula Χ²= Σ [(observed - expected)² / expected], we calculate the chi-square value for the data:

Χ²= ((180-103)²/103) + ((22-103)²/103) + ((19-103)²/103) + ((191-103)²/103) = (5929/103) + (6561/103) + (7056/103) + (7776/103) = 57.37 + 63.69 + 68.5 + 75.5 = 265.06.

However, this calculated value does not match any of the provided options (a-d), suggesting that the student may have made an error in their calculations or in the distribution of the options. Moreover, the degrees of freedom (df) would be 3, because there are four categories of offspring and df = number of categories - 1.