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 progeny phenotypes from this testcross are shown below.
py+ r+ 180
py+ r 22
py r+ 19
py r 191
Total 412
What is the frequency of recombination between these two genes?
Carry out a series of chi-square tests to determine if these genes are assorting independently. What does your chi-square value and associated probability indicate about whether these genes are linked?
The frequency of recombination is calculated by (recombinant/total) ×100
{(22+19) /412}×100=9.95 centiMorgan.
Hence the recombination frequency between two genes is 9.95%
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Null hypothesis: Two genes are assorted independently.
Then the expected number of each individual is (1/4) ×412=103
Please look in the image for chi square test:

Hence these two genes are not assorted independently.
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In flower beetles, pygmy (py) is recessive to normal size (py+), and red color (r) is...