Question

In a species of plant, two genes control flower color. The red allele (R) is dominant to the white allele (r); the color producing allele (C) is dominant to the non color producing allele (c). You suspect that either an rr homozygote or a cc homozygote will produce white flowers. In other words, rr is epistatic to C, and cc is epistatic to R. to test your hypothesis, you allowed heterozygous plants (RrCc) to self fertilize and count the offspring. You obtained the following data:201 plants with red flowers and 144 with white flowers. Conduct a chi square analysis to see if your observed data are consistent with your hypothesis. How do I get the ratio? I know its 9:7 bc its on my textbook but Im not understanding how they got that number?

Answer 1

null hypothesis: functional copies of both R and C genes are required to produce red flowers

RrCc * RrCc

	RC	Rc	rC	rc
RC	RRCC( red flowers)	RRCc ( red flowers)	RrCC ( red flowers)	RrCc ( red flowers)
Rc	RRCc ( red flowers)	RRcc (white flowers)	RrCc ( red flowers)	Rrcc (white flowers)
rC	RrCC ( red flowers)	RrCc ( red flowers)	rrCC (white flowers)	rrCc (white flowers)
rc	RrCc ( red flowers)	Rrcc (white flowers)	rrCc (white flowers)	rrcc(white flowers)

the expected ratio is

red flowers: white flowers=9:7

the observed ratio is

red flowers : white flowers=201:144

total number of progenies= 345

from the punnet square there are 16 possibilities, 345/16=21.5625

now to simplify the ratio divide with 21.5625

red flowers: white flowers=201/21.5625:144/21.5625=9.3:6.67

phenotype	expected (E)	observed (O)	(E-O)^2/E
red flowers	9	9.3	0.01
white flowers	7	6.67	0.0156

chi-square value= sum of (O-E)^2/E=0.01+0.0156=0.0256

degrees of freedom= number of phenotypes-1=2-1=1

for df=1 and P<0.05 the critical value is 3.841

here the chi-square value is less than the critical value, so we accept the null hypothesis.

that is functional copies of both genes are required to produce red flowers.