In: Biology
In carrying out crosses with the nematode Caenorhabditis elegans, a geneticist hypothesizes that the allele for dumpy body shape (dpy) is recessive to the allele for normal body (dpy+), and the allele for uncoordinated (unc) is recessive to the coordinated body movement allele (unc+). Moreover, she hypothesizes that these two genes are unlinked (i.e., they assort independently). In a mating between a normal bodied, coordinated worm and a dumpy, uncoordinated worm, all of the F1 worms were normal bodied and coordinated in their movements. Selfing these F1's (it should be noted here that C. elegans are capable of self- fertilization) yielded an F2 generation with the following phenotypes:
o normal body, coordinated 95
o normal body, uncoordinated 21
o dumpy body, coordinated 19
o dumpy body, uncoordinated 25
TOTAL 160
a. What is the expected ratio and number of each class of F2 worms for this cross?
b. Determine the Chi-square (X2) value for the observed data under the proposed hypothesis.
c. What is the probability value for this Chi-square value?
d. Do these data support the hypothesis that these loci are unlinked? Explain.
Answer:
Based on the given information:
dominant | recessive | ||
normal body | dpy+ | dpy | dumpy body |
coordinated body movement | unc+ | unc | uncoordinated body movement |
F1: dpy+ unc+ x dpy unc
Progeny are all: dpy+ dpy unc+ unc
F2 Self cross: dpy+ dpy unc+ unc x dpy+ dpy unc+ unc
Punnett Square for F2 cross:
dpy+ unc+ | dpy+ unc | dpy unc+ | dpy unc | |
dpy+ unc+ | dpy+ dpy+ unc+ unc+ | dpy+ dpy+ unc+ unc | dpy+ dpy unc+ unc+ | dpy+ dpy unc+ unc |
dpy+ unc | dpy+ dpy+ unc+ unc | dpy+ dpy+ unc unc | dpy+ dpy unc+ unc | dpy+ dpy unc unc |
dpy unc+ | dpy+ dpy unc+ unc+ | dpy+ dpy unc+ unc | dpy dpy unc+ unc+ | dpy dpy unc+ unc |
dpy unc | dpy+ dpy unc+ unc | dpy+ dpy unc unc | dpy dpy unc+ unc | dpy dpy unc unc |
Phenotype:
normal coordinated | normal coordinated | normal coordinated | normal coordinated |
normal coordinated | normal, uncoordinated | normal coordinated | normal, uncoordinated |
normal coordinated | normal coordinated | dumpy coordinated | dumpy coordinated |
normal coordinated | normal, uncoordinated | dumpy coordinated | dumpy uncoordinated |
Phenotype | Frequency |
normal body, coordinated movement | 9 |
normal body, uncoordinated movement | 3 |
dumpy body, coordinated movement | 3 |
dumpy body, uncoordinated movement | 1 |
Phenotypic ratio 9:3:3:1
Chi Square Test:
Phenotype | Observed Frequency (O) | Expected Frequency ('E) | (O-E) | (O-E)^2/E |
normal body, coordinated movement | 95 | 90 | 5 | 0.278 |
normal body, uncoordinated movement | 21 | 30 | -9 | 2.700 |
dumpy body, coordinated movement | 19 | 30 | -11 | 4.033 |
dumpy body, uncoordinated movement | 25 | 10 | 15 | 22.500 |
Total | 160 | 160 | Chi Square (sum) | 29.511 |
Degree of freedom = number of categories - 1 = 4 - 1 = 3
P-Value corresponding to Chi square value of 29.511 with 3 degree of freedom is P-Value is < 0.00001.
The result is significant at a significance level of 0.05. Therefore Null Hypothesis is rejected. Based on the evidence, there is significant difference in observed frequency from expected frequency.