Probability and Statistics

Biol. 240 Probability and Statistics Name_____________________
As a student of genetics, you become interested in the phenotype of feathered
legs in Black Langshan fowl and featherless legs found in Buff Rocks fowl. Your
first inclination is that this trait is controlled by a single gene - two allele
genetic system. To test this hypothesis you mate a true breeding Black Langshan
with a true breeding Buff Rocks, and all of the offspring develop feathered
legs. Reciprocal crosses yielded the same results.
1. Using the letter, F, outline the proposed genotypes in this mating.
After your first breeding experiment you become more convinced that you are
dealing with a single locus system with one allele showing complete dominance
over the other allele. Continuing the breeding study, you breed two of the F 1
birds.
2. Given your working hypothesis, what are the expected F 2 genotypes and
phenotypes in this cross?
Upon performing the F 1 cross, the F 2 generation consists of 10 individuals, all
of whom are feathered.
3. Given the genetic system proposed above, what is the probability that all 10
of the F 2 generation would be feathered? [HINT: What is the probability of a
single F 2 individual being feathered? …the probability of 2? …of 3? …of all
10?]

4. Which probability rule (Sum or Product?) did you use to answer this question?
You explain the lack of any featherless individuals in the F 2 generation as
"sampling error".
5. What is meant by the phrase "sampling error?" [HINT: read next sentence]
You increase your sample size by cross-mating several adults of the F 1
generation. The F 2 generation now consists of 348 individuals.
6. State your hypothesis for this experiment. (Given your working hypothesis,
what F 2 ratio do you expect?)
7. How many feathered and featherless individuals do you expect from this
sample?

After the F 2 generation matures, you find that it consists of 325 feathered
individuals and 23 featherless individuals.
8. Calculate the chi-square value for your hypothesis. Show all calculations.
9. Determine the degrees of freedom for this analysis.
10. What probability value does your chi-square value give you?
11. Does the analysis support or refute your hypothesis? Explain how this
decision was made.
12. Given that out of 348 F 2 individuals, 325 were feathered and 23 featherless,
can you propose (in prose, not a ratio yet) an alternative hypothesis? [If a
hypothesis with one gene, two alleles and complete dominance cannot explain
these results, propose a two-gene model that could produce these F 2 proportions
and yet still explain the F 1 results.]

13. What F 2 ratio does your new hypothesis predict?
14. Calculate the expected phenotypic values.
15. Calculate the chi-square value for your new hypothesis.
16. Determine the probability level for your hypothesis.
17. Does the analysis support or refute the hypothesis?
18. Even if the preceding analysis supports your hypothesis, it does not prove
your explanation is the correct one. Explain why?