Population Genetics Problems and Exercises

1. Assume a single di-allelic locus following Mendelian genetics in a species of invasive Drosophila, where T=dominant long wings, and t=recessive short wing. In the recently invaded region there are two parental genotypes: Tt and tt. Over the life span of the second-generation (F1), there is a third genotype introduced TT, which mates with all of the F1 offspring. What is the expected proportion of TT, tt and Tt that you would obtain from all possible combination in the third generation (F2)? (Hint: account for all 16 possible genotypes in F2)

2. If the parents are TT and tt, what percentage of the offspring (F1) will have long wings, given that the trait is completely dominant? If any of the F1 mates with a heterozygote, what would be the proportion of short wings in F2?

3. Suppose that a random sample of 400 individuals pulled from different populations of blue mussels include the following genotype configuration: FF=185 individuals, FS=150 and SS=65. Estimate the allele frequency p and q. assuming random combinations of alleles in the genotype; what are the expected numbers of the three genotypes? Do the observed numbers fit the expected?

4. You have sampled a mesquite population in which you know that the percentage of the homozygous recessive genotype (rr) for an allopathic trait is 29%. Using that 29%, calculate the following:

a. The frequency of the "rr" genotype.

b. The frequency of the "r" allele (Remember that rr=q2,therefor r=q).

c. The frequency of the "R" allele.

d. The expected frequencies of the genotypes "RR" and "Rr."

e. In a population of 100, what is the expected number of individuals that should not have the allopathic genotype, given that “R” is completely dominant and only the “r” allele confers the trait?

5. A new wave of Aedes mosquitos is invading the South East of United States, and re-introducing previously eradicated malaria strains into the population. This is prompting public health researchers to look at the current immunity of the human population by quantifying the percentage of people with Sickle-cell anemia. Sickle-cell anemia is a blood disease where normal homozygous individuals (SS) have normal blood cells that are easily infected with the malarial parasite. Individuals homozygous for the sickle-cell trait (ss) have red blood cells that readily collapse when deoxygenated. Although malaria cannot grow in these red blood cells, individuals often die because of the genetic defect. However, individuals with the heterozygous condition (Ss) have some sickling of red blood cells, that are not enough to cause the genetic disease but enough to provide immunity to malaria. Thus, heterozygotes tend to survive better than either of the homozygous conditions. If 1.8% of an American population is born with a severe form of sickle-cell anemia (ss), what percentage of the population is expected to be more resistant to malaria because they are heterozygous (Ss) for the sickle-cell gene?

6. Within gypsy moth populations the color brown (B) is completely dominant over the color white (b). Researchers found that in the founding populations of gypsy moth 75% are brown; however, in sampled invasive populations 40% of all moths are white. Given these information,

a. Calculate the percentage of moths in the founding population that are heterozygous.

b. Calculate the percentage of moths in the invasive population that are heterozygous.

c. What can you interpret from the difference in heterozygosity?

7. Recently geneticists have found that the white (b) allele is linked to a trait that confers gipsy moth the ability to withstand colder weather while overwintering as a larvae. Assume that the 75% brown moths come from a sample size of 1000 individuals of the founding population and 40% are heterozygote. Assume 40% white moths come from 500 individuals from the invasive population in higher latitudes, and 60% of all the population is heterozygote.

a. What number of the populations is expected to be white in the founder vs. the invasive population?

b. Calculate the global Fst between the two populations, and give an interpretation of the value and its ecological significance.

8. Imagine there is a single, self-pollinating plant that germinates in a barren island. The plant is heterozygous (Aa), and will reproduce and die before its offspring germinate. What is the probability that either gene will become fixated in the second generation? Do you think fixation of either gene can ever occur if the population is ever growing? (Hint: self-pollinating implies that it is mating with its own genotype). 