## 182 Practice Problems: Population Genetics

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1. Suppose 25 out of 750 students are redheads. What is frequency of redheads? If a random student is choosen, what is the probability they are a redhead?

2. Consider a locus with two alleles, A and a. If the frequency of AA is 0.25, what is the frequency of A under Hardy-Weinberg?

3. If the genotypes AA, Aa, and aa have frequencies 0.5, 0.25, and 0.25 (respectively), what are p = freq(A)? q = freq (a)? After a single generation of random mating, what is the expected frequency of AA? of Aa? of aa?

4. Consider a locus with 12 alleles, A1, A2, ... , A12. What is the frequency of allele A1 if we know that freq(A1A1) = 0.10, and that the frequency of all heterozygote genotypes containing A1 is 0.40. Under the assumption of Hardy-Weinberg, what is the expected frequency of A1A1? Of any heterozygote involving A1?

5. Assume Hardy-Weinberg and a locus with two alleles. If p = freq(A), what fraction of all copies of allele a. are found in heterozygotes?

6. Assume that A is completely dominant over a, with aa individuals displaying a disease while all others are normal. An individual of genotype is Aa is called a carrier as they appear normal, but can have offspring with the disease. (i) Under Hardy-Weinberg, if freq(a) = 0.001 what fraction of all copies of a are in carriers? (ii) What fraction of all aa individuals had both parents as carriers (i.e., neither parent displays the trait).

7. If the genotypes AA, Aa, and aa have fitnesses 1: 1.5: 1.6, what allele is fixed?

8. The genotype aa is lethal and yet the population has an equilibrium frequency for a of .40. If the fitness of Aa is 1, what is the fitness of the AA genotype?

9. Suppose a population starts out with 10,000 AA individuals, 20,000 Aa, and 10,000 aa. (i) What is the frequency of A? Is this population in Hardy-Weinberg? (ii) Suppose all aa individuals die before reproducing, while (on average) AA and Aa individuals leave the same number of offspring. What are the fitnesses of these three genotypes? (iii) Following selection, what fraction of the surviving adults are AA? Aa? aa? What is the frequency of a? (iv) If these surviving adults mate at random, what is the frequency of aa in the next generation (before selection acts).

Solutions