# Population Genetics

### Contents

#### Problems

Problem : In a given plant population, the gene that determines height has two alleles, H and h. In one generation, H has a frequency of p=0.8 and h has a frequency of q=0.2. in the next generation, p=0.7 and q=0.3. Is this population in Hardy- Weinberg equilibrium? Why or why not?

This population is not in Hardy-Weinberg equilibrium because the allelic frequencies of H and h change from one generation to the next.

Problem : In a population of giraffes, the gene that determines neck length has two alleles, N for longer necks and n for shorter necks. Only giraffes with two N alleles will have long necks. In one generation, the frequency of N is p=0.4 and the frequency of n is q=0.6. This generation experiences a large forest fire that kills all low-growing plants, leaving tall trees with high branches as the only food source. In the next generation, 49% of giraffes have long necks. How much has selection contributed to the allele frequencies in the second generation?

The Hardy-Weinberg equation for a two-allele system is (p + q)^2 = 1 or p^2 +2pq +q^2 = 1. The frequency of giraffes with two N alleles is determined by p^2. In the first generation, this is (0.4)^2 = .16 or 16%. Since 49% of giraffes in the second generation have two N alleles, selection has increased the frequency of N in the population. Working backwards we find that 49% = 0.49 = p^2, so p = 0.7 in the second generation. Selection has caused the frequency of N to change from 0.4 to 0.7 in one generation.

Problem : In a population of giraffes, the gene that determines spot size has two alleles, S for larger spots and s for smaller spots. Giraffes with one of each allele have medium-sized spots. In one generation, the frequency of S is p=0.4 and the frequency of s is q=0.6. Since spots help the giraffes blend in with their surroundings, they are acted upon by natural selection. In the next generation, 64% of giraffes have small spots. What percentage of giraffes in the second generation will have medium spots? Large spots?

The Hardy-Weinberg equation for a two-allele system is (p + q)^2 = 1 or p^2 +2pq +q^2 = 1. The frequency of giraffes with twos alleles is determined by q^2. From the problem, we see that q^2 is 64% or 0.64. From this we find that the frequency of s in the second generation is q=0.8. Using the original equation, we plug in this value of q and solve for p, which we find is 0.2. The frequency of giraffes with large spots is p^2 = 0.04 or 4%. The frequency of giraffes with medium spots is 2pq = 0.32 or 32%.