Cracking the AP Biology Exam
Mendel’s laws can also extend to the population level. Suppose you caught a bunch of fruit flies—about 1,000. Let’s say that 910 of them were red-eyed and 90 were green-eyed. If you allowed the fruit flies to mate and counted the next generation, we’d see that the ratio of red-eyed to green-eyed fruit flies would remain the same: 91 percent red-eyed and 9 percent green-eyed. That is, the allele frequency would remain constant. At first glance you may ask, how could that happen?
The Hardy-Weinberg law states that even with all the shuffling of genes that goes on, the relative frequencies of genotypes in a population still prevail over time. The alleles don’t get lost in the shuffle. The dominant gene doesn’t become more prevalent, and the recessive gene doesn’t disappear.
Let’s say that the allele for red eyes, R, is dominant over the allele for green eyes, r. Red-eyed fruit flies include homozygous dominants, RR, and heterozygous, Rr. The green-eyed fruit flies are recessive, rr.
The frequency of each allele is described in the equation below. The allele must be either R or r. Let “p” represent the frequency of the R allele and “q” represent the frequency of the other allele in the population.
p + q = 1
This sum of the frequencies must add up to one. If you know the value of one of the alleles, then you’ll also know the value of the other allele.
We can also determine the frequency of the genotypes in a population using another equation:
p2 + 2pq + q2 = 1
In this equation, p2 represents the homozygous dominants, 2pq represents the heterozygotes and q2 represents the homozygous recessives.
So how do we use these equations? Use the proportions in the population to figure out both the allele and genotype frequencies. Let’s calculate the frequency of the genotype for green-eyed fruit flies. If 9 percent of the fruit flies are green-eyed, then the genotype frequency, q2, is 0.09. You can now use this value to figure out the frequency of the recessive allele in the population. The allele frequency for green eyes is equal to the square root of 0.09—that’s 0.3. If the recessive allele is 0.3, the dominant allele must be 0.7. That’s because 0.3 + 0.7 equals 1.
Using the second equation, you can calculate the genotypes of the homozygous dominants and the heterozygotes. The frequency for the homozygous dominants, p2, is 0.7 × 0.7, which equals 0.49. The frequency for the heterozygotes, 2pq, is 2 × 0.3 × 0.7, which equals 0.42. If you include the frequency of the recessive genotype—0.09—the numbers once again add up to 1.
The Hardy-Weinberg law says that a population will be in genetic equilibrium only if it meets these five conditions: 1) a large population, 2) no mutations, 3) no immigration or emigration, 4) random mating, and 5) no natural selection.
Violations of the Hardy-Weinberg Law
When these five conditions are met, the gene pool in a population is pretty stable. Any departure from them results in changes in allele frequencies in a population. For example, if a small group of your fruit flies moved to a new location, the allele frequency may be altered and result in evolutionary changes. That’s an example of genetic drift called the founder effect. In other words, the gene frequency may differ from the original gene pool. Genetic drift often occurs in new colonies.