Population Genetics
Key Principles
Population genetics is the study of genetic variation and evolutionary forces in breeding populations (aka, microevolution).
Population geneticists are interested in the genetic structure, i.e., the allele and genotype frequencies, over generations.
The Hardy-Weinberg equation is widely used to calculate all possible allele combinations in a generation, based upon the genotypes of the previous generation;
- The full Hardy-Weinberg equation is p2 + 2pq + q2 = 1; where p and q refer to the two alleles followed over time.
- The equation predicts that there will be no changes in genetic structure in a non-evolving population; in other words, as long as there are no mutations, selection forces, genetic drift or flow, and mating is truly random, parental and offspring generations will have the same allele and genotype frequencies.
- The Hardy-Weinberg equation is a null hypothesis: if its predictions do not hold true, then we know that the genetic structure of the population is, in fact, evolving.
- Equations only apply to genes that with two alleles that produce three phenotypes; more advanced versions must be used if there are more than two alleles.
Example population data set:
- 98 pink-feathered birds with the AA genotype
- 84 purple birds with the AB genotype
- 18 blue birds with the BB genotype
With this information, we can calculate the total number of alleles, the number of A alleles, and, the number of B alleles.
- Because each bird contributes 2 alleles to the gene pool, double the number of birds to get the total number of alleles:
- 196 alleles from the pink birds, 168 from the purple birds, and, 36 from the blue birds, for a total of 400 alleles.
- Calculate how many of these alleles are of the A variety:
- By definition, each of the 98 AA genotype birds contributes two A alleles, so, 196
- Each of the 84 AB genotype birds contributes one A allele
- None of the 18 BB genotype birds contribute A alleles
- Total of 280 A alleles in the gene pool.
- Calculate how many alleles of the B variety:
- AA birds contribute 0 B alleles
- AB birds contribute 84
- BB birds contribute 36
- Total of 120 B alleles in the gene pool.
Calculate the observed allele and genotype frequencies in our population.
Allele frequencies describe the proportions of each allele in the gene pool.
- Mathematically: the allele frequency is equal to the number of its copies in the population divided by the sum of all alleles in the population.
Re-call our earlier equation, p + q = 1, which simply states that, if there are two alleles, their proportions must sum to 1
- Set p equal to the A allele frequency
- Set q equal to the B allele frequency
- Solve:
- The frequency of the A allele is 280/400; 0.7
- The frequency of the B allele is 120/400; 0.3
- The proportions sum to 1.
- Recognize that, even if we'd only had counts for one of the alleles, we could still determine both alleles' frequencies: if p + q = 1, then p = 1 – q.
Calculate the genotype frequencies
Genotype frequencies describe the proportions of each genotype in the population.
- Mathematically: the number of individuals with a genotype divided by the total number of individuals.
- Frequency of the AA genotype is 98 divided by 200; 0.49
- Frequency of the AB genotype is 84 divided by 200; 0.42
- Frequency of the BB genotype is 18 divided by 200; 0.09
- The sum of these proportions is equal to 1.
Use the Hardy-Weinberg equation
Show that, in the absence of evolutionary forces, the genotype frequencies of the next generation will be the same as those observed in our original population.
Calculate the predicted genotype frequencies of the next generation, based on the allele frequencies of the parent generation:
- The frequency of the AA genotype will be equal to the frequency of the A allele of the parent generation, squared (p2) = (7)2 = 0.49
- The frequency of the AB genotype will be equal to 2 times the product of the A and B allele frequencies in the parent generation (2pq) = 2(0.7)(0.3) = 0.42 and,
- The frequency of the BB genotype will be equal to the frequency of the B allele in the parent generation, squared (q2) = (0.3)2 = 0.09.
- The predicted genotype frequencies sum to 1.
Notice that the predicted genotype frequencies of the next generation match those of the parental generation – again, this is exactly what the Hardy-Weinberg equilibrium theorem predicts.
- To actually test this prediction in real life, we would need to collect the genotype frequencies in the next generation of our population, and compare them to the expected frequencies.
- If the observed frequencies matched the predicted frequencies, then we would conclude that no evolution occurred;
- If the observed frequencies of the next generation did not match the predicted frequencies, we would conclude that evolution did occur – though we wouldn't know exactly which forces were behind it.
If the frequencies did not match, we would have to perform a Pearson chi-squared test to determine whether there was a statistically significant difference between the two generations before we could conclude that evolutionary forces were at work.