Population Genetics and the Gene Pool

The sum of all the alleles of all the genes of all the individuals in a population is called the gene pool.

The Hardy-Weinberg Principle

• Frequencies of dominant and recessive alleles would remain constant over time, so
  long as five key conditions about the population were met:

1. There are no mutations, so no new alleles are created.
2. There is no immigration, so no new alleles are introduced, and no emigration, so no alleles are lost.
3. There is no selection, so no alleles are favoured or eliminated.
4. Mating is random, so alleles are mixed randomly.
5. The population is large, so there are no genetic bottlenecks.

• These conditions mean that there is nothing to disturb the gene pool, which therefore remains in a stable genetic equilibrium.
• In other words, the allele frequencies in the population will remain constant from
  generation to generation.

If the gene pool is stable then we can use a simple equation to calculate the gene frequencies in a population.

This is called the Hardy-Weinberg equation. There are three kinds of frequencies:

•  Phenotype frequencies are proportions of the different characteristics in the population (e.g.red or white). These are the easiest, because we can see and count them in a population. 
• Genotype frequencies are the proportions of the three possible genotypes (BB, Bb and bb) in the population. This isn’t so easy, because we can’t see the genotypes, but we can calculate them.
• Allele frequencies are the proportions of the two alleles B and b in the population. Allele frequencies are particularly interesting because evolution causes the allele frequencies to change.

• The sum of the two allele frequencies must add up to one, by definition (because there are only two alleles of this gene).
• Mathematically, if p is the frequency of the dominant allele A, and qis the frequency of the recessive allele a, then
• p+ q= 1
• The sum of the genotype frequencies must add up to one (by definition), so:

p2+ 2pq + q2= 1

The Hardy-Weinberg equation can be used to calculate any of the three types of frequencies:
•  Allele frequencies.The frequency of the recessive allele (a) isqand the frequency of the dominant allele (A) isp.
•  Genotype frequencies.The frequency of the homozygous recessive genotype(aa) is q2; the frequency of the homozygous dominant genotype (AA) is p2; and the frequency of the heterozygous genotype (Aa) is 2pq.
•  Phenotype frequencies.The frequency of the recessive phenotype is  q2, and the frequency of the dominant phenotype is p2+ 2pq.