Hardy–Weinberg Equilibrium

Evolution vs. Non-Evolution

• Evolution Defined
  • A change in allele frequencies in a population
  • Therefore: If there is no change in allele frequency in a population, we assume that no evolution has occurred.
• Hardy and Weinberg defined five conditions (see the next lecture) under which no evolution would occur.
  • If these five conditions are met, no evolution occurs, and we have a Hardy–Weinberg Equilibrium.
  • It is called an equilibrium because the allele frequency does not change: it is in a state of equilibrium.
• We determine allele frequencies using the Hardy–Weinberg equations.
• These equations require two assumptions about the population:
  • There are only two alleles for a trait (e.g. A and a).
  • One allele is dominant (A) and one allele is recessive (a).

Hardy–Weinberg Equations

General

• p represents the frequency of the dominant allele (in this example, A).
• q represents the frequency of the recessive allele (in this example, a).
• Both variables range from 0 (none of the population has that allele) to 1 (100 % of the population has that allele).
• Both equations below will always be true if the two assumptions mentioned above are met.

Allele Frequency Equation: p + q = 1

• p is the frequency of the A allele.
• q is the frequency of the a allele.

Genotype Frequency Equation: p² + 2pq + q² = 1

• p² is the frequency of the AA genotype.
• 2pq is the frequency of the Aa genotype.
• q² is the frequency of the aa genotype.

Practice Problem

(See page 431 in Campbell's Biology, 5th Edition for a discussion of this problem.)

Parental Population

Figure 23.3(a), page 431, Campbell's Biology, 5th Edition

Second Generation

Figure 23.3(b), page 431, Campbell's Biology, 5th Edition

Result

• No change in allele frequency
• Thus, no evolution
• Therefore, all five Hardy–Weinberg equilibrium conditions must have been met!