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Evolutionary Genetics: H-W Equilibrium

Hardy-Weinberg equilibrium describes the null model evolution. For a population to be in Hardy-Weinberg equilibrium, five conditions must be met:

1. No Genetic Drift (Infinite Population Size)

2. No Migration (No Gene Flow)

3. No Mutation

4. No Selection (No Differential Selection)

5. Random Mating (No Differential Reproduction)

If all five of these conditions are met, the allelic and genotypic frequencies will remain the same from generation to generation. Under these conditions, the relationships among allelic and genotypic frequencies hold true:

,

, ,

where p= f(A), q= f(a), P= f(AA), H= f(Aa), and Q= f(aa).

The following relationships always hold true:

,

To determine whether or not population is in H-W Equilibrium for a particular locus, one needs to calculate p and q from the genotypic frequencies, then compare the known genotypic frequencies with those calculated using:

, ,

If there is a significant difference between the known and calculate genotypic frequencies, then the population is not in H-W Equilibrium. This result implies that one of the five conditions is not met for the locus in question. A Chi-Square test is typically used to determine whether or not there is significance between the known and calculated genotypic frequencies.

Evolutionary Genetics: H-W Equilibrium

The five evolutionary forces have the following effect:

1. Selection typically changes both allelic and genotypic frequencies. In this simulation selection is acting against both the yellow (AA) and the green (Aa) individuals. Thus, the blue (aa) individuals are favored.

2. Recurrent Mutation typically changes both allelic and genotypic frequencies, but is usually a much weaker force than the others. In this simulation, recurrent mutation acts to change the A allele to the a allele, opposing selection.

3. Migration also opposes selection in this simulation. This force introduces A alleles into the population, changing both the genotypic and allelic frequencies.

4. Assortative Mating changes only genotype frequencies. In this simulation, positive assortative mating, decreases the frequency of heterozygotes while increasing the frequency of the homozygotes. This decrease in heterozygotes can best be observed via the DeFinetti diagram (see below).

5. Genetic Drift introduces stochasticity into the population. For this simulation the size of the population undergoing genetic drift is 400. For obvious computational reasons, the size of the population "without drift" is 4000, instead of infinity.

Combining two or more forces complicates things somewhat. In general, combining two opposing forces (such as selection and migration) produces an equilibrium in the population. Combining two complimentary forces amplifies their effect.

The DeFinetti diagram is useful when determining if a population is in H-W Equilibrium. In this diagram, each of the three genotype frequencies is plotted along one of the sides of the diagram. The curve through the diagram represents the H-W Equilibrium genotypic frequencies. When the population frequencies lie below this line positive assortative mating may be at play. Negative assortative mating is possible when the population frequencies lie above this line. Genetic drift causes the population to deviate noticeable from this line.