Frozen Evolution. Or, that’s not the way it is, Mr. Darwin. A Farewell to Selfish Gene.

The frequency of the individual genotypes in the equilibrium state can be readily calculated from the frequency of the alleles in a certain locus. This equilibrium state is called the Hardy-Weinberg equilibrium. In a large panmictic population, i.e. in a population whose members reproduce together quite at random, this equilibrium is established during a single generation. It follows from the laws of combinatorics that, at equilibrium, genotypes a₁a₁, a₁a₂ and a₂a₂ will be present in a ratio of ¦²: 2¦_a¦_a:¦², where ¦_aand ¦_adenote the frequency of alleles a₁ and a₂ in the previous generation (Fig. II.14).  Here, the ratio in which the individual genotypes were present in the previous generation is not in any way important. During a single generation, the same representation of the individual genotypes is established, regardless of whether the original population contained, for example, only homozygotes a₁a₁ and a₂a₂, or only heterozygotes a₁a₂.

Fig. II.14 Graphical depiction of Hardy-Weinberg equilibrium as division of the area in an equilateral triangle. Division of the base into two parts depicts the frequency of two alleles in the studied locus and the areas of the equilateral triangles and the rhomboid depict the relative contents of all three genotypes in the population located in H.-W. equilibrium.

            If we study several genes, amongst which there is no genetic linkage, for example, if each of them is located on a different chromosome, equilibrium is again established within a single generation; the numbers of the individual genotypes can be calculated for this state according to the simple rules of combinatorics.