Stabilizing selection

If we plot $\bar w$ as a function of $p$ when $w_{11} < w_{12}$ and $w_{22} < w_{12}$, we see a third pattern. The plot is shaped like an upside down bowl (Figure 3).

Figure 3: With stabilizing selection ( $w_{11} < w_{12} > w_{22}$; also called balancing selection or heterozygote advantage) viability selection will lead to a stable polymorphism. All three genotypes will be present at equilibrium.

In this case we can see that no matter what allele frequency the population starts with, the only way that $\bar w' \ge \bar w$ can hold is if the allele frequency changes in such a way that it gets close to the value where $\bar w$ is maximized every generation. Unlike directional selection or disruptive selection, in which natural selection tends to eliminate one allele or the other, stabilizing selection tends to keep both alleles in the population. You'll also see this pattern of selection referred to as balancing selection, because the selection on each allele is ``balanced'' at the polymorphic equilibria.²⁰ We can summarize the results by saying that the monomorphic equilibria are unstable and that the polymorphic equilibrium is stable. By the way, if we write the fitness as $w_{11} = 1 - s_1$, $w_{12} = 1$, and $w_{22}=1-s_2$, then the allele frequency at the polymorphic equilibrium is $\hat p = s_2/(s_1+s_2)$.²¹

These notes are licensed under the Creative Commons Attribution-ShareAlike License. To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/3.0/us/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.