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Evolutionary graph theory: Difference between revisions
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== [[Evolutionary graph theory/Evolutionary amplifiers|Evolutionary amplifiers]] == | == [[Evolutionary graph theory/Evolutionary amplifiers|Evolutionary amplifiers]] == | ||
[[Image:Evolutionary amplifier (star).png|thumb|300px|Evolutionary amplifiers are structures that enhance (suppress) the fixation probability of advantageous (deleterious) mutants as compared to unstructured populations.]] | [[Image:Evolutionary amplifier (star).png|thumb|300px|Evolutionary amplifiers are structures that enhance (suppress) the fixation probability of advantageous (deleterious) mutants as compared to unstructured populations. The simplest example is the star graph, which consists of a single, central hub that is (bidirectionally) connected to all other vertices.]] | ||
Interestingly, it is also possible to create population structures that amplify selection and suppress random drift. For example, on the star | Interestingly, it is also possible to create population structures that amplify selection and suppress random drift. For example, on the star graph, where all nodes are connected to a central hub and vice versa, the fixation probability of a single, randomly placed mutant becomes | ||
\[ | \[ | ||
\rho_2 = \frac{\displaystyle 1-\frac1{r^2}}{\displaystyle 1-\frac1{r^{2N}}}. | \rho_2 = \frac{\displaystyle 1-\frac1{r^2}}{\displaystyle 1-\frac1{r^{2N}}}. | ||
