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,  16:58, 30 August 2016
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Evolutionary amplifiers are probably the most intriguing structures in [[evolutionary graph theory]] and represent the counterpart to [[evolutionary suppressors]]. For the [[spatial Moran process]] these population structures tilt the balance between selection and random drift in favor of selection such that the fixation probabilities $$\rho$$ of advantageous mutants ($$r>1$$) is larger than in the original [[Moran process]] or on [[Moran graphs|circulation graphs]], $$\rho>\rho_1$$. Because selection is enhanced, this also implies that disadvantageous mutants ($$r<1$$) have a smaller fixation probability, $$\rho<\rho_1$$. Evolutionary amplifiers are also characterized by hierarchical population structures with the crucial addition of positive feedback loops.
The simplest example of an evolutionary amplifier is the [https://en.wikipedia.org/wiki/Star_(graph_theory) star graph], which connects a central hub to a reservoir of leaf vertices through undirected (bi-directional) links. The hub represents a bottleneck for the evolutionary progression because if one leaf vertex is occupied by a mutant it needs to conquer the hub before another leaf vertex can be taken over. Most of the time, the ‘hot’ hub is repeatedly replaced by reproducing leaf vertices and only occasionally the hub itself reproduces and replaces a leaf vertex. For an advantageous mutant in a leaf vertex this means that compared to a resident leaf vertex it has a relative advantage of $$r$$ to occupy the hub and similarly the mutant hub has again a relative reproductive advantage of $$r$$. Thus, the overall relative advantage of a mutant leaf vertex to proliferate and occupy another leaf vertex is $$r^2$$. Note that there is no other way for a mutant to spread through the population. As a consequence, a mutant with fitness $$r^2$$ on the star graph has (approximately) the same fixation probability as a mutant with fitness $$r^2$$ on a circulation graph. Thus, the fixation probability is approximately
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