Moran graphs: Difference between revisions

According to their definition, mutations on Moran graphs maintain the same fixation probabilities as in the original Moran process in unstructured populations. However, this has no implications on the fixation times of a mutant or on the absorption time, i.e. the time until the population reaches either one of the absorbing states with all mutants or all residents. In fact, fixation and absorption times vary greatly even between different circulation graphs, as illustrated with the following simulations for diverse examples of circulations. Even though to date rigorous connections between structural features and fixation times are lacking, the [https://en.wikipedia.org/wiki/Distance_(graph_theory) diameter of a graph] correlates with fixation times. The diameter of a graph \(d\) is defined as the longest shortest path between any two vertices and provides a measure for how many updates are at least required until the progeny of any one particular vertex could occupy any other vertex. Other, related measures such as the [https://en.wikipedia.org/wiki/Distance_(graph_theory) radius of a graph] or the average [https://en.wikipedia.org/wiki/Shortest_path_problem shortest distance] seem to work equally well.