  Evolution in finite populations is often modelled using the classical Moran
process. Over the last ten years this methodology has been extended to
structured populations using evolutionary graph theory. An important question
in any such population, is whether a rare mutant has a higher or lower chance
of fixating (the fixation probability) than the Moran probability, i.e. that
from the original Moran model, which represents an unstructured population. As
evolutionary graph theory has developed, different ways of considering the
interactions between individuals through a graph and an associated matrix of
weights have been considered, as have a number of important dynamics. In this
paper we revisit the original paper on evolutionary graph theory in light of
these extensions to consider these developments in an integrated way. In
particular we find general criteria for when an evolutionary graph with general
weights satisfies the Moran probability for the set of six common evolutionary
dynamics.
