Evolutionary dynamics on graphs for the Moran process have been previously examined within the context of fixation behaviour for introduced mutants, where it was demonstrated that certain spatial structures act as amplifiers of selection. This paper will revisit the assumptions for this spatial Moran process and show that the assumption of proportional global fitness, introduced as part of the Moran process, is necessary for the amplification of selection to occur. Under the circumstances of local proportional fitness selection the amplification property no longer holds, which supports the original results from population genetics that spatial structure does not alter fixation probability for fixed population sizes with constant migration.
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