Evolutionary dynamics 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 article will revisit the assumptions for this spatial Moran process and show that proportional global fitness, introduced as part of the Moran process, is necessary for the amplification of selection to occur. Here it is shown that under the condition of local proportional fitness selection the amplification property no longer holds. In addition, regular structures are also shown to have a modified fixation probability from a panmictic population when local selection is applied. Theoretical results from population genetics, which suggest fixation probabilities are independent of geography, are discussed in relation to these local graph-based models and shown to have different assumptions and therefore not to be in conflict with the presented results. This paper examines the issue of fixation probability of an introduced advantageous allele in terms of spatial structure and various spatial parent selection models. The results describe the relationship between structured populations and individual selective advantage in a problem independent manner. This is of significant interest to the theory of fine-grained spatially-structured evolutionary algorithms since the interaction of selection and space for diversity maintenance, selection strength and convergence underlies resulting evolutionary trajectories.
Moran process Spatial evolutionary algorithm Graph-based model Fixation Genetic drift Local selection