Аннотация
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.
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