Abstract or Additional Information
Spatial structures as a model for variable migration patterns between
different spatial points in an evolutionary system has been wildly discussed in
the literature with applications in ecology, epidemiology, social networks and
cancer evolution. In this talk we address another form of heterogeneity due to
environment, where the fitness of an individual is determined by the spatial
environment it resides on. This can resemble spatial distribution of resources
in a habitat or spatial variation of drug concentration in the case of
infectious deceases treatment and/or acidic and hypoxic regions inside a
tumour. We discuss random fitness distributions and investigate the probability
of success of new mutant (fixation probability) as a function of distribution of
a quenched random environment in spatially and non-spatially structured
populations. In the presence of spatial structures, fixation probability depends
on the functional distribution of fitness values on the spatial structure as
well as the connectivities of the lattice that population lives on. This can
lead to localization-delocalization-type transitions.