Making the most of potential: potential games and genotypic convergence

We consider genotypic convergence of populations and show that under fixed fitness asexual haploid sexual attain monomorphic (even genetic linkage between loci) to basins attraction with locally exponential rates; the same obtains in single locus diploid reproduction but polymorphic populations. Furthermore, we there is a unified theory underlying these convergences: all them can be interpreted as instantiations players potential game implementing multiplicative weights updating algorithm converge equilibrium, making use Baum–Eagon Theorem. To analyse varying environments, introduce concept ‘virtual convergence’, which, even if fixation not attained, population nevertheless achieves growth rate it would have had an optimal genotype. Virtual attained by asexual, multi-locus reproducing populations, environments vary arbitrarily. also study conditions for true asexually environments.