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Major climatic and geological events but also population history (secondary contacts) have generated cycles of population isolation and connection of long and short periods. Recent empirical and theoretical studies suggest that fast evolutionary processes might be triggered by such events, as commonly illustrated in ecology by the adaptive radiation of cichlid fishes (isolation and reconnection of lakes and watersheds) and in epidemiology by the fast adaptation of the influenza virus (isolation and reconnection in hosts). We test whether cyclic population isolation and connection provide the raw material (standing genetic variation) for species evolution and diversification. Our analytical results demonstrate that population isolation and connection can provide, to populations, a high excess of genetic diversity compared with what is expected at equilibrium. This excess is either cyclic (high allele turnover) or cumulates …