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Mating preferences of many biological species are not constant butseason-dependent. Within the framework of evolutionary game theory this can bemodeled with two finite opposite-sex populations playing against each otherfollowing the rules that are periodically changing. By combining Floquet theoryand the concept of quasi-stationary distributions, we reveal existence ofmetastable time-periodic states in the evolution of finite game-drivenpopulations. The evolutionary Floquet states correspond to time-periodicprobability flows in the strategy space which cannot be resolved within themean-field framework. The lifetime of metastable Floquet states increases withthe size $N$ of populations so that they become attractors in the limit $N\rightarrow \infty$.

Seasonal Floquet states in a game-driven evolutionary dynamics