  Selection in a time-periodic environment is modeled via the continuous-time
two-player replicator dynamics, which for symmetric pay-offs reduces to the
Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic
[fine-grained] environment, the time-averaged population frequencies are shown
to obey a replicator dynamics with a non-linear fitness that is induced by
environmental changes. The non-linear terms in the fitness emerge due to
populations tracking their time-dependent environment. These terms can induce a
stable polymorphism, though they do not spoil the polymorphism that exists
already without them. In this sense polymorphic populations are more robust
with respect to their time-dependent environments. The overall fitness of the
problem is still given by its time-averaged value, but the emergence of
polymorphism during genetic selection can be accompanied by decreasing mean
fitness of the population. The impact of the uncovered polymorphism scenario on
the models of diversity is examplified via the rock-paper-scissors dynamics,
and also via the prisoner's dilemma in a time-periodic environment.
