  We study evolutionary games with a continuous trait space in which replicator
dynamics are restricted to the manifold of multidimensional Gaussian
distributions. We demonstrate that the replicator equations are natural
gradient flow for maximization of the mean fitness.
  Our findings extend previous results on information-geometric aspects of
evolutionary games with a finite strategy set.
  Throughout the paper we exploit the information-geometric approach and the
relation between evolutionary dynamics and Natural Evolution Strategies, the
concept that has been developed within the framework of black-box optimization.
This relation sheds a new light on the replicator dynamics as a compromise
between maximization of the mean fitness and preservation of diversity in the
population.
