  We consider an infinite-sized population where an infinite number of traits
compete simultaneously. The replicator equation with a diffusive term describes
time evolution of the probability distribution over the traits due to selection
and mutation on a mean-field level. We argue that this dynamics can be
expressed as a variant of the Fisher equation with high-order correction terms.
The equation has a traveling-wave solution, and the phase-space method shows
how the wave shape depends on the correction. We compare this solution with
empirical time-series data of given names in Quebec, treating it as a
descriptive model for the observed patterns. Our model explains the reason that
many names exhibit a similar pattern of the rise and fall as time goes by. At
the same time, we have found that their dissimilarities are also statistically
significant.
