title: Theory of fads: traveling-wave solution of evolutionary dynamics in a one-dimensional trait space.
abstract: 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.
authors: Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea.
authors: Mi Jin
authors: MJ
authors: Lee
authors: Department of Physics, Pukyong National University, Busan 608-737, Korea.
authors: Su Do
authors: SD
authors: Yi
authors: Department of Physics, Sungkyunkwan University, Suwon 440-746, Korea.
authors: Beom Jun
authors: BJ
authors: Kim
authors: Department of Physics, Pukyong National University, Busan 608-737, Korea.
authors: Seung Ki
authors: SK
authors: Baek