Theory of fads: traveling-wave solution of evolutionary dynamics in a one-dimensional trait space.

  title={Theory of fads: traveling-wave solution of evolutionary dynamics in a one-dimensional trait space.},
  author={Mi Jin Lee and Su Do Yi and Beom Jun Kim and Seung Ki Baek},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={91 1},
  • Mi Jin Lee, S. Yi, S. Baek
  • Published 21 January 2015
  • Mathematics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
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… 
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