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arXiv · 1501.05206

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

Mi Jin Lee·Su Do Yi·Beom Jun Kim·Seung Ki Baek
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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.

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Mi Jin Lee, Su Do Yi, Beom Jun Kim, Seung Ki Baek. 2015-01-21. Theory of fads: Traveling-wave solution of evolutionary dynamics in a one-dimensional trait space. https://doi.org/10.1103/physreve.91.012815

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