Path-integral calculation for the emergence of rapid evolution from demographic stochasticity

Hong Yan Shih, Nigel Goldenfeld

Research output: Contribution to journalArticlepeer-review


Genetic variation in a population can sometimes arise so fast as to modify ecosystem dynamics. Such phenomena have been observed in natural predator-prey systems and characterized in the laboratory as showing unusual phase relationships in population dynamics, including a π phase shift between predator and prey (evolutionary cycles) and even undetectable prey oscillations compared to those of the predator (cryptic cycles). Here we present a generic individual-level stochastic model of interacting populations that includes a subpopulation of low nutritional value to the predator. Using a master equation formalism and by mapping to a coherent state path integral solved by a system-size expansion, we show that evolutionary and cryptic quasicycles can emerge generically from the combination of intrinsic demographic fluctuations and clonal mutations alone, without additional biological mechanisms.

Original languageEnglish (US)
Article number050702
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
StatePublished - Nov 26 2014

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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