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

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 90; no. 5-1; p. 050702
• Main Authors: Shih, Hong-Yan, Goldenfeld, Nigel
• Format: Journal Article
• Language: English
• Published: United States 01.11.2014
• ISSN: 1550-2376
• DOI: 10.1103/PhysRevE.90.050702

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.