  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 $\pi$ 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.
