Crossing the Hopf bifurcation in a live predator–prey system. Large-amplitude cycles of Daphnia and its algal prey in enriched environments.
Prevention of population cycles by parasite removal. Impact of food and predation on the snowshoe hare cycle. Coexistence in laboratory populations of Paramecium aurelia and its predator Didinium nasutum. Experimental studies on predation: dispersion factors and predator–prey oscillations. Cyclic fluctuations of population density intrinsic to the host–parasite system. Further studies of interaction between predators and prey. Competition-induced starvation drives large-scale population cycles in Antarctic krill. Cyclic dynamics in a simple vertebrate predator–prey community. Complex dynamics and phase synchronization in spatially extended ecological systems. The ten-year cycle in numbers of the lynx in Canada. (ed.) Population Cycles: The Case for Trophic Interactions (Oxford Univ. Why do populations cycle? A synthesis of statistical and mechanistic modeling approaches. Limit cycles in predator–prey communities. Fluctuations in the abundance of a species considered mathematically. Our findings empirically demonstrate the potential for infinite persistence of predator and prey populations in a cyclic dynamic regime that shows resilience in the presence of stochastic events. A mathematical model suggests that stochasticity is probably responsible for the reversible shift from coherent to non-coherent oscillations, a notion that was supported by experiments with external forcing by pulsed nutrient supply. However, the predator–prey system showed a strong tendency to return to the dominant dynamical regime with a defined phase relationship.
Despite constant experimental conditions, we also observed shorter episodes of irregular, non-coherent oscillations without any significant phase relationship. The dominant type of dynamics was characterized by regular, coherent oscillations with a nearly constant predator–prey phase difference. Here we performed microcosm experiments with a planktonic predator–prey system and repeatedly observed oscillatory time series of unprecedented length that persisted for up to around 50 cycles or approximately 300 predator generations. Field observations have been restricted to a few cycle periods 5, 6, 7, 8 and experimental studies indicate that oscillations may be short-lived without external stabilizing factors 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19. However, it remains an open question for how long cyclic dynamics can be self-sustained in real communities. Predator–prey cycles rank among the most fundamental concepts in ecology, are predicted by the simplest ecological models and enable, theoretically, the indefinite persistence of predator and prey 1, 2, 3, 4.