Theoretical ecologists are increasingly recognizing the importance of transient dynamics, as opposed to asymptotic dynamics, as the important aspect of ecological models to relate to real world ecological questions. Focusing primarily on systems with two patches, and with the potential for cyclic dynamics in local populations and coupling by passive dispersal as an example where transient dynamics may be important in understanding the ecological attributes which either lead to or prevent synchrony and are potentially responsible for increasing the likelihood of persistence. We study these systems using ideas from the theory of weakly coupled oscillators to look at predator-prey dynamics and also ideas from dynamical systems to look at coupled single species models
Results/Conclusions
For the systems we study we obtain conditions that are likely to lead to transients. The systems are instructive because we focus on very different kinds of local dynamics. We show that transients are essentially likely in all coupled systems with complex enough local dynamics. For systems with cyclic local dynamics we obtain estimates of the time to reach asymptotic synchronous behavior in terms of the propensity for local outbreaks. We also delineate conditions under which there are precursors to sudden changes in dynamical behavior, and also conditions when regime shifts would occur without any obvious prior changes in dynamics. We relate our findings to questions of synchrony and persistence.
