The shapes of predator-prey cycles: Examples and theory of how evolution changes the community dynamics of predator-prey systems

Background/Question/Methods

In this talk we explore how the shapes of predator-prey cycles change when the predator, the prey, or both species are evolving.  As is known from classic work on ecological models, predator-prey systems without evolution are predicted to exhibit counterclockwise cycles where the peak in predator abundance lags behind the peak in prey abundance by less than a quarter of the period.  Recent experimental and theoretical studies have shown that evolution in one species can cause predator-prey systems to exhibit antiphase oscillations (where the species oscillate exactly out of phase) or cryptic cycles (where one species cycles while the other remains constant).  Here we analyze the shapes of cycles predicted by theoretical eco-evolutionary models where one or both species are evolving.  We then compare the shapes of the predicted cycles to predator-prey cycles from experimental and natural systems in order to evaluate if those time series exhibit signatures of evolution or coevolution. 

Results/Conclusions

Based on theoretical eco-evolutionary models, we categorize the kinds of cycles that can arise when one or more species are evolving.  Prey evolution can yield counterclockwise cycles, and additional shapes including antiphase and cryptic oscillations.  Predator evolution tends to yield counterclockwise or in-phase oscillations, but in some cases antiphase oscillations are also possible.  Coevolution can yield all of the above in addition to a novel prediction of clockwise cycles.  In clockwise cycles, the peak in prey abundance lags behind the peak in predator abundance - the opposite of what happens in the absence of evolution.  We also categorize the signatures of (co)evolution in those oscillations (e.g. cycle orientation in the phase plane and the ordering of predator and prey peaks and troughs).  Finally, we revisit published time series from phage-cholera, mink-muskrat, and  gyrfalcon-rock ptarmigan systems and show that those systems exhibit clockwise cycles.  Our work suggests that coevolution may have a significant influence on the community dynamics observed in those systems.