Mathematical Biology Seminar

Michael Cortez
Department of Mathematics and Statistics, Utah State University

Eco-evolutionary predator-prey dynamics: Using fast-slow dynamical systems theory to identify how (co)evolution alters population cycles?

Wednesday, February 10, 2016, at 3:05pm
LCB 215

Predators and their prey can exhibit cyclic temporal fluctuations. Lotka-Volterra and other ecological predator-prey models predict that in predator-prey cycles, peaks in prey abundance precede peaks in predator abundance. However, other kinds of cycles have been observed in predator-prey systems, e.g., antiphase cycles where the species oscillate exactly out of phase. This motivates the question, 'why do cycle characteristics differ across systems?' Using eco-evolutionary models and fast-slow dynamical systems theory, I explore and characterize how evolution in prey, predators, or both species alter cycle characteristics. In addition to unifying theory on known cycle types, I identify a new kind of predator-prey cycle: coevolution can drive clockwise cycles where peaks in prey abundance follow peaks in predator abundance - the reverse of classical Lotka-Volterra models without evolution. I revisit empirical time series and show how my theory can be used to identify predator-prey systems where evolution or coevolution is altering population-level dynamics.