Predator-prey dynamics drive cycles, which keep ecological systems continually in flux through time.  These dynamics can result in complex patterns in space and time — and affect the selective pressures on both predators and prey:

1. • The canonical Lotka-Volterra model generates stable limit cycles, but there are lots of other cyclic behaviors that can be generated when you add real-life ecology to that simple math
   • Disturbance can maintain cycles even in presence of intraspecific competition
   • Cycles necessarily go through numerical bottlenecks — low numbers are susceptible to demographic stochasticity and local extinction
   • Metapopulation dynamics can rescue unstable cycles
   • Predation can drive strong selection in both predator and prey species — the positive feedback loop can drive co-evolution (i.e. the Red Queen hypothesis)
   • Evolution can be directional — e.g. cheetahs and gazelles