Predator–prey cycles – snowshoe hares and lynx
Integrated ScienceEcologyAges 13–14
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Sign in to playHare and lynx populations follow a Lotka–Volterra model with a carrying capacity for the hares. A snowy field shows every animal, a population–time graph marks the peaks and the lag between hare and lynx peaks, and a phase plot traces the orbit around the equilibrium. Sliders change the birth, hunting and death rates and the carrying capacity; buttons trigger lynx hunting or a hare disease outbreak.
Lesson: Predator–prey relationships and population dynamics
What it shows
Predators and their prey can make each other's numbers rise and fall in regular cycles. When hares are plentiful, lynx find food easily and raise more young; the growing lynx population eats more hares, so the hares decline; then the lynx go hungry and decline, letting the hares recover. The lynx peak therefore comes after the hare peak. The Lotka–Volterra equations describe this with a hare birth rate b, a hunting rate a, a lynx death rate d and a conversion factor c. A carrying capacity K limits hare growth and makes the cycles slowly shrink toward an equilibrium.
How to use
Press Pause to freeze the animation and compare the time graph with the phase plot. Change Hare birth rate b, Hunting rate a and Lynx death rate d, and watch where the equilibrium moves. Switch Model to Classic Lotka–Volterra (no limit) to see cycles that never fade. Press Hunt lynx (−50 %) or Hare disease (−60 %) and measure the lag between the peaks. Tap the phase plot to start from new numbers.
Parameters you can change
- Initial number of hares 50–800 animals
- Initial number of lynx 5–100 animals
- Hare birth rate b 0.3–1.5 /year
- Hunting rate a 0.005–0.05 /lynx/year
- Lynx death rate d 0.2–1 /year
- Carrying capacity K 500–6000 hares
- Model Carrying capacity K for hares, Classic Lotka–Volterra (no limit)
Questions to explore
- Why does the lynx population always peak after the hare population?
- Does hunting half of the lynx make the hare population grow forever? Why?
- How does increasing the hunting rate a change the equilibrium numbers of hares and lynx?
