Predator–prey dynamics – rabbits and foxes
BiologyEcology & EnvironmentAges 17–18
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Ecology & Environment
The rabbit population grows logistically, dN/dt = rN(1 − N/K), heading toward the environment's carrying capacity K; once foxes are added, the two populations oscillate out of phase under the Lotka–Volterra model: rabbits rise → foxes rise → rabbits fall → foxes fall. The meadow shows both densities live, alongside a population-over-time graph and a phase plot, and students can release more rabbits or foxes, change r, K, or predation efficiency, and watch the equilibrium point shift.
Lesson: Population ecology: population size and growth; predator–prey relationships in communities
What it shows
Without predators, a prey population grows almost exponentially at first and then slows as it approaches the carrying capacity K, following the logistic equation and tracing an S-shaped curve. Adding a predator gives the Lotka–Volterra model: prey numbers rise, predators then increase, prey decline, and predators fall in turn, so the two populations oscillate with the predator peak lagging behind the prey peak. On the phase plot this cycle spirals towards an equilibrium point set by the predation efficiency, the conversion efficiency, the predator death rate and the carrying capacity.
How to use
Start with “Model: rabbits only (logistic)” and compare the S-shaped curve with the dashed exponential line. Then switch to “Model: rabbits and foxes” and watch the population graph and the phase plot together. Change the parameters r, K or Fox mortality rate m and see where the equilibrium moves. During a run, press +100 rabbits or +10 foxes to disturb the system and follow how it settles again.
Parameters you can change
- Model Rabbits and foxes (Lotka–Volterra + carrying capacity), Rabbits only: logistic vs. exponential growth
- Rabbits' intrinsic growth rate r 0.1–3 /year
- Environment's carrying capacity K (rabbits) 100–5000 rabbits
- Predation efficiency a (rabbits caught per fox per year ÷ rabbit count) 0.001–0.05
- Conversion efficiency of rabbits into new foxes b 0.02–0.5
- Fox mortality rate m 0.1–2 /year
Questions to explore
- Why does the peak in fox numbers always come after the peak in rabbit numbers?
- How does increasing the carrying capacity K change the oscillations of both populations?
- If all the foxes are removed, what happens to the rabbit population over time?
