University · Ecology Round 1/6 Score 0

Predator–Prey Lab

Investigate equilibria, oscillations and limiting prey resources.

Coexistence challenge

Assumption: a closed predator–prey system with fixed rates.

Population trajectories

Prey x Predators y

Phase plane

Trajectories use the calculation module's fourth-order Runge–Kutta solver.

Adjust the controls, then check your prediction.

The biology

Prey: dx/dt = αx(1 − x/K) − βxy. Predator: dy/dt = δxy − γy. With unlimited prey, remove the carrying-capacity factor. Coexistence gives x* = γ/δ and y* = α/β. With capacity K, predator coexistence requires K greater than γ/δ, and y* = (α/β)(1 − x*/K). Small-oscillation period without K = 2π/√(αγ). The unrestricted conserved quantity is H = δx − γln(x) + βy − αln(y). Logistic prey limitation can damp oscillations or exclude predators.