Biology · Introductory biology · Worked example
Predict how prey growth shifts the equilibrium
In the same model, with β = 0.02, δ = 0.004 and γ = 0.8 per year, better food lets the prey grow at α = 0.9 per year instead of 0.6. How does the equilibrium change?
Recompute the prey level
X* = γ/δ does not involve α, so it stays at 200 prey.
Recompute the predator level
Y* = α/β rises in proportion to α.
Explain the result
The extra prey production is eaten: predators increase until they remove prey as fast as the prey now grow. Helping the prey ends up supporting more predators, not more prey.
Check the simulation
Simulated from 300 prey and 20 predators, the cycle is shorter, about 7.9 years, and wider, with the prey ranging from about 72 to 429 and the predators from about 17 to 93. Averaged over a cycle, the populations are 200 prey and 45 predators.
Result
The prey equilibrium stays at 200, while the predator equilibrium rises from 30 to 45: faster prey growth supports more predators.
Your turn
With α = 0.6, β = 0.02 and δ = 0.004, the predator death rate γ rises from 0.8 to 1.2 per year. Where is the new equilibrium?
Show the answer and explanation
300 prey and 30 predators.
X* = γ/δ = 1.2/0.004 = 300, while Y* = α/β = 30 does not change. Predators that die faster need more prey to hold steady.
Keep exploring
The predator–prey tool opens with α = 0.9; its summary shows the equilibrium at 200 prey and 45 predators.
Return to the concept →Sources and scope
Authored study material. Tool results depend on the stated inputs and model assumptions.
Try in the workspace
Open the example inputs, change a value and keep a useful result on your board.
Open the predator–prey tool Open worked example on a board Lotka–Volterra equations in Biology ReferenceYour existing work stays on this device. Examples open as editable copies.