Predator-Prey Calculator: Lotka-Volterra Ecologi...

The Lotka-Volterra Model

The Lotka-Volterra equations describe the cyclical dynamics between predator and prey populations. Developed independently by Alfred Lotka (1925) and Vito Volterra (1926), they reveal why predator and prey populations oscillate out of phase — more prey → more predators → fewer prey → fewer predators → prey recovers → cycle repeats.

🐺 Lotka-Volterra Calculator

Free calculator for instant results.

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📐 Formula

dN/dt = rN − αNP | dP/dt = βNP − mP

N=prey, P=predators, r=prey growth rate, α=predation rate, β=conversion efficiency, m=predator death rate. Both populations oscillate continuously.

📝 Worked Example

Rabbits (r=0.5/yr), Fox (m=0.2/yr), α=0.02, β=0.01
Equilibrium: N*=m/β=20 foxes, P*=r/α=25 rabbits... wait:
Prey equilibrium: N* = m/β = 0.2/0.01 = 20
Predator equilibrium: P* = r/α = 0.5/0.02 = 25

📝 How to Use

Enter Prey ParametersInitial population, birth rate (r), and predation rate (α).

Enter Predator ParametersInitial population, conversion rate (β), and death rate (m).

Set Time RangeNumber of years/generations to simulate.

View OscillationsWatch population cycles plotted over time and as a phase portrait.

❓ FAQ

Do real populations follow Lotka-Volterra exactly?

No — real populations show similar cycles (Canadian lynx-snowshoe hare data) but the classic model ignores carrying capacity, seasonality, and other species.

What is the phase portrait of Lotka-Volterra?

A plot of predator vs. prey population forms a closed loop (orbit). The populations cycle indefinitely — a neutrally stable equilibrium.