🐇 Lotka-Volterra Calculator
Simulate the classic Lotka-Volterra predator-prey equations to see how two interacting populations change over time and where they naturally balance out.
What the Lotka-Volterra model describes
The Lotka-Volterra equations are a classic pair of differential equations used in ecology to model how a predator population and a prey population interact over time. Prey grow on their own but are reduced by predation; predators decline on their own but grow by consuming prey. The result is often a cyclical pattern where predator and prey numbers rise and fall in a repeating rhythm.
The equations and inputs
dx/dt = alpha·x − beta·x·y (prey) and dy/dt = delta·x·y − gamma·y (predators), where x and y are the population sizes, alpha is the prey growth rate, beta is the rate prey are consumed, delta is how efficiently consumed prey convert to predator growth, and gamma is the predator death rate. This calculator numerically steps the equations forward in small time increments (Euler’s method) to project both populations after your chosen time period, and also reports the theoretical equilibrium point where both populations would stay constant.
This is a simplified textbook model for education and exploration — real ecosystems involve many more factors (resource limits, multiple species, migration, seasonality) not captured here.