Calculadora Lotka-Volterra
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
dX/dt = α×X − β×X×Y; dY/dt = δ×X×Y − γ×Y (integração Euler)
About this calculator
The Lotka-Volterra Calculator simulates the dynamics between prey and predator populations using the classic Lotka-Volterra equations. The model assumes prey grow exponentially without predators, while predators decline without prey. Interaction is modeled by encounter terms, where predation rate depends on the product of populations. Euler's method approximates the temporal evolution numerically, allowing visualization of typical oscillatory cycles in ecological systems.
To use the calculator, enter parameters: prey growth rate (α), predation rate (β), conversion efficiency (δ), and predator mortality rate (γ). Set initial populations and time step. The generated graph shows how populations change over time, revealing stability or extinction patterns. The tool is useful for understanding theoretical ecology concepts like equilibria and limit cycles.
When to use? Ideal for students and researchers exploring simple ecological interactions. It can be applied in biology classes, mathematical modeling, or conservation simulations. Helps visualize how parameter changes affect species coexistence. It does not replace complex models but serves as an introduction to population dynamics.
Cautions: Euler's method may accumulate errors for large steps; prefer small steps. The model assumes a homogeneous environment and no resource limitation for prey, which is unrealistic long-term. Use cautiously for quantitative predictions, focusing on qualitative patterns.
Frequently asked questions
What do the parameters α, β, δ, and γ mean?
α is the prey growth rate, β the predation rate, δ the conversion efficiency of prey into new predators, and γ the predator mortality rate.
Why do populations oscillate in the graph?
Oscillations arise from feedback between prey and predators: more prey feed more predators, which reduce prey, leading to predator decline and prey recovery.
What happens if I set a very large time step?
Euler's method may become unstable, yielding inaccurate results with negative populations or numerical blow-ups. Use small steps (e.g., 0.01) for better accuracy.
Can this model predict real species extinction?
Not directly. The model is simplified, ignoring carrying capacity, migration, and environmental heterogeneity. Use for educational purposes, not real management.
How should I choose initial populations?
Any positive values work. To see cycles, avoid populations near zero. Try values like prey=10 and predators=5.