Lotka-Volterra Calculator
Explore cyclical predator-prey interactions by setting initial populations and interaction parameters. The calculator simulates population trajectories and highlights equilibrium states.
Final prey population
37.58
Trend: decrease
Final predator population
87.05
Trend: increase
Prey equilibrium (γ/δ)
40
Predator equilibrium (α/β)
30
How to Use This Calculator
Set initial populations
Provide starting prey and predator counts, e.g., deer and wolves in a habitat.
Adjust interaction coefficients
Use literature or field data to define growth, predation, mortality, and conversion efficiencies.
Simulate dynamics
Choose step size and number of steps to observe oscillations, convergence, or extinction risks.
Formula
dX/dt = αX − βXY
dY/dt = δXY − γY
Example: With α = 0.6, β = 0.02, γ = 0.4, δ = 0.01, the equilibrium occurs at 40 prey and 30 predators. Starting from 40 prey and 9 predators, the system oscillates around this equilibrium.
Use smaller time steps for higher accuracy or longer time spans to observe multiple cycles.
About the Lotka-Volterra Calculator
The Lotka-Volterra equations are foundational in ecology for modeling predator-prey interactions. This calculator helps ecologists, educators, and students simulate these dynamics without coding differential equations.
When to Use This Calculator
- Field studies: Evaluate how parameter changes (e.g., hunting rates) affect stability.
- Classroom demos: Visualize cyclical dynamics in biology or math lessons.
- Scenario planning: Explore impacts of introducing predators or prey to new habitats.
- Research summaries: Communicate modeling results to stakeholders with simple metrics.
Why Use Our Calculator?
- ✅ Interactive: Instantly updates results as parameters change.
- ✅ Insightful: Reports equilibrium populations and trend direction.
- ✅ Accessible: Requires no specialized software or advanced math.
- ✅ Extensible: Modify coefficients to represent disease spread or competition models.
Common Applications
Wildlife management: Forecast the effects of predator control programs.
Invasive species research: Model interactions between native predators and newcomer prey.
Data storytelling: Explain complex ecological dynamics with intuitive outputs.
Tips for Best Results
- Validate parameters against empirical data when available.
- Use smaller time steps for systems with rapid dynamics.
- Run multiple simulations to explore parameter sensitivity.
- Note that real ecosystems include additional factors (seasonality, carrying capacity, multiple species).
Frequently Asked Questions
Does the model include carrying capacity?
No. Classic Lotka-Volterra assumes unlimited prey resources. For carrying capacity, use predator-prey models with logistic terms.
Can populations become negative?
We clamp populations at zero to avoid negative values introduced by numerical simulation.
How do I see the full trajectory?
This tool summarizes final values and trends. Export results via API or replicate in spreadsheets for step-by-step data.
What if I want stochastic effects?
Add random noise to parameters or initial populations externally; this calculator focuses on deterministic dynamics.