Lotka-Volterra Model Variables
X (Prey)
Population of prey species. Increases when not being eaten and decreases due to predation.
Y (Predator)
Population of predator species. Increases when consuming prey and decreases due to natural death.
α
Prey reproduction rate. Determines how quickly prey population grows in the absence of predators.
β
Predation rate. Determines how effectively predators consume prey.
γ
Predator death rate. Determines how quickly predators die in the absence of prey.
δ
Predator efficiency. Determines how effectively predators convert consumed prey into predator offspring.
Mathematical Equations
dX/dt = αX - βXY
dY/dt = δXY - γY
How to Use This Simulation
This simulation shows the oscillating relationship between prey and predator populations. Adjust parameters to see how they affect population dynamics:
- Higher prey reproduction rate (α) leads to faster prey population growth
- Higher predation rate (β) causes more rapid decline in prey population
- Higher predator death rate (γ) causes faster predator decline when prey is scarce
- Higher predator efficiency (δ) allows predators to grow faster when prey is abundant