Lotka-Volterra Predator-Prey Dynamics – AP Biology

Learning Objectives

Identify cyclic oscillations in coupled dynamic populations.

Analyze the phase-space graph to find equilibrium orbits.

Correlate parameter rates ($\alpha, \beta, \gamma, \delta$) to system crashes or explosions.

Lotka-Volterra Equations

$ \frac{dx}{dt} = \alpha x - \beta x y $

$ \frac{dy}{dt} = \delta x y - \gamma y $

$x = \text{Prey (Rabbits)}$ ●
$y = \text{Predator (Foxes)}$ ●

Why It Matters

It demonstrates how two species interacting (one eating the other) can establish stable continuous mathematical cycles in an ecosystem, rather than one wiping the other out completely.