Stochastic Lotka-Volterra — Population Fluctuations
Individual-based model: extinction risk, demographic stochasticity, and noise-induced cycles
0.60
0.040
0.40
0.020
0.30
Prey N: —
Predators P: —
Time: —
Extinct: No
Deterministic LV: dN/dt = αN − βNP, dP/dt = γNP − δP — neutral cycles in (N,P) plane.
Stochastic version (Gillespie algorithm / SDE): demographic noise drives the system off closed orbits. Near extinction, noise is amplified: trajectories spiral inward/outward.
Key results: stochastic LV eventually goes extinct in finite populations (unlike the deterministic model); noise generates quasi-cycles with amplitude ~ 1/√N; extinction time grows exponentially with N.