Stochastic Lotka-Volterra with Demographic Noise
Population extinction events emerge from integer-valued stochastic dynamics
Stochastic Lotka-Volterra: integer populations X (prey), Y (predator).
Reactions: X→2X at rate αX, X+Y→2Y at rate βXY/N, Y→∅ at rate δY.
Deterministic fixed point: X*=δ/β, Y*=αN/β.
Demographic noise ~ 1/√N causes spiraling trajectories to random-walk into extinction.
Large N: quasi-cycles persist; small N: rapid extinction.