Birth-Death with Catastrophes

Stochastic Population Dynamics · Extinction Probability · Quasi-Stationary Distribution

Birth rate λ (per capita) 0.80

Death rate μ (per capita) 0.60

Catastrophe rate c 0.05

Catastrophe severity γ 0.50

Carrying capacity K 80

Replicates 5

dN/dt = (λ-μ)N − logistic correction

P_ext = (μ/λ)^N₀ (pure birth-death, λ>μ)

Catastrophe: N → N(1-γ) instantly

QSD: π_n ∝ stationary dist | n>0