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In large but finite populations, weak demographic stochasticity due to randombirth and death events can lead to population extinction. The process isanalogous to the escaping problem of trapped particles under random forces.Methods widely used in studying such physical systems, for instance,Wentzel-Kramers-Brillouin (WKB) and Fokker-Planck methods, can be applied tosolve similar biological problems. In this article, we comparatively analyseapplications of WKB and Fokker-Planck methods to some typical stochasticpopulation dynamical models, including the logistic growth, endemic SIR,predator-prey, and competitive Lotka-Volterra models. The mean extinction timestrongly depends on the nature of the corresponding deterministic fixedpoint(s). For different types of fixed points, the extinction can be driveneither by rare events or typical Gaussian fluctuations. In the former case, thelarge deviation function that governs the distribution of rare events can bewell-approximated by the WKB method in the weak noise limit. In the later case,the simpler Fokker-Planck approximation approach is also appropriate.

Applications of WKB and Fokker-Planck methods in analyzing population extinction driven by weak demographic fluctuations