Diffusion approximations with autocorrelation and nonlinearity.
Haridas, Chirakkal*,1, Tuljapurkar, Shripad1, Al-Khafaji, Karim1, 1 Stanford University, Stanford, CA
ABSTRACT- Stage strutured models of single populations are becoming a standard tool for population projection and viabiliy assessment. Methods for stochastic models now make it possible to analyze extinction in terms of the time to reach a boundary and the probability of getting there. Existing methods assume that stochastic variation is temporal and independent between years in its distribution. In many practical cases, temporal variability is correlated over time, especially in disturbance-driven systems. We provide results to analyze extinction when temporal variability follows a Markov process with arbitrary autocorrelation. We exploit recent results to provide a generally useful analytical diffusion, and also analyze numerical cases to show when autocorrelation matters to extinction.
Key words: diffusion, autocorrelation, extinction
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