2010/02/07 by David Steinsaltz, Steinsaltz, David, Shripad Tuljapurkar +4
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Biological sciences #Markov Chains and Monte Carlo Methods #Populations and Evolution (q-bio.PE) #Stochastic processes and statistical mechanics #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1002.1424
35 pages
arxiv created 2010/02/07 · openalex publication_date 2010/02/07 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider stochastic matrix models for population driven by random environments which form a Markov chain. The top Lyapunov exponent a, which describes the long-term growth rate, depends smoothly on the demographic parameters (represented as matrix entries) and on the parameters that define the stochastic matrix of the driving Markov chain. The derivatives of a -- the "stochastic elasticities" -- with respect to changes in the demographic parameters were derived by \citetuljapurkar1990pdv. These results are here extended to a formula for the derivatives with respect to changes in the Markov chain driving the environments. We supplement these formulas with rigorous bounds on computational estimation errors, and with rigorous derivations of both the new and the old formulas.