TY - JOUR

T1 - Derivatives of the stochastic growth rate

AU - Steinsaltz, David

AU - Tuljapurkar, Shripad

AU - Horvitz, Carol

N1 - Funding Information:
We thank NIA (BSR) for support under 1P01 AG22500 . David Steinsaltz was supported by a New Dynamics of Ageing grant, a joint interdisciplinary program of the UK research councils.

PY - 2011/8

Y1 - 2011/8

N2 - 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 Tuljapurkar (1990). 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 old formulas.

AB - 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 Tuljapurkar (1990). 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 old formulas.

KW - Demographic elasticity

KW - Lyapunov exponent

KW - Stage-structured population

KW - Stochastic growth rate

KW - Stochastic matrix models

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U2 - 10.1016/j.tpb.2011.03.004

DO - 10.1016/j.tpb.2011.03.004

M3 - Article

C2 - 21463645

AN - SCOPUS:79959376947

VL - 80

SP - 1

EP - 15

JO - Theoretical Population Biology

JF - Theoretical Population Biology

SN - 0040-5809

IS - 1

ER -