Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-15 |
| Number of pages | 15 |
| Journal | Theoretical Population Biology |
| Volume | 80 |
| Issue number | 1 |
| DOIs | |
| State | Published - Aug 1 2011 |
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Keywords
- Demographic elasticity
- Lyapunov exponent
- Stage-structured population
- Stochastic growth rate
- Stochastic matrix models
ASJC Scopus subject areas
- Ecology, Evolution, Behavior and Systematics
Cite this
Derivatives of the stochastic growth rate. / Steinsaltz, David; Tuljapurkar, Shripad; Horvitz, Carol C.
In: Theoretical Population Biology, Vol. 80, No. 1, 01.08.2011, p. 1-15.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Derivatives of the stochastic growth rate
AU - Steinsaltz, David
AU - Tuljapurkar, Shripad
AU - Horvitz, Carol C
PY - 2011/8/1
Y1 - 2011/8/1
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
UR - http://www.scopus.com/inward/record.url?scp=79959376947&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79959376947&partnerID=8YFLogxK
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 -