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Sensitivity analysis of transient population dynamics
Author(s) -
Caswell Hal
Publication year - 2007
Publication title -
ecology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.852
H-Index - 265
eISSN - 1461-0248
pISSN - 1461-023X
DOI - 10.1111/j.1461-0248.2006.01001.x
Subject(s) - eigenvalues and eigenvectors , perturbation (astronomy) , nonlinear system , population model , mathematics , population , term (time) , statistical physics , econometrics , biological system , computer science , physics , biology , demography , quantum mechanics , sociology
Short‐term, transient population dynamics can differ in important ways from long‐term asymptotic dynamics. Just as perturbation analysis (sensitivity and elasticity) of the asymptotic growth rate reveals the effects of the vital rates on long‐term growth, the perturbation analysis of transient dynamics can reveal the determinants of short‐term patterns. In this article, I present a completely new approach to transient sensitivity and elasticity analysis, using methods from matrix calculus. Unlike previous methods, this approach applies not only to linear time‐invariant models but also to time‐varying, subsidized, stochastic, nonlinear and spatial models. It is computationally simple, and does not require calculation of eigenvalues or eigenvectors. The method is presented along with applications to plant and animal populations.