Calculating second derivatives of population growth rates for ecology and evolution.

Methods in Ecology and Evolution
Esther Shyu, Hal Caswell

Abstract

1. Second derivatives of the population growth rate measure the curvature of its response to demographic, physiological or environmental parameters. The second derivatives quantify the response of sensitivity results to perturbations, provide a classification of types of selection and provide one way to calculate sensitivities of the stochastic growth rate. 2. Using matrix calculus, we derive the second derivatives of three population growth rate measures: the discrete-time growth rate λ, the continuous-time growth rate r = log λ and the net reproductive rate R0, which measures per-generation growth. 3. We present a suite of formulae for the second derivatives of each growth rate and show how to compute these derivatives with respect to projection matrix entries and to lower-level parameters affecting those matrix entries. 4. We also illustrate several ecological and evolutionary applications for these second derivative calculations with a case study for the tropical herb Calathea ovandensis.

References

Oct 18, 2000·Biological Reviews of the Cambridge Philosophical Society·J E Brommer
Oct 29, 2003·The American Naturalist·Shripad TuljapurkarJohn B Pascarella
Nov 9, 2004·The Cancer Journal·Ellen T MatloffChristina M Chimera
Sep 2, 2005·Journal of Evolutionary Biology·D Waxman, S Gavrilets
Oct 15, 2005·The American Naturalist·C V Haridas, Shripad Tuljapurkar
Jan 6, 2007·Ecology Letters·Hal Caswell
May 10, 2008·Theoretical Population Biology·David CarslakeDave J Hodgson
Jul 16, 2008·Theoretical Population Biology·Dominic McCarthyDave Hodgson
Aug 1, 1995·Trends in Ecology & Evolution·E D BrodieF J Janzen
Jul 7, 2011·Journal of Theoretical Biology·Matthew D Herron, Michael Doebeli
Jun 7, 2013·The Journal of Ecology·Hal Caswell, Roberto Salguero-Gómez
Nov 1, 1983·Evolution; International Journal of Organic Evolution·Russell Lande, Stevan J Arnold
Sep 1, 1989·Evolution; International Journal of Organic Evolution·Patrick C Phillips, Stevan J Arnold

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Citations

Feb 24, 2016·Ecology and Evolution·Esther Shyu, Hal Caswell
Aug 31, 2019·Journal of Mathematical Biology·Arnaud Z Dragicevic

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Software Mentioned

atlab
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