Calculating second derivatives of population growth rates for ecology and evolution
MetadataShow full item record
KeywordEigenvalues; Hessian matrix; Invasion exponent; Matrix population models; Net reproductive rate; Sensitivity analysis
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. 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. 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. We also illustrate several ecological and evolutionary applications for these second derivative calculations with a case study for the tropical herb Calathea ovandensis.
© The Author(s), 2014. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Methods in Ecology and Evolution 5 (2014): 473–482, doi:10.1111/2041-210X.12179.
The following license files are associated with this item:
Showing items related by title, author, creator and subject.
Stochastic flood and precipitation regimes and the population dynamics of a threatened floodplain plant Smith, Marian; Caswell, Hal; Mettler-Cherry, Paige (Ecological Society of America, 2005-06)Boltonia decurrens is an endangered plant restricted to the Illinois River Valley. Its complex life cycle has evolved in response to the dynamics of the historic flood regime, which has changed dramatically in the last ...
Hunter, Christine M.; Caswell, Hal; Runge, Michael C.; Regehr, Eric V.; Amstrup, Steve C.; Stirling, Ian (Ecological Society of America, 2010-10)The polar bear (Ursus maritimus) depends on sea ice for feeding, breeding, and movement. Significant reductions in Arctic sea ice are forecast to continue because of climate warming. We evaluated the impacts of climate ...
Caswell, Hal; Shyu, Esther (2012-04)Periodic matrix models are frequently used to describe cyclic temporal variation (seasonal or interannual) and to account for the operation of multiple processes (e.g., demography and dispersal) within a single projection ...