TY - JOUR

T1 - Calculating the variance of the finite rate of population change from a matrix model in Mathematica

AU - Skalski, John R.

AU - Millspaugh, Joshua J.

AU - Dillingham, Peter

AU - Buchanan, Rebecca A.

PY - 2007/3

Y1 - 2007/3

N2 - The finite annual rate of population increase (λ) is a fundamental demographic parameter that characterizes the relative annual change in animal numbers. Uncertainty in the estimation of λ from demographic population viability analyses (PVAs) has been largely limited to sensitivity analysis, calculating a pseudo-distribution for over(λ, ̂) using Monte Carlo methods, or by use of bootstrap methods. The delta method has been used and suggested by several researchers, but no one has provided the computational means to implement it. In this paper, we present Mathematica code to calculate λ and its variance based on eigenvalue calculations of a Leslie transition matrix. We demonstrate the procedure using data from a Hawaiian hawk (Buteo solitarius) study.

AB - The finite annual rate of population increase (λ) is a fundamental demographic parameter that characterizes the relative annual change in animal numbers. Uncertainty in the estimation of λ from demographic population viability analyses (PVAs) has been largely limited to sensitivity analysis, calculating a pseudo-distribution for over(λ, ̂) using Monte Carlo methods, or by use of bootstrap methods. The delta method has been used and suggested by several researchers, but no one has provided the computational means to implement it. In this paper, we present Mathematica code to calculate λ and its variance based on eigenvalue calculations of a Leslie transition matrix. We demonstrate the procedure using data from a Hawaiian hawk (Buteo solitarius) study.

KW - Delta method

KW - Eigenvalue

KW - Lambda

KW - Leslie matrix

KW - Rate of increase

KW - Wildlife

UR - http://www.scopus.com/inward/record.url?scp=33749519791&partnerID=8YFLogxK

U2 - 10.1016/j.envsoft.2005.12.003

DO - 10.1016/j.envsoft.2005.12.003

M3 - Article

AN - SCOPUS:33749519791

SN - 1364-8152

VL - 22

SP - 359

EP - 364

JO - Environmental Modelling and Software

JF - Environmental Modelling and Software

IS - 3

ER -