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

Abstract

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 '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.