exactLTRE (version 0.1.2)

lamDiff: Difference in lambda

Description

In population projection matrices, the eigenvalue with the largest magnitude is the asymptotic population growth rate, referred to as lambda. This function calculates the difference in lambda between two population projection matrices, which must have the same dimensions. This function also has the option to hold some of the vital rates at the value in the baseline matrix. The resulting calculation is the difference in lambda when all the non-fixed vital rates are varying. For example, if all the vital rates are held fixed except for adult fertility, then the output is the difference in lambda due to difference in adult fertility. The difference is taken as \(baseline matrix - observed matrix\), and the function assumes that the provided matrices are ordered [baseline, observed].

Usage

lamDiff(Aobj, which.fixed = NULL)

Value

A single value for the difference in lambda.

Arguments

Aobj

An object containing the population projection matrices to be included in the analysis. It should either be a list, or a matrix where each row is the column-wise vectorization of a matrix. Exactly 2 matrices should be provided. If more than 2 matrices are provided, the function will assume that the first is the baseline and the second is the observed matrix to be compared. Matrices beyond the first two will be ignored.

which.fixed

The column-wise indices (single-value index) of the vital rates to be held at their baseline values across the matrices in Aobj.

Details

This function differs from lamDiff_symmetric because it uses the first matrix in Aobj as the baseline matrix. So fixed parameters are set to the values in the baseline matrix. In lamDiff_symmetric, the fixed parameters would be set to their mean values.

lamDiff is most appropriate for comparisons between a control and treatment population in a controlled experiment or other settings where one of the populations can be considered as a standard-of-reference. lamDiff_symmetric is more appropriate for comparisons where none of the population matrices are obviously suitable as a baseline or standard-of-reference (for example, when comparing a wet and a dry year).

See Also

lamDiff_symmetric lamVar

Examples

Abaseline<- matrix(data=c(0,0.8,0, 0,0,0.7, 5,0,0.2), nrow=3, ncol=3)
Aobserved<- matrix(data=c(0,0.9,0, 0,0,0.5, 4,0,0.3), nrow=3, ncol=3)
A_all<- list(Abaseline,Aobserved)
diff_all_vary<- lamDiff(A_all)
diff_fert_vary<- lamDiff(A_all, which.fixed=c(2,6,9))