lamDiff_symmetric {exactLTRE}

Difference in lambda, with the mean as baseline

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 their mean values across the provided matrices. 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 observed matrix 1 - observed matrix 2, where the provided matrices are ordered [observed matrix 1, observed matrix 2].

Usage

lamDiff_symmetric(Aobj, which.fixed = NULL)

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 only use the first two.

which.fixed

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

Details

This function differs from lamDiff because it uses the mean matrix as the baseline. So fixed parameters are set to their mean values. In lamDiff, the fixed parameters would be set to their respective values given by the baseline matrix.

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).

Value

A single value for the difference in lambda.

See Also

lamDiff lamVar

Examples

Aobs1<- matrix(data=c(0,0.8,0, 0,0,0.7, 5,0,0.2), nrow=3, ncol=3)
Aobs2<- matrix(data=c(0,0.9,0, 0,0,0.5, 4,0,0.3), nrow=3, ncol=3)
A_all<- list(Aobs1,Aobs2)
diff_all_vary<- lamDiff_symmetric(A_all)
diff_fert_vary<- lamDiff_symmetric(A_all, which.fixed=c(2,6,9))