classicalLTRE_random {exactLTRE}

Classical LTRE analysis: random design

Description

Life Table Response Experiments (LTREs) are a method of comparative demographic analysis. The purpose is to quantify how the difference or variance in vital rates (stage-specific survival, growth, and fertility) among populations contributes to the difference or variance in the population growth rate, "lambda." The equations and descriptions for the classical methods of LTRE analysis can be found in Caswell's 2001 textbook.

Usage

classicalLTRE_random(Aobj)

Arguments

Aobj

An object containing all 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. Any set of 2 or more matrices can be provided. The set of matrices passed in must all have the same dimensions.

Details

Lambda is the asymptotic population growth rate, defined as the largest eigenvalue of the population projection matrix.

A random design LTRE decomposes the variance in lambda due to variance and covariance in the entries at each position in the matrices. For a random design LTRE, at least 2 matrices must be provided. The matrix of contributions returned from a classical method random design LTRE will include both first-order terms (due to variance) and interaction terms (due to covariance). Therefore, if the provided matrix is 3x3, the matrix of contributions will be 9x9 (the size of the variance-covariance matrix is the square of the size of the original matrix). The contributions of variances are found on the diagonal of the contribution matrix, and the contributions of covariances are symmetric. So the contribution of covariance between two vital rate parameters is the sum of the two corresponding off-diagonal terms.

The equations and descriptions for the classical methods of LTRE analysis can be found in Caswell's 2001 textbook.

Value

A matrix of contributions to variance in lambda.

Examples

A1<- matrix(data=c(0,0.8,0, 0,0,0.7, 5,0,0.2), nrow=3, ncol=3)
A2<- matrix(data=c(0,0.9,0, 0,0,0.5, 4,0,0.3), nrow=3, ncol=3)
A3<- matrix(data=c(0,0.4,0, 0,0,0.6, 6,0,0.25), nrow=3, ncol=3)
# contributions to the variance of lambda
cont_var<- classicalLTRE(list(A1,A2,A3), method='random')