classicalLTRE {exactLTRE}

Classical LTRE analysis

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 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. The function we provide here can perform a one-way fixed design LTRE, or a random design LTRE.

Usage

classicalLTRE(Aobj, method = "random")

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.

For one-way fixed design, exactly 2 matrices must be provided, ordered as ⁠[reference matrix, treatment matrix⁠]. For random design, any set of 2 or more matrices can be provided. The set of matrices passed in to this function must all have the same dimensions.

method

Either "random" or "fixed." The default behavior is "random." See details for more information.

Details

Lambda is the asymptotic population growth rate, defined as the largest eigenvalue of the population projection matrix. A one-way fixed design LTRE decomposes the difference in lambda due to differences at each position of the matrices. It should be used when the particular treatment levels are of interest. For a one-way fixed design LTRE, exactly 2 matrices must be provided, ordered as ⁠[reference matrix, treatment matrix⁠]. The matrix of contributions returned from a classical method fixed design LTRE will have the same shape as the provided matrices.

A random design LTRE decomposes the variance in lambda due to variance and covariance in the entries at each position in the matrices. It assumes that the matrices being analyzed come from a population of similar matrices, without the particular treatment levels or population conditions being of interest in themselves. 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 (random design) or difference (one-way fixed design) in lambda. Lambda is the asymptotic population growth rate, defined as the largest eigenvalue of the population projection matrix.

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)
cont_diff<- classicalLTRE(list(A1,A2), method='fixed') # contributions to the difference in lambda
cont_var<- classicalLTRE(list(A1,A2,A3), method='random') # contributions to the variance of lambda