exactLTRE_random {exactLTRE}

Exact 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 difference or variance in the population growth rate, "lambda." The exact method of LTRE is based on the principles of functional ANOVA. The equations and descriptions for the exact method will be published in a forthcoming paper, which we will link to.

Usage

exactLTRE_random(Aobj, maxint = "all")

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 random design, any set of 2 or more matrices can be provided. The set of matrices passed in must all have the same dimensions.

maxint

The maximum interaction order to be evaluated. The default input is "all" but this input can take any integer value. If maxint=3, then the output will include contributions terms up to 3-way interactions.

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.

Value

This returns a list object, with 3 items: (1) a vector of the matrix indices where the parameters vary between/among the matrices in Aobj; (2) a list of the indices varying for each of the contribution terms provided; (3) a vector of the contribution terms.If the method is "fixed" then these are contributions to the difference in lambda. If the method is "random" then these are the contributions to the variance in lambda.

indices.varying is a vector with the indices of parameters that vary. The numeric indices count down the columns of a given population projection matrix. For example, in a 3x3 matrix, the (2,2) position would be identified with a 5.

varying.indices.list is a list object, where each entry is a vector containing the indices (matching the indices.varying part of the output) that varied for the corresponding entry in the epsilon vector.

epsilon is a vector of contributions to the variance in lambda due to the observed values of the various life history parameters. For example, the contribution to the variance in lambda of adult survival is determined by setting all parameters except adult survival to their mean values, and then calculating the variance in lambda in this manipulated set of matrices.

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_var<- exactLTRE_random(list(A1,A2,A3), maxint='all') # contributions to the variance of lambda