classicalLTRE_fixed {exactLTRE}

Classical LTRE analysis: one-way fixed 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_fixed(Aref, Atreatment)

Arguments

Aref

The population projection matrix of the reference population. Depending on the experimental or observational dataset, this may be the control treatment, the first time period, the unharvested population, etc.

Atreatment

The population projection matrix of a treatment population.

Details

Lambda is the asymptotic population growth rate, defined as the largest eigenvalue of the population projection matrix. A fixed design LTRE decomposes the difference in lambda due to differences at each position of the matrices. For a 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.

In some cases, it may not be obvious how to identify the reference and the treatment matrix. The sum of contributions will be approximately equal to the observed difference in lambda between these two matrices, evaluated as lambda(Atreatment) - lambda(Aref). In cases where it doesn't 'matter' which way you, as a user, input these matrices, it is important to understand how to interpret positive and negative contributions.

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 the difference 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)
cont_diff<- classicalLTRE_fixed(A1, A2) # contributions to the difference in lambda