| exactLTRE {exactLTRE} | R Documentation |
Exact 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 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(Aobj, method = "random", maxint = "all", fixed.directional = FALSE)
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. For a
"directional" analyses, one of the provided matrices will serve as the
baseline state (for example, a control or standard-of-reference). In this
case, the matrices need to be ordered as |
method |
Either "random" or "fixed." The default behavior is "random." See details for more information. |
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. |
fixed.directional |
A true/false switch that allows the user to specify whether a directional LTRE should be used. The default behavior is to calculate a symmetric LTRE, where the mean matrix is used as the baseline matrix. See details for more guidance. |
Details
Lambda is the asymptotic population growth rate, defined as the largest eigenvalue of the population projection matrix.
In a one-way fixed design LTRE, the particular treatment levels or conditions faced by a population are of interest, so one-way 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.
A random design LTRE treats the different matrices being compared as random samples from a set of population conditions, without specific focus on the treatments or conditions that each population experienced. This analysis 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.
fixed.directional=FALSE is most appropriate for comparisons where
none of the matrices are appropriate for use as a baseline or
standard-of-reference. For example, if we want to ask which vital rates
drive the difference in population growth rate for two populations of fish
in separate but similar lakes, we want to use a symmetric analysis. In
this case, the difference in lambda is decomposed using the mean matrix as
the baseline. The decomposition is symmetric, meaning that if the treatment
and reference matrix are swapped, the contributions from the vital rates
will be equal in magnitude, but positive contributions will become negative
and vice versa. In this case, it does not matter which order you provide the
matrices in Aobj, but interpretation will require that you pay
attention to the fact that the sum of contributions will be equal to the
observed difference in lambda between the two matrices in Aobj,
evaluated as lambda(A1) - lambda(A2).
fixed.directional=TRUE is most appropriate for comparisons between a
control and treatment population in a controlled experiment, or for other
cases where one of the populations can serve as a standard of reference (for
example, the lowest elevation population, or one near the range center). In
this case, the first matrix in Aobj is used as the baseline. This is
a directional analysis, meaning that if the order in which the two matrices
are provided were to be swapped (switching the baseline matrix and other
observed matrix), the contributions of the vital rates would change. If you
choose a directional analysis, be sure to provide the matrices in
Aobj ordered as [baseline matrix, observed matrix].
We set fixed.directional=FALSE as the default behavior because most
population projection models are built with field-collected data rather than
controlled experiment data.
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 differed or varied for the corresponding entry in the epsilon vector.
epsilon is a vector of contributions to the variance or difference in
lambda due to the observed values of the various life history parameters.
For example, the contribution of adult survival to the Var(lambda) is
determined by setting all parameters except adult survival to their mean
values, and then calculating the variance of lambda across 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_diff<- exactLTRE(list(A1,A2), method='fixed') # contributions to the difference in lambda
cont_var<- exactLTRE(list(A1,A2,A3), method='random') # contributions to the variance of lambda