The goal of exactLTRE is to provide a set of friendly tools to increase use of exact LTRE methods. Life Table Response Experiments are a valuable tool for advancing our knowledge about how stage-specific vital rates influence population dynamics. The results of LTREs also inform conservation goals, by identifying the life stage and vital rate (for example, juvenile survival or adult reproductive success) that had the largest impact on population growth rate in past observations or following a management intervention.

The classical methods of LTRE, presented in the Caswell (2001) textbook, use Taylor expansion approximations to calculate the contributions of vital rates. These classical methods also do not include many interactions terms which may be important. Exact LTRE provides an exact calculation of each contribution term, including interactions terms, by directly calculating the impact on population growth rate of differences or variation in vital rates.

This package includes functions for the classical methods as well as the fANOVA-based exact methods that we introduce. This will allow researchers to use both the methods that are standard in the literature up until now (2021), and the new methods that we encourage as a new standard.

You can install the development version of exactLTRE from GitHub with:

```
# install.packages("devtools")
::install_github("chrissy3815/exactLTRE")
devtools# if that doesn't work, try:
::install_github("chrissy3815/exactLTRE", ref="main") devtools
```

A fixed design LTRE decomposes the difference in population growth rate (“lambda,” i.e. the leading eigenvalue of the population projection matrix) into the contributions from differences in the vital rates, and their interactions.

A fixed design LTRE compares exactly two matrices. This can be done either as a symmetric or directional analysis, and it should match the experimental design for the data collection.

```
library(exactLTRE)
## basic example code
<- matrix(data=c(0,0.8,0, 0,0,0.7, 5,0,0.2), nrow=3, ncol=3)
A1<- matrix(data=c(0,0.9,0, 0,0,0.5, 4,0,0.3), nrow=3, ncol=3)
A2# contributions to the difference in lambda for a directional design
<- exactLTRE(list(A1,A2), method='fixed', fixed.directional=TRUE)
cont_directional# contributions to the difference in lambda for a symmetric design
<- exactLTRE(list(A1,A2), method='fixed', fixed.directional=FALSE) cont_symmetric
```

A random design LTRE decomposes the variance in population growth rate (“lambda,” i.e. the leading eigenvalue of the population projection matrix) into the contributions from (co)variances of the vital rates and their interactions.

A random design LTRE can be used on an unordered list of two or more matrices.

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