LTRE: Life Table Response Experiment

In popbio: Construction and Analysis of Matrix Population Models

Description

Evaluate sensitivities in a fixed Life Table Response Experiment (LTRE)

Usage

LTRE(trts, ref)

Arguments

trts	A treatment matrix or a list of two or more treatment matrices
ref	A reference matrix

Details

Sensitivities are evaluated midway between the treatment and reference matrices as described in section 10.1.1 in Caswell (2001).

Value

A matrix of contributions (equation 10.4 in Caswell) or a list of matrices with one matrix of contributions per treatment

Note

The examples of a fixed LTRE are from Horvitz, C. C., D. W. Schemske, and H. Caswell. 1997. The relative importance of life-history stages to population growth: prospective and retrospective analyses. Pages 247-271 in S. Tuljapurkar and H. Caswell, editors. Structured population models in marine, terrestrial and freshwater systems. Chapman and Hall, New York. A.L. Angert. 2006. Demography of central and marginal populations of monkeyflowers (Mimulus cardinalis and M. lewisii). Ecology 87:2014-2025.

Author(s)

Chris Stubben

See Also

Check the demo(Caswell) for variance decomposition in a random design using killer whale.

Examples

#######  Calathea ovandensis
calathea_pool <- calathea[['pooled']]
## Create plots like FIGURE 7 in Horvitz et al 1997
plots <- split(calathea[-17], rep(1:4,each=4))
## use Mean matrix since pooled not available by plot
plots <- lapply(plots, mean)
Cm <- LTRE(plots, calathea_pool)
pe <- sapply(Cm, sum)
barplot(pe, xlab="Plot", ylab="Plot effect" , ylim=c(-.25, .25),
col="blue", las=1)
abline(h=0)
box()
title(expression(italic("Calathea ovandensis")))

##YEARS -- split recycles vector
yrs <- split(calathea[-17], 1:4)
yrs <- lapply(yrs, mean)
names(yrs) <- 1982:1985
Cm <- LTRE(yrs, calathea_pool)
ye <- sapply(Cm, sum)
barplot(ye, xlab="Year", ylab="Year effect" , ylim=c(-.25, .25), col="blue", las=1)
abline(h=0)
box()
title(expression(italic("Calathea ovandensis")))
## INTERACTION
Cm <- LTRE(calathea[-17], calathea_pool)
ie <- sapply(Cm, sum)
## minus plot, year effects
ie<- ie - rep(pe, each=4) - rep(ye, 4)
names(ie) <- NULL
names(ie)[seq(1,16,4)] <- 1:4
barplot(ie, xlab="Plot (years 82-83 to 85-86)", ylab="Interaction effect" ,
  ylim=c(-.25, .25), col="blue", las=1)
abline(h=0)
box()
title(expression(italic("Calathea ovandensis")))

#######  Mimulus
## Pooled M. cardinalis reference matrix kindly provided by Amy Angert 1/2/2008.
m_card_pool <- matrix( c(
1.99e-01, 8.02e+02, 5.82e+03, 3.05e+04,
2.66e-05, 7.76e-02, 2.31e-02, 1.13e-03,
7.94e-06, 8.07e-02, 3.22e-01, 2.16e-01,
2.91e-07, 1.58e-02, 1.15e-01, 6.01e-01), byrow=TRUE, nrow=4)
## Population effects using pooled population matrices
card <- subset(monkeyflower,  species=="cardinalis" & year=="pooled")
## split rows into list of 4 matrices
Atrt <- lapply(split(as.matrix(card[,4:19]), 1:4),  matrix, nrow=4, byrow=TRUE)
names(Atrt) <- card$site
Cm <- LTRE(Atrt, m_card_pool)
x <- sapply(Cm, sum)
x
names(x) <- c("BU", "RP", "WA", "CA")
## Plot like Figure 2A in Angert (2006)
op <- par(mar=c(5,5,4,1))
barplot(x, xlab="Population", ylab="", xlim=c(0,6.5), ylim=c(-.4, .4),
  las=1, space=.5, col="blue")
abline(h=0)
mtext(expression(paste(sum(a[ij]), " contributions")), 2, 3.5)
title(expression(paste(italic("M. cardinalis"), " Population effects")))
box()
## and Plot like Figure 3A
x <- matrix(unlist(Cm), nrow=4, byrow=TRUE)
colnames(x) <- paste("a", rep(1:4, each=4), 1:4, sep="")
bp <- barplot(x[1:2,], beside=TRUE, ylim=c(-.2,.2), las=1,
xlab="Transition", ylab="", xaxt='n')
mtext(expression(paste("Contribution of ", a[ij], "to variation in ", lambda)), 2, 3.5)
## rotate labels
text(bp[1,]-0.5, -.22, labels=colnames(x), srt=45, xpd=TRUE)
title(expression(paste(italic("M. cardinalis"), " Range center")))
box()
par(op)

popbio documentation built on March 26, 2020, 8:44 p.m.