popbio (version 2.4.3)

LTRE: Life Table Response Experiment

Description

Function to 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

Value

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

Details

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

References

Caswell, H. 2001. Matrix population models: construction, analysis, and interpretation, Second edition. Sinauer, Sunderland, Massachusetts, USA.

Examples

# NOT RUN {
#######  Calathea ovandensis
data(calathea)
calathea_pool<-calathea[['pooled']]

## Create plots like FIGURE 7 in Horvitz et al 1997
##PLOTS
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 
data(monkeyflower)
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)


# }