# Life Table Response Experiment Evaluate sensitivities in a fixed Life Table Response Experiment (LTRE) ```r LTRE(trts, ref) ``` ## Arguments - `trts`: A treatment matrix or a list of two or more treatment matrices - `ref`: A reference matrix ## Returns 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). ## 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. ## Examples ```r ####### 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) ``` ## See Also Check the `demo(Caswell)` for variance decomposition in a random design using killer whale. ## Author(s) Chris Stubben

LTRE function