whale {popbio} | R Documentation |
Transition and Fertility matrices for killer whales
data(whale)
A list with T and F matrices
see Chapter 5 in Caswell (2001)
Brault, S., and H. Caswell. 1993. Pod-specific demography of killer whales (Orcinus orca). Ecology 74:1444-1454.
Caswell, H. 2001. Matrix population models: construction, analysis, and interpretation, Second edition. Sinauer, Sunderland, Massachusetts, USA.
data(whale) A <- whale$T + whale$F A n <- c(4, 38, 36, 22) ## matrix multiplication (see pop.projection) A %*% n A %*% A %*% n ######### section 5.3.1 Age-specific survival ########### # equation 5.35 fundamental.matrix(whale$T)$N # Survivorship plot like figure 5.1 in Caswell. # Note example on page 120 uses matrix powers and not element by element # which is R default. Matrix power is not part of base R, but for simple cases # this works to do A %*% A %*% A %*% A... mp<-function(A,pow){ if(pow==1){A} else{ x<-A for(i in (2:pow)){ A<-x%*%A } } A } ## also use colSums for sum of matrix columns e^T surv<-matrix(numeric(150*4), ncol=4) for(x in 1:150) { surv[x,]<-colSums(mp(whale$T,x)) } ## Just plot first stage column? plot(surv[,1]/surv[1,1], type="l", ylim=c(0,1), las=1, xlab="Age (years)", ylab=expression(paste("Survivorship ", italic(l(x))))) ######### section 5.3.2 Age-specific fertility ########### # equation 5.44 T<- mp(whale$T,20) whale$F %*% T %*% diag(1/colSums(T)) ## Figure 5.2 in Caswell fert<-numeric(200) for(x in 1:200) { T<-mp(whale$T,x) phi<-whale$F %*% T %*% diag(1/colSums(T)) fert[x]<-phi[1,1] } plot(fert, type="l", ylim=c(0,0.07), las=1, xlab="Age (years)", ylab="Age-specific fertility")