# Lab exercise 4
# Based on example in Chapter 3

# load library that contains many useful functions
library(popbio)

# provide names for the stages
stages=c("seeds","seedlings","saplings","repro.trees","sensc.trees")

# provide the values for the matrix
A=matrix(c
   (0.30, 0.0, 0.0, 100.00, 0.00,
    0.03, 0.3, 0.0,   0.00, 0.00,
    0.00, 0.1, 0.1,   0.00, 0.00,
    0.00, 0.0, 0.2,   0.90, 0.00,
    0.00, 0.0, 0.0,   0.08, 0.82),
   nrow=5,byrow=T,dimnames=list(stages,stages))

# check that matrix is entered correctly
A

# project population forward using a starting population vector
N=c(100,1,0,0,0)
p<-pop.projection(A,N,13)
p

# create table of proportions using built-in R function
prop.table(p$stage.vectors,2)

# plot the proportion in each stage over time
stage.vector.plot(p$stage.vectors, col=2:6)

# plot the lambda values
plot(1:12,p$pop.changes,typ='o',xlab='Time (years)',
  ylab='Population Growth Rate',ylim=c(0,max(p$pop.changes)))

# conduct the eigen analysis
E=eigen.analysis(A)
E
# print out rounded values of aspects of the eigen analysis
round(E$lambda1,4)
round(E$stable.stage,3)
round(E$sensitivities,4)
round(E$elasticities,4)

# look at sensitivity values for transitions = 0
E2=eigen.analysis(A, zero=FALSE)
round(E2$sensitivities,4)

# Calculate net reproductive rate
net.reproductive.rate(A)

# Calculate generation time
generation.time(A)

# Calculate time spent in each stage class and 
#  the mean and variance of the time to death
#  based on the survival data in the matrix
fundamental.matrix(A)