popbio (version 2.8)

stoch.projection: Project stochastic growth from a sequence of matrices

Description

Projects stochastic growth using whole matrix selection techniques in an independently and identically distributed (iid) environment from a set of two or more projection matrices

Usage

stoch.projection(
  matrices,
  n0,
  tmax = 50,
  nreps = 5000,
  prob = NULL,
  nmax = NULL,
  sumweight = rep(1, length(n0)),
  verbose = FALSE
)

Value

A matrix listing final population sizes by stage class with one iteration per row.

Arguments

matrices

a list with two or more projection matrices

n0

initial population vector

tmax

number of time steps or projection intervals to predict future population size

nreps

number of iterations

prob

a vector of probability weights used by sample for selecting the projection matrices, defaults to equal probabilities

nmax

a maximum number of individuals beyond which population projections cannot exceed. Default is no density dependence

sumweight

A vector of ones and zeros used to omit stage classes when checking density threshold. Default is to sum across all stage classes

verbose

Print comments at start of iteration 1, 100, 200, 300, etc.

Author

Chris Stubben

Details

converted Matlab code from Box 7.3 in Morris and Doak (2002) with nmax option added to introduce simple density dependence

References

Morris, W. F., and D. F. Doak. 2002. Quantitative conservation biology: Theory and practice of population viability analysis. Sinauer, Sunderland, Massachusetts, USA.

Examples

n <- c(4264, 3,30,16,25,5)
names(n) <- c("seed",  "seedlings", "tiny", "small", "medium" , "large")
## use equal and unequal probabilities for matrix selection
x.eq   <- stoch.projection(hudsonia, n, nreps=1000)
x.uneq <- stoch.projection(hudsonia, n, nreps=1000, prob=c(.2,.2,.2,.4))
hist(apply(x.eq, 1, sum), xlim=c(0,5000), ylim=c(0,200), col="green",
breaks=seq(0,5000, 100), xlab="Final population size at t=50", main='')
par(new=TRUE)
## use transparency for overlapping distributions - may not work on all systems
hist(apply(x.uneq, 1, sum), xlim=c(0,5000), ylim=c(0,200), col=rgb(0, 0, 1, 0.2),
 xaxt='n', yaxt='n', ylab='', xlab='', breaks=seq(0,10000, 100), main='')
legend(2500,200,  c("equal", "unequal"),fill=c("green", rgb(0, 0, 1, 0.2)))
title(paste("Projection of stochastic growth for Hudsonia
using equal and unequal probabilities"), cex.main=1)
## initial pop size
sum(n)
abline(v=sum(n), lty=3)