popbio (version 2.8)

multiresultm: Incorporate demographic stochasticity into population projections

Description

Generates multinomial random numbers for state transitions and lognormal or binomial (for clutch size=1) random numbers for fertilities and returns a vector of the number of individuals per stage class at t+1.

Usage

multiresultm(n, T, F, varF = NULL)

Value

a vector of the number of individuals per class at t+1.

Arguments

n

the vector of numbers of individuals per class at t

T

a transition T matrix

F

a fertility F matrix

varF

a matrix of inter-individual variance in fertilities, default is NULL for simulating population where clutch size = 1, so that fertilities give the probabilities of birth

Author

Patrick Nantel

Details

Adapted from Matlab code in Box 8.11 in Morris and Doak (2002) and section 15.1.3 in Caswell (2001)

References

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

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

Examples

x <- splitA(whale)
whaleT <- x$T
whaleF <- x$F
multiresultm(c(1,9,9,9),whaleT, whaleF)
multiresultm(c(1,9,9,9),whaleT, whaleF)
## create graph similar to Fig 15.3 a
reps <- 10    # number of trajectories
tmax <- 200   # length of the trajectories
totalpop <- matrix(0,tmax,reps)  # initializes totalpop matrix to store trajectories
nzero <- c(1,1,1,1) # starting population size
for (j in 1:reps) {
   n <- nzero
   for (i in 1:tmax) {
      n <- multiresultm(n,whaleT,whaleF)
      totalpop[i,j] <- sum(n)
   }
}
matplot(totalpop, type = 'l', log="y",
        xlab = 'Time (years)', ylab = 'Total population')