vitalsim: Stochastic vital rate simulations

In popbio: Construction and Analysis of Matrix Population Models

Stochastic vital rate simulations

Description

Calculates the extinction time CDF and stochastic growth rate by sampling vital rates from a beta, stretched beta, or lognormal distribution and includes within-year, auto- and cross-correlations

Usage

vitalsim(
  vrmeans,
  vrvars,
  corrin,
  corrout,
  makemx,
  n0,
  yrspan,
  Ne = 500,
  tmax = 50,
  runs = 500,
  vrtypes = NULL,
  vrmins = NULL,
  vrmaxs = NULL,
  sumweight = NULL
)

Arguments

vrmeans	means of vital rates
vrvars	variance of vital rates
corrin	within year correlation
corrout	between year correlations
makemx	a function that creates a square projection matrix from a vector of vrmeans
n0	initial population vector
yrspan	the number of years of correlations to build into the M12 matrix
Ne	quasi-extinction threshold
tmax	latest time to calculate extinction probability, default 50
runs	the number of trajectories, default is 500. 1000 is recommended
vrtypes	identifies the distribution for each rate in vrmeans where 1 =beta, 2 = stretched beta, 3 = lognormal, default is all ones
vrmins	minimum value for each vital rate; use zeros for rates that are not stretched betas, default is all zeros
vrmaxs	maximum value for each vital rate; use zeros for rates that are not stretched betas, default is all zeros
sumweight	a vector of weights, with 0 to omit a class and 1 to include it when computing the summed density to compare to the quasi-extinction threshold, default is to include all classes

Details

Vital rates used must be either fertility values or binomial probabilities, i.e., probabilities for events with only two possible outcomes (such as survival). Means and variances of the vital rates should preferably be corrected to remove sampling errors and demographic stochasticity. Note that this version of the function does not simulate demographic stochasticity and is density-independent.

Value

Plots a histogram of log stochastic growth rates and the cumulative probability of quasi-extinction and returns a list with 4 items:

detLambda	the deterministic population growth rate computed from the mean matrix
stochlambda	the mean stochastic growth rate with 95% confidence intervals.
logLambdas	a vector of all log stochastic growth rates in first plot
CDFExt	a vector of cumulative probabilities of quasi-extinction in second plot

Note

The correlation matrices for Hudsonia in Morris and Doak 2002 include some correlations > 1. A corrected set of correlations was sent by D. Doak on 8/4/2007. Therefore the results from the simulation below are different than the book.

Author(s)

Original MATLAB code from Box 8.10 in Morris and Doak (2002). Adapted to R by Patrick Nantel, 12 July 2005

See Also

hudmxdef, hudvrs and hudcorrs

Examples

## set vrtypes
hudvrtypes <- c(rep(1,13), rep(3,5), rep(1,6))
## run Full model- using 100 runs here for speed
full <- vitalsim(hudvrs$mean, hudvrs$var, hudcorrs$corrin,
 hudcorrs$corrout, hudmxdef, vrtypes=hudvrtypes,
 n0=c(4264,3,30,16,25,5), yrspan=20 , runs=100)
## deterministic and stochastic lambda
full[1:2]
## log stochastic lambda
log(full$stochLambda)
sd(full$logLambdas)
## SKIP the next two simulations- however, sample output is included for plotting
#NO between year correlations so corrout = diag(0,13)  - all zeros
# no.between <- vitalsim(hudvrs$mean, hudvrs$var, hudcorrs$corrin,
# diag(0,13), hudmxdef, vrtypes=hudvrtypes,
# n0=c(4264,3,30,16,25,5), yrspan=20 )
no.between <- list(CDFExt=c(rep(0,40),0.01,0.04,0.12,0.15,
0.20,0.31,0.49,0.58,0.72,0.78))
#NO correlations so corrout = diag(0,13) AND corrin=diag(13) - ones on diagonal
# no.corr<-vitalsim(hudvrs$mean, hudvrs$var, diag(13),
# diag(0,13), hudmxdef, vrtypes=hudvrtypes,
# n0=c(4264,3,30,16,25,5), yrspan=20 )
no.corr <- list(CDFExt=c(rep(0,39),0.03,0.03,0.06,0.12,0.20,
0.30,0.42,0.52,0.65,0.76,0.83))
## Figure 8.3 with corrected correlation matrices for full model
matplot(cbind(a=full$CDFExt, no.between$CDFExt, no.corr$CDFExt), type='l',
 ylim=c(0,1), lty=1:3, col=2:4, lwd=2, las=1,
 xlab="Years into the future", ylab="Cumulative probability of quasi-extinction")
legend(2,1, c("Full model", "No between-year correlations", "No correlations"),
 lty=1:3, col=2:4, lwd=2)

popbio documentation built on May 29, 2024, 4:35 a.m.