popbio (version 2.8)

vitalsim: 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
)

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

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

Author

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

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.

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)