count.DD.PVA: Count-Based Density-Dependent PVA
In BruceKendall/PVA: Population viability analysis in R

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Simulation-based method, as described in Morris and Doak (2002)

count.DD.PVA(Nt, Yeart=seq(along=Nt), Nc=Nt[length(Nt)], Nx=1, 
    year.max=100, nsim=1000, nboot=0, alpha=0.05, 
    boot.type=c("nonparametric","parameteric"),
    model=c("Ricker","theta","logistic","Beverton","delay"), 
    enoise=c("normal","resample","DS"),
    par.start=NULL, meas.err=FALSE, ...)

`Nt`	Vector containing the time series of population abundance estimates. Must be yearly estimates.
`Yeart`	Vector of census times; must be the same length as `Nt`. Defaults to a sequence of integers
`Nc`	Current population size. Defaults to the last value of `Nt`
`Nx`	The quasi-extinction threshold. Defaults to 1
`year.max`	The number of years over which to do the projection. Defaults to 100.
`nsim`	Number of replicate stochastic simulations
`nboot`	Number of bootstrap replicates to use for putting confidence intervals on the extinction risk calculations. Defaults to 0.
`alpha`	One minus the desired confidence limits.
`boot.type`	Use parametric or nonparametric bootstrap?
`model`	Type of density-dependence model to use
`enoise`	In stochastic simulations, are the epsilons (environmenatal stochasticity) normally distributed (`enoise="normal"`), incorporate demograhic stochasticity (`enoise="DS"`) or resampled from the observed residuals (`enoise="resample"`)?
`par.start`	Initial estimates of the parameters, useful for difficult nonlinear least squares problems
`meas.err`	Not yet used.
`...`	Additional parameters to pass to plot or nls.

Implements the simulation-based approach to count-based PVA, as described in Morris and Doak (2002: ch. 4). The censuses must be annual. Currently implemented models are Density-independent, Ricker, theta-logistic, logistic, Beverton-Holt, and delay-Ricker.

If nboot=0, then all the components related to the confidence intervals are set to NULL. Otherwise, nonparametric or parametric bootstrap is performed. For nonparametric bootstrap (the default) the (rt, Nt) pairs are sampled with replacement and the regression re-run to get the new parameter estimates. For parametric bootstrap, the parameters are sampled from the multivariate normal distribution defined by the covariance matrix that is returned by lm or nls.

Both approaches have problems. For models that are fit by nls, it is well-nigh impossible to guarantee convergence of the fitting algorthithm on every nonparametric bootstrap replicate; this failure stops the whole program. You can attempt to alleviate this by passing in control parameters (see nls and nls.control), but success is unlikely, especially for models like the theta-logistic that are intrinsically ill-behaved. See Examples for a labour-intensive workaround.

In contrast, parametric bootstrap may generate biologically implausible parameter values, such as negative values of K. This creates programming as well as biological problems, for the resulting simulations tend to blow up. Thus, the program discards any bootstrap replicates that have K < 0; this has the unfortunate side effect that the mean of the bootstrapped parameter values does not equal the original parameter estimates.

The confidence intervals are pointwise estimates at each projection year, and so might not represent any actual extinction curve.

Demographic stochasticity is simulated by regressing the squared residuals on the inverse of population size, and then using this relationship to generate a variance in the epsilons that depends inversly on population size.

Returns an object of class ext.risk. Also displays a plot of the CDF of extinction risk; if nboot>0 then the plot also shows the confidence intervals.

This function assumes that the units of time are years, and that there is at most one census per year. If these are violated, I make no guarantee as to the meaningfulness of the results....

There is currently no testing of the sensibility of the input parameters, so if you get an arcane error message check that your inputs make sense and have correct dimensions.

Bruce E. Kendall (kendall@bren.ucsb.edu)

Morris, W. F. and Doak D. F. (2002) Quantitative Conservation Biology: Theory and Practice of Population Viability Analysis. Sunderland: Sinauer Associates.

sim.Ricker, sim.theta, and sim.logistic, for the simulation models; for a description of the components of the returned object see ext.risk.

## Load the checkerspot butterfly data
data(checkerspot)

## Run a PVA with the Ricker model
jrh.ext <- count.DD.PVA(checkerspot$N, Nx=20, nboot=100)

## Fit the theta-logistic model to the data
rt <- diff(log(checkerspot$N))
Nt <- checkerspot$N[-dim(checkerspot)[1]]
thetalog.nls <- nls(rt ~ mu*(1-(Nt/K)^theta), start=list(mu=1,K=500,theta=1))

## Run the corresponding PVA, using parametric bootstrap
jrh2.ext <- count.DD.PVA(checkerspot$N, Nx=20, nboot=100, boot.type="parametric",
    model="theta", par.start=coef(thetalog.nls))

## To generate nonparametric bootstrap reps for the theta logistic model,
##   first run the following two lines...
base.ext <- count.DD.PVA(checkerspot$N,Nx=20,nboot=0,model="theta")
boot.out <- as.matrix(base.ext$extrisk)  

## Then cut and paste the following four lines repeatedly until you have
##  100 reps.  Each column of boot.out will be a replicate
while (dim(boot.out)[2] < 100) {
    boot.ext <- count.DD.PVA(checkerspot$N,Nx=20,nboot=1,model="theta")
    boot.out <- cbind(boot.out, boot.ext$ext.boot)
}