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

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

Implements the method of Dennis et al. (1991), as described in Morris and Doak (2002)

1 2	count.DI.PVA(Nt, Yeart=seq(along=Nt), Nc=Nt[length(Nt)], Nx=1, year.max=100, nboot=0, alpha=0.05, meas.err=c("none","simple"), Nt.se=NULL, ...)

`Nt`	Vector containing the time series of population abundance 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.
`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.
`meas.err`	Is there measurement error in the census data? If not, set `meas.err="none"` (the default); `meas.err="simple"` uses eq. (5.5) in Morris and Doak (2002) to correct the estimatee of the sampling variance.
`Nt.se`	Standard errors of each of the population estimates. Must be specified if `meas.err="simple"`.
`...`	Additional plotting parameters.

Implements the method of Dennis et al. (1991), as described in Morris and Doak (2002). If the censuses are not evenly spaced in time, then the parameters (mu and sigma2) are estimated using the regression method.

If nboot=0, then all the components related to the confidence intervals are set to NULL. Otherwise, nonparametric bootstrap is performed: either the rt values or the (x,y) pairs for the regression are sampled with replacement for each bootstrap replicate.

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

When correcting for sampling errors, the smallest allowable value of sigma2 is 0.001. Smaller values result in numerical errors in the inverse Gaussian function. This correction only works if you have a continuous time series – I'm not sure how to do the correction when using the regression approach to estimate mu and sigma2.

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)

Dennis, B., Munholland, P. L. and Scott, J. M. (1991) Estimation of growth and extinction parameters for endangered species. Ecological Monographs 61, 115–143.

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

pinvGauss for the important part of the computation; for a description of the components of the returned object see ext.risk.

## Load the grizzly bear data
data(grizzly)

## Run the PVA with the defaults, plotting risk on a log scale, and print the result
count.DI.PVA(grizzly$N, log='y')

## Specify some non-default parameters, and get confidence intervals
grizzly.ext <- count.DI.PVA(grizzly$N, Nx=20, Nc=50, nboot=1000, year.max=500)
plot(grizzly.ext)
grizzly.ext