PVAClone (version 0.1-0)

pva: Population Viability Analysis

Description

Populatio Viability Analysis (PVA).

Usage

pva(x, model, n.clones, ...)

Arguments

x

Numeric, a time series. Values must be non-negative, missing values are allowed (but first and last observation must not be missing).

model

A 'pvamodel' object returned by a function, see Examples.

n.clones

Numeric, number of clones (possibly a vector).

...

Arguments passed to underlying fitting functions, most notably n.update, n.iter, n.chains, thin, cl. See dcmle.

Value

• An object of class 'pva', see pva-class.

Details

The function implements the first step in PVA, i.e. to fit a given growth model to a population time series data (Nadeem and Lele, 2012). The function employs Lele et. al's (2007, 2010) data cloning (DC) algorithm for computing the maximum likelihood estimates of model parameters along with the corresponding standrad errors. See Solymos (2010) for an R implementaion of the DC algorithm. The growth models currently available in the package PVAClone are Gompertz (gompertz), Ricker (ricker), logistic, theta-logistic, Beverton-Holt and the generalized Beverton-Holt. These models can also be fitted assuming the presence of observation error using the general state-space model formulation (Nadeem and Lele, 2012). Currently the Normal and Poisson observation error models are supported. Normal observation error model: $y_{t} \sim Normal(x_{t}, \tau^2)$, where $y_{t}$ is the estimated abundance on the log scale at time $t$. Poisson observation error model: $O_{t} \sim Poisson(e^{x_{t}})$, where $O_{t}$ is the estimated abundance at time $t$. In addition, missing observations can be accommodated in both with or without observation error cases.

References

Lele, S.R., B. Dennis and F. Lutscher, 2007. Data cloning: easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methods. Ecology Letters 10, 551-563. Lele, S. R., K. Nadeem and B. Schmuland, 2010. Estimability and likelihood inference for generalized linear mixed models using data cloning. Journal of the American Statistical Association 105, 1617-1625. Nadeem, K., Lele S. R., 2012. Likelihood based population viability analysis in the presence of observation error. Oikos. doi: 10.1111/j.1600-0706.2011.20010.x Solymos, P., 2010. dclone: Data Cloning in R. The R Journal 2(2), 29-37. URL: http://journal.r-project.org/archive/2010-2/RJournal_2010-2_Solymos.pdf

See Also

model.select pva-class, pvamodel-class

Examples

data(redstart)
data(paurelia)

## Gompertz
m1 <- pva(redstart, "gompertz", c(5,10))
m2 <- pva(redstart, gompertz("poisson"), c(5,10))
m3 <- pva(redstart, gompertz("normal"), c(5,10))
m1na <- pva(paurelia, "gompertz", c(5,10))
m2na <- pva(paurelia, gompertz("poisson"), c(5,10))
m3na <- pva(paurelia, gompertz("normal"), c(5,10))
m1x <- pva(redstart, gompertz("normal"), 5)
m2x <- pva(redstart, gompertz("normal", fixed=c(tau=0.1)), 5)

## Ricker
m1 <- pva(redstart, "ricker", c(5,10))
m2 <- pva(redstart, ricker("poisson"), c(5,10))
m3 <- pva(redstart, ricker("normal"), c(5,10))
m1na <- pva(paurelia, "ricker", c(5,10))
m2na <- pva(paurelia, ricker("poisson"), c(5,10))
m3na <- pva(paurelia, ricker("normal"), c(5,10))
m1x <- pva(redstart, ricker("normal"), 5)
m2x <- pva(redstart, ricker("normal", fixed=c(tau=0.1)), 5)

m2x
summary(m2x)
coef(m2x)
vcov(m2x)
confint(m2x)
plot(m2x)
plot(as.mcmc.list(m2x, diagn_scale=TRUE))