growthmodels: Growth models

In psolymos/PVAClone: Population Viability Analysis with Data Cloning

Growth models

Description

Population growth model to be used in model fitting via pva.

Usage

gompertz(obs.error = "none", fixed)
ricker(obs.error = "none", fixed)
thetalogistic(obs.error = "none", fixed)
thetalogistic_D(obs.error = "none", fixed)
bevertonholt(obs.error = "none", fixed)

Arguments

obs.error	Character, describing the observation error. Can be "none", "poisson", or "normal".
fixed	Named numeric vector or list with fixed parameter names and values. Can be used for providing alternative prior specifications, see Details and Examples.

Details

These functions can be called in pva to fit the following growth models to a given population time series assuming both with and without observation error. When assuming the presence of observation error, either the Normal or the Poisson observation error model must be assumed within the state-space model formulation (Nadeem and Lele, 2012). The growth models are defined as follows.

Gompertz (gompertz):

x_{t} = a + x_{t-1} + b x_{t-1} + \epsilon_{t}

where x_{t} is log abundance at time t and \epsilon_{t} \sim Normal(0, \sigma^2).

Ricker (ricker):

x_{t} = x_{t-1} + a + b e^{x_{t-1}} + \epsilon_{t}

where x_{t} is log abundance at time t and \epsilon_{t} \sim Normal(0, \sigma^2.

Theta-Logistic (thetalogistic):

x_{t} = x_{t-1} + r[1-(e^{x_{t-1}}/K)^theta] + \epsilon_{t}

where x_{t} is log abundance at time t and \epsilon_{t} \sim Normal(0, \sigma^2.

Theta-Logistic with Demographic Variability (thetalogistic_D):

x_{t} = x_{t-1} + r[1-(e^{x_{t-1}}/K)^theta] + \epsilon_{t}

where x_{t} is log abundance at time t and \epsilon_{t} \sim Normal(0, \sigma^2 + sigma.d^2, where sigma.d^2 is the demographic variability. If sigma.d^2 is missing or fixed at zero, Theta-Logistic model is fitted instead.

Generalized Beverton-Holt (bevertonholt):

x_{t} = x_{t-1} + r- log[1+(e^{x_{t-1}}/K)^theta] + \epsilon_{t}

where x_{t} is log abundance at time t and \epsilon_{t} \sim Normal(0, \sigma^2.

Observation error models are described in the help page of pva.

The argument fixed can be used to fit the model assuming a priori values of a subset of the parameters. For instance, fixing theta equal to one reduces Theta-Logistic and Generalized Beverton-Holt models to Logistic and Beverton-Holt models respectively. The number of parameters that should be fixed at most is p-1, where p is the dimension of the full model. See examples below and in pva and model.select.

The fixed argument can be used to provide alternative prior specification using the BUGS language. In this case, values in fixed must be numeric. Use a list when real fixed values (numeric) and priors (character) are provided at the same time (see Examples). Alternative priors can be useful for testing insensitivity to priors, which is a diagnostic sign of data cloning convergence.

Value

An S4 class of 'pvamodel' (see pvamodel-class)

Author(s)

Khurram Nadeem and Peter Solymos

References

Nadeem, K., Lele S. R., 2012. Likelihood based population viability analysis in the presence of observation error. Oikos 121, 1656–1664.

See Also

pvamodel-class, pva

Examples

gompertz()
gompertz("poisson")
ricker("normal")
ricker("normal", fixed=c(a=5, sigma=0.5))
thetalogistic("none", fixed=c(theta=1))
bevertonholt("normal", fixed=c(theta=1))

## alternative priors
ricker("normal", fixed=c(a="a ~ dnorm(2, 1)"))@model
ricker("normal", fixed=list(a="a ~ dnorm(2, 1)", sigma=0.5))@model

psolymos/PVAClone documentation built on Feb. 5, 2024, 4:48 a.m.