pomp (version 6.3)

verhulst: Verhulst-Pearl model

Description

The Verhulst-Pearl (logistic) model of population growth.

Usage

verhulst(
  n_0 = 10000,
  K = 10000,
  r = 0.9,
  sigma = 0.4,
  tau = 0.1,
  dt = 0.01,
  seed = 73658676L
)

Value

A ‘pomp’ object containing the model and simulated data. The following basic components are included in the ‘pomp’ object: ‘rinit’, ‘rprocess’, ‘rmeasure’, ‘dmeasure’, and ‘skeleton’.

Arguments

n_0

initial condition

K

carrying capacity

r

intrinsic growth rate

sigma

environmental process noise s.d.

tau

measurement error s.d.

dt

Euler timestep

seed

seed of the random number generator

Details

A stochastic version of the Verhulst-Pearl logistic model. This evolves in continuous time, according to the stochastic differential equation $$dn_t = r\,n_t\,\left(1-\frac{n_t}{K}\right)\,dt+\sigma\,n_t\,dW_t.$$

Numerically, we simulate the stochastic dynamics using an Euler approximation.

The measurements are assumed to be log-normally distributed: $$N_t \sim \mathrm{Lognormal}\left(\log{n_t},\tau\right).$$

See Also

More examples provided with pomp: blowflies, childhood_disease_data, compartmental_models, dacca(), ebola, gompertz(), ou2(), pomp_examples, ricker(), rw2()

Examples

 # takes too long for R CMD check
  verhulst() -> po
  plot(po)
  plot(simulate(po))
  pfilter(po,Np=1000) -> pf
  logLik(pf)
  spy(po)