blowflies: Nicholson's blowflies.

In pomp: Statistical Inference for Partially Observed Markov Processes

Nicholson's blowflies.

Description

blowflies is a data frame containing the data from several of Nicholson's classic experiments with the Australian sheep blowfly, Lucilia cuprina.

Usage

blowflies1(
  P = 3.2838,
  delta = 0.16073,
  N0 = 679.94,
  sigma.P = 1.3512,
  sigma.d = 0.74677,
  sigma.y = 0.026649
)

blowflies2(
  P = 2.7319,
  delta = 0.17377,
  N0 = 800.31,
  sigma.P = 1.442,
  sigma.d = 0.76033,
  sigma.y = 0.010846
)

Arguments

P	reproduction parameter
delta	death rate
N0	population scale factor
sigma.P	intensity of e noise
sigma.d	intensity of eps noise
sigma.y	measurement error s.d.

Details

blowflies1() and blowflies2() construct ‘pomp’ objects encoding stochastic delay-difference equation models. The data for these come from "population I", a control culture. The experiment is described on pp. 163–4 of Nicholson (1957). Unlimited quantities of larval food were provided; the adult food supply (ground liver) was constant at 0.4g per day. The data were taken from the table provided by Brillinger et al. (1980).

The models are discrete delay equations:

R(t+1) \sim \mathrm{Poisson}(P N(t-\tau) \exp{(-N(t-\tau)/N_{0})} e(t+1) {\Delta}t)

S(t+1) \sim \mathrm{Binomial}(N(t),\exp{(-\delta \epsilon(t+1) {\Delta}t)})

N(t) = R(t)+S(t)

where e(t) and \epsilon(t) are Gamma-distributed i.i.d. random variables with mean 1 and variances {\sigma_P^2}/{{\Delta}t}, {\sigma_d^2}/{{\Delta}t}, respectively. blowflies1 has a timestep ({\Delta}t) of 1 day; blowflies2 has a timestep of 2 days. The process model in blowflies1 thus corresponds exactly to that studied by Wood (2010). The measurement model in both cases is taken to be

y(t) \sim \mathrm{NegBin}(N(t),1/\sigma_y^2)

i.e., the observations are assumed to be negative-binomially distributed with mean N(t) and variance N(t)+(\sigma_y N(t))^2.

Default parameter values are the MLEs as estimated by Ionides (2011).

Value

blowflies1 and blowflies2 return ‘pomp’ objects containing the actual data and two variants of the model.

References

\Nicholson

1957

\Xia

2011

\Ionides

2011

\Wood

2010

\Gurney1980a \Brillinger

1980

See Also

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

More data sets provided with pomp: bsflu, childhood_disease_data, dacca(), ebola, parus

Examples

plot(blowflies1())
plot(blowflies2())

pomp documentation built on Sept. 13, 2024, 1:08 a.m.