blowflies {pomp} | R Documentation |

## 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 |

`sigma.d` |
intensity of |

`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

A.J. Nicholson. The self-adjustment of populations to change. *Cold Spring Harbor Symposia on Quantitative Biology* **22**, 153–173, 1957. doi:10.1101/SQB.1957.022.01.017.

Y. Xia and H. Tong. Feature matching in time series modeling. *Statistical Science* **26**, 21–46, 2011. doi:10.1214/10-sts345.

E.L. Ionides. Discussion of “Feature matching in time series modeling” by Y. Xia and H. Tong. *Statistical Science* **26**, 49–52, 2011. doi:10.1214/11-sts345c.

S. N. Wood Statistical inference for noisy nonlinear ecological dynamic systems. *Nature* **466**, 1102–1104, 2010. doi:10.1038/nature09319.

W.S.C. Gurney, S.P. Blythe, and R.M. Nisbet. Nicholson's blowflies revisited. *Nature* **287**, 17–21, 1980. doi:10.1038/287017a0.

D.R. Brillinger, J. Guckenheimer, P. Guttorp, and G. Oster. Empirical modelling of population time series: The case of age and density dependent rates. In: G. Oster (ed.), *Some Questions in Mathematical Biology* vol. 13, pp. 65–90, American Mathematical Society, Providence, 1980. doi:10.1007/978-1-4614-1344-8_19.

### 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*version 5.11.0.0 Index]