budmoth: Larch budmoth model POMPs with real and simulated data.

In kingaa/pompExamples: Additional POMP Examples

Description

pompExample(budmoth.sim) constructs a pomp object containing the larch budmoth model and simulated budmoth density, parasitism rate, and food quality (needle-length) data. Four datasets, representing four distinct parameter regimes, are available.

The model has three state variables:

1. Q_t (measure of food quality on [0,1])

2. N_t (budmoth density)

3. S_t (fraction of budmoth larvae infected with parasitoids)

There are three observables:

1. \hat Q_t (needle length)

2. \hat N_t

3. \hat S_t

State process

Uncorrelated random effects, for t=1,…,T:

α_t \sim \mathrm{LogitNormal}(\mathrm{logit}(α),σ_{α}^2)

λ_t \sim \mathrm{Gamma}(λ,σ_{λ}^2)

a_t \sim \mathrm{LogNormal}(\log(a),σ_{a}^2)

Note: X is \mathrm{LogitNormal}(μ,σ) if \mathrm{logit}(X) is \mathrm{Normal}(μ,σ).

The inverse of \mathrm{logit} is \mathrm{expit}. R functions logit, expit, rlogitnorm, dlogitnorm are defined in pompExamples.

The state process, for t=1,…,T:

Q_{t} = (1-α_{t})\frac{γ}{γ+N_{t-1}} +α_{t}Q_{t-1}

N_{t} = λ_t N_{t-1} (1-S_{t-1})\exp\big\{-gN_{t-1}-δ(1-Q_{t-1})\big\}

S_{t} = 1-\exp≤ft(\frac{-a_tS_{t-1}N_{t-1}}{1+a_twS_{t-1}N_{t-1}} \right)

Measurement process

For t=1,…,T:

\hat Q_t \sim \mathrm{LogNormal}(\log(β_0+β_1Q_t),σ_Q)

\hat N_t \sim \mathrm{LogNormal}(\log(N_t),σ_N)

\hat S_t \sim \mathrm{LogitNormal}(\mathrm{logit}(uS_t),σ_S)

Examples

## three regimes, high and low noise regimes for parasitism and tritrophic
bm <- pompExample(budmoth,envir=NULL)
plot(bm$food)
plot(bm$para1)
plot(bm$para2)
plot(bm$tri)

kingaa/pompExamples documentation built on May 20, 2019, 10:01 a.m.