The diffusion rate \(d_i(w)\) for species \(i\)
and weight \(w\) has contributions from the encounter of
fish prey and of resource. This is determined by summing over all prey
species and the resource spectrum and then integrating over all prey sizes
\(w_p\), weighted by predation kernel \(\phi(w,w_p)\):
$$
d_i(w) = (1-f_i(w))(\alpha_i(1-\psi_i(w)))^2\gamma_i(w) \int
\left( \theta_{ip} N_R(w_p) + \sum_{j} \theta_{ij} N_j(w_p) \right)
\phi_i(w,w_p) w_p^2 \, dw_p.
$$
Here \(N_j(w)\) is the abundance density of species \(j\) and
\(N_R(w)\) is the abundance density of resource.
The overall prefactor \(\gamma_i(w)\) determines the predation power of the
predator. It could be interpreted as a search volume and is set with the
setSearchVolume() function. The predation kernel
\(\phi(w,w_p)\) is set with the setPredKernel() function. The
species interaction matrix \(\theta_{ij}\) is set with setInteraction()
and the resource interaction vector \(\theta_{ip}\) is taken from the
interaction_resource column in params@species_params.
\(f(w)\) is the feeding level calculated with
getFeedingLevel(). \(\psi(w)\) is the proportion of the available energy
that is invested in reproduction instead of growth, as stored in params@psi.
Usage
getDiffusion(
params,
n = initialN(params),
n_pp = initialNResource(params),
n_other = initialNOther(params),
t = 0,
order = 2,
...
)Arguments
- params
A MizerParams object
- n
A matrix of species abundances (species x size).
- n_pp
A vector of the resource abundance by size
- n_other
A list of abundances for other dynamical components of the ecosystem
- t
The time for which to do the calculation (Not used by standard mizer rate functions but useful for extensions with time-dependent parameters.)
- order
By setting this to integer values above 2 one can get the coefficients of higher-order terms in the expansion of the jump-growth equation. The default is 2, which gives the diffusion rate.
- ...
Unused