Get encounter rate needed to project a mizerReef model

Calculates the rate $E_i(w)$ at which a predator from group $i$ and weight $w$ encounters food (grams/year). You would not usually call this function directly but instead use getEncounter(), which then calls this function.

Usage

reefEncounter(
  params,
  n,
  n_pp,
  n_other,
  t,
  vulnerable = reefVulnerable(params, n, n_pp, n_other, t, new_rd = reefDegrade(params,
    n, n_pp, n_other, t)),
  ...
)

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.)
vulnerable: A two dimensional array (prey species x prey size) with the proportion of prey vulnerable to being encountered.
...: Unused

Value

A named two dimensional array (predator species x predator size) with the encounter rates.

Predation encounter

The encounter rate $E_i(w)$ at which a predator of species $i$ and weight $w$ encounters food has contributions from the encounter of fish prey and of resources. 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 $\phi(w,w_p)$:

$$ E_i(w) = \gamma_i(w) \int \left( \theta_{ip} N_R(w_p) + \sum_{j} \theta_{ij} V_{ji}(w_p) N_j(w_p) \right) \phi_i(w,w_p) w_p \, dw_p. $$ 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 vulnerability to predation, $V_{ji}(w)$ accounts for protective behavior of the prey. The parameters that control this are set with the setRefuge() function.

The species interaction matrix $\theta_{ij}$ is set with setInteraction() and the resource interaction vector $\theta_{ip}$ is taken from the interaction_resourcecolumn in params@species_params.

Details

The encounter rate is multiplied by $1-f_0$ to obtain the consumption rate, where $f_0$ is the feeding level calculated with getFeedingLevel(). This is used by the project() function for performing simulations.

The function returns values also for sizes outside the size-range of the species. These values should not be used, as they are meaningless.

If your model contains additional components that you added with setComponent() and for which you specified an encounter_fun function then the encounters of these components will be included in the returned value.