Get vulnerability level at in time range t

Returns the proportion of fish at size \(w\) that are not hidden in predation refuge and thus vulnerable to being encountered by predators.

Usage

getDegrade(object, n, n_pp, n_other, time_range, drop = TRUE, ...)

Arguments

object: A MizerParams object or a MizerSim 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
time_range: A numeric or character vector of times. Only the range of values matters, so all saved times between min(time_range) and max(time_range) are selected.
drop: If TRUE then any dimension of length 1 will be removed from the returned array.
...: Unused

Value

If a MizerParams object is passed in, the function returns a numeric vector of the refuge density for each size bin.

     If a `MizerSim` object is passed in, the function returns a two
     dimensional array (time step x refuge size bin) with the refuge
     density calculated at every time step in the simulation. If
     \code{drop = TRUE} then the dimension of length 1 will be
     removed from the returned array.

Details

This function uses reefVulnerable() to calculate the vulnerability to predation.

Setting the refuge profile

 The mizerReef package provides three methods to define the refuge profile.

 \itemize{

 \item **Sigmoidal Method**: \cr

     This method is preferred for data-poor reefs or reefs where the refuge
     distribution is unknown. It is also ideal for systems where only one
     species is expected to be utilizing refuge. The sigmoidal method defines
     a smooth transition in refuge availability around a threshold body size.

     The threshold for refuge can be set in two ways, depending on how your
     refuge data was collected:

     - If `use_dummy_fish_bins = FALSE`, the threshold weight is calculated as:
             \deqn{ W_{i.refuge} = a_i \cdot L_{refuge}^{b_i} }
      where \eqn{a_i} and \eqn{b_i} are the length-weight parameters for species i.

     - If `use_dummy_fish_bins = TRUE`, the weight threshold is:

             \deqn{ W_{refuge} = a_{bar} \cdot L_{refuge}^{b_{bar}} }

      The proportion of fish with access to refuge is then given by:
             \deqn{ R_{j}(w_p) = \frac{r}{1 + e^{\Delta(w - W_{refuge})}} }
     where $r$ is the maximum proportion protected, $\Delta$ is the slope,
     $w$ is body weight, and $W_{refuge}$ is the threshold (species-specific or dummy fish)

     For this method, `method_params` should contain columns named
     `prop_protect` and `L_refuge` that give the values for \eqn{r}
     and the length at which refuge becomes scarce in cm.

 \item **Binned Method**: \cr

     This method is appropriate for theoretical applications
     and does not rely on empirical data. It sets refuge to a constant
     proportion of fish within a given size range. The proportion of fish
     in group \eqn{j} with access to refuge is given by

     \deqn{ R_j(w_p) = r_k ~~~~~~~ w_p ∈ (~w_{k-1}, w_k~] }{
              R_j(w_p) = r_k ~~~~~~~ w_p ∈ (~w_{k-1}, w_k~] }

         where \eqn{r_k} is the proportion of fish with access to refuge in
     size class \eqn{k}.

     For this method, `method_params` should contain columns named
     `start_L` and `end_L` which contain the starting and ending lengths [cm]
     of each size bin and `prop_protect`, the proportion of fish protected
     within each corresponding size bin.

 \item **Competitive Method**: \cr
     This method is appropriate when refuge density data is available for
     the modelled reef. The refuge density describes the distribution of
     refuges \eqn{(no./m^2)} across predefined fish body size categories.
     The proportion of fish in size class \eqn{k} with access to refuge
     is given by

     \deqn{R_{j}(w_p) = \tau \cdot \frac{ \eta_{k} }
                                            { \sum_i \int_{w_{k-1}}^{w-k} N_i(w) \, dw}}{
              R_{j}(w_p) = \tau \eta_{k} /
                          ( \sum_i \int_{w_{k-1}}^{w-k} N_i(w) \, dw ) }

     where \eqn{ \tau } is the proportion of fish with access to refuge that
     are expected to actually utilize  it, \eqn{ \eta_{k}} is the density of
     refuges in size range \eqn{(w_{k-1}, w_k]} and
     \eqn{\sum_{i} \int_{w_{k-1}}^{w_k} N_i(w)~dw} gives the density
     of fish from any group in size range \eqn{(w_{k-1}, w_k]}.
     This represents the density of competitors for refuges in
     size class \eqn{k}.

     For this method, `method_params` should contain columns named
     `start_L`and `end_L` which contain the starting and ending lengths [cm]
     of each size bin and `refuge_density`, the number of refuges available
     in each size bin (no/m^2).

 }

Users can also set a noncomplex reef with no habitat refuge. This option is convenient for finding steady state parameters and is the default when no parameters are provided.

This function checks that the supplied refuge parameters are valid, adds relevant columns to the species_params data frame, and stores refuge parameters in the refuge_params slot of the params object.

Refuge profile parameters can be input in a spreadsheet program and saved as a .csv file. The data can then be read into R using the command read.csv().