Find the proportion of fish vulnerable to being encountered by predators at each time step

This function calculates the proportion of fish that are not hidden in predation refuge and thus vulnerable to being encountered by predators.

Usage

reefVulnerable(params, n, n_pp, n_other, t, new_rd = NULL, ...)

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.)
new_rd: Optional numeric vector of refuge densities for each size bin, as returned by reefDegrade(). If NULL (the default), the refuge density is taken from the current competitive method parameters (no degradation) or computed via reefDegrade() when degradation is active.
...: Unused

Value

Array (species x size) with the proportion of individuals that are not protected from predation by refuge

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().

Find the proportion of fish vulnerable to being encountered by predators at each time step

Usage

Arguments

Value

Setting the refuge profile

See also