calc_Q: Calculate gear catchability
In LeMaRns: Length-Based Multispecies Analysis by Numerical Simulation

Description Usage Arguments Details Value References See Also Examples

Calculates the catchability for each fishing gear.

calc_Q(
  curve = rep("logistic", nfish),
  species = ((0:(length(curve) - 1))%%nfish) + 1,
  max_catchability = rep(1, length(curve)),
  gear_name = paste("gear_", 1:length(curve), sep = ""),
  custom = NULL,
  nsc,
  nfish,
  l_bound,
  u_bound,
  mid,
  eps = 1e-05,
  species_names,
  ...
)

get_Q(curve, species, gear_name, nsc, nfish, l_bound, u_bound, mid, eps, ...)

logistic_catch(species, nsc, nfish, mid, eps, L50 = 50, eta = 0.25, ...)

log_gaussian_catch(species, nsc, nfish, mid, eps, Lmu = 50, Lsigma = 1, ...)

knife_edge_catch(species, nsc, nfish, l_bound, u_bound, Lmin = 50, ...)

`curve`	A character vector of almost any length describing the type of curve to be used to determine the catchability of each species by the fishing gear. By default, `curve` is a character vector of length `nfish` that takes the value `"logistic"` in each element, but it can also take `"log-gaussian"` or `"knife-edge"`. If a custom curve is required for a particular species and/or fishing gear, the curve must be specified in `custom`. See 'Details' for more information.
`species`	A numeric or character vector of the same length as `curve` describing the species that each element of `curve` relates to. By default, `species` is a numeric vector of length `curve` that takes the values `(0:(length(curve)-1))%%(nfish)+1`.
`max_catchability`	A numeric vector of length `curve` describing the maximum catchability for each catchability curve.
`gear_name`	A character vector of the same length as `curve` and `species` describing the fishing gear that each element of `curve` and `species` relates to. By default, `gear_name` is a character vector of length `curve` that takes the value `paste("gear_", 1:length(curve), sep = "")`.
`custom`	An array of dimensions `nsc`, `nfish` and the number of custom catchability curves that are required. `custom` represents the catchability of each species by the gears specified using custom catchability curves. By default, `custom` is set to `NULL`.
`nsc`	A numeric value representing the number of length classes in the model.
`nfish`	A numeric value representing the number of fish species in the model.
`l_bound`	A numeric vector of length `nsc` representing the lower bounds of the length classes.
`u_bound`	A numeric vector of length `nsc` representing the upper bounds of the length classes.
`mid`	A numeric vector of length `nfish` representing the mid-point of the length classes.
`eps`	A numeric value specifying a numerical offset. The default is `1e-5`.
`species_names`	A character vector of length `nfish` that is the name of the species in the same order as the species parameters.
`...`	Vectors of the same length as `curve` representing the parameters of the catchability curves. See 'Details' for more information.
`L50`	A numeric value representing the length at 50% of the maximum catchability of the catchability curve. This is used with the `logistic_catch` function. The default value is 50.
`eta`	A numeric value representing the steepness of the slope of the catchability curve. This is used with the `logistic_catch` function. The default value is 0.25
`Lmu`	A numeric value representing the length at the maximum catchability of the catchability curve. This is used with the `log_gaussian_catch` function. The default value is 50.
`Lsigma`	A numeric value representing the standard deviation of the catchability curve. See 'Details' for more information. This is used with the `log_gaussian_catch` function. The default value is 1.
`Lmin`	A numeric value representing the minimum length that is caught by the catchability curve. This is used with the `knife_edge_catch` function. The default value is 50.

This function allows three different models for catchability, all of which are rescaled so that their maximum catchability is equal to one:

(1) "logistic" is proportional to

1/(1+exp(-eta*(mid-L50)));

(2) "log-gaussian" is proportional to

dlnorm(mid, log(Lmu), Lsigma);

and (3) "knife-edge" is equal to 1 for the length classes indexed by max(which(l_bound<Lmin)):nsc and 0 for all other length classes. This means that all of the individuals in the length class containing Lmin will have a catchability of 1.

In calc_Q the catchability is rescaled so that the maximum catchability is one.

calc_Q returns an array of dimensions nsc, nfish and gear representing the catchability of each species by each of the fishing gears, scaled from 0 to max_catchability.

get_Q returns a catchability curve for a given species and gear scaled from 0 to 1. If an invalid catchability curve is selected, NULL is returned and a warning message is shown.

logistic_catch returns a matrix with dimensions nsc and nfish with all elements set to zero excluding one column that represents the logistic catchability curve for the selected species scaled from 0 to 1.

log_gaussian_catch returns a matrix with dimensions nsc and nfish with all elements set to zero excluding one column that represents the log-gaussian catchability curve for the selected species scaled from 0 to 1.

knife_edge_catch returns a matrix with dimensions nsc and nfish with all elements set to zero excluding one column that represents the knife-edge catchability curve for the selected species scaled from 0 to 1.

Hall, S. J., Collie, J. S., Duplisea, D. E., Jennings, S., Bravington, M., & Link, J. (2006). A length-based multispecies model for evaluating community responses to fishing. Canadian Journal of Fisheries and Aquatic Sciences, 63(6):1344-1359.

Thorpe, R.B., Jennings, S., Dolder, P.J. (2017). Risks and benefits of catching pretty good yield in multispecies mixed fisheries. ICES Journal of Marine Science, 74(8):2097-2106.

dlnorm

# Set up the inputs to the function
nfish <- nrow(NS_par)
nsc <- 32
maxsize <- max(NS_par$Linf)*1.01 # the biggest size is 1% bigger than the largest Linf
l_bound <- seq(0, maxsize, maxsize/nsc); l_bound <- l_bound[-length(l_bound)]
u_bound <- seq(maxsize/nsc, maxsize, maxsize/nsc)
mid <- l_bound+(u_bound-l_bound)/2

# Set up the inputs to the function - species-specific parameters
Linf <- NS_par$Linf # the von-Bertalanffy asymptotic length of each species (cm).
W_a <- NS_par$W_a # length-weight conversion parameter.
W_b <- NS_par$W_b # length-weight conversion parameter.
k <- NS_par$k # the von-Bertalnaffy growth parameter.
Lmat <- NS_par$Lmat # the length at which 50\% of individuals are mature (cm).

# Calculate gear catchability
Qs <- calc_Q(curve=rep("logistic", nfish), species=NS_par$species_names,
             max_catchability=rep(1, nfish), gear_name=NS_par$species_names,
             nsc=nsc, nfish=nfish, mid=mid, l_bound=l_bound, u_bound=u_bound,
             species_names=NS_par$species_names, eta=rep(0.25, nfish), L50=Lmat)

# Calculate logistic catchability for the first species
logistic_catch(species=1, nsc, nfish, mid, eps=1e-5,L50=Lmat[1], eta=0.25)

# Calculate log-gaussian catchability for the first species
log_gaussian_catch(species=1, nsc, nfish, mid, eps=1e-5, Lmu=50, Lsigma=1)

# Calculate knife-edge catchability for the first species
knife_edge_catch(species=1, nsc, nfish, l_bound, u_bound, Lmin=50)