Selectivity at age and length — conv

Calculate selectivity at age and length from a matrix of parameters.

conv_selpar() converts parameters from log or logit space to real units.
calc_sel_len() calculates selectivity at length.
calc_fsel_age() calculates selectivity at age for fisheries, and coordinates dummy fleets.
calc_isel_age() calculates selectivity at age for indices, and can map selectivity from fisheries or population parameters (e.g, mature or total biomass).

Usage

conv_selpar(x, type, maxage, maxL)

calc_sel_len(sel_par, lmid, type, fsel_type, fsel_len)

calc_fsel_age(
  sel_len,
  LAK,
  type,
  sel_par,
  sel_block = seq(1, length(type)),
  mat,
  a = seq(1, nrow(LAK)) - 1
)

calc_isel_age(
  sel_len,
  LAK,
  type,
  sel_par,
  fsel_age,
  maxage,
  mat,
  a = seq(1, nrow(LAK)) - 1,
  fsel_type,
  fsel_len
)

Arguments

x: Estimated parameters. Matrix [3, f]
type, fsel_type: Character string to indicate the functional form of selectivity. See details below.
maxage: Maximum value of the age of full selectivity
maxL: Maximum value of the length of full selectivity
sel_par: Matrix of parameters returned by conv_selpar()
lmid: Midpoints of length bins for calculating selectivity at length
fsel_len: Selectivity at length matrix for fleets, returned by previous call to calc_sel_len()
sel_len: Selectivity at length matrix returned by calc_sel_len()
LAK: Length-at-age probability matrix. Matrix [a, length(lmid)]
sel_block: Integer vector. Length length(type). See details below.
mat: Maturity at age vector
a: Integer vector of ages corresponding to the rows of LAK (as well as mat)
fsel_age: Matrix returned by calc_fsel_age()

Value

conv_selpar() returns a matrix of the same dimensions as x.

calc_sel_len() returns a matrix [l, f], i.e., [length(lmid), length(type)].

calc_fsel_age() returns a matrix [a, f], i.e., [a, length(sel_block)]

calc_isel_age() returns a matrix [a, i], i.e., [a, length(type)]

Details

Options for argument type include:

functional forms with respect to length: "logistic_length", "dome_length"
functional forms with respect to age: "logistic_age", "dome_age"
for surveys, an integer (f) to map index selectivity at age to fleet f (will be coerced to integer)
"SB" to fix to maturity at age schedule
"B" to fix selectivity to 1 for all ages
"length_x_y" to specify selectivity to 1 between lengths x and y (example: "length_20_50")
"age_x_y" to specify selectivity to 1 between age x and y (example: "age_2_4")
for surveys, "f_x_y" uses selectivity values from fleet f between bins x and y (either length or age depending on definition of selectivity for f) (example: "3_2_4")

Converting selectivity parameters (conv_selpar)

The first row of x corresponds to the length or age of full selectivity: $\mu_f = L_{max}/(1 + \exp(-x_{1,f}))$

The second row of x corresponds to the width of the ascending limb for selectivity: $\sigma_f^{asc} = \exp(x_{2,f})$

The third row of x corresponds to the width of the descending limb for selectivity (if dome-shaped): $\sigma_f^{des} = \exp(x_{3,f})$

Length selectivity (calc_sel_len)

The selectivity at length is $$ s_{\ell} = \begin{cases} \exp(\alpha) & L_{\ell} < \mu_f\\ \exp(\beta) & L_{\ell} \ge \mu_f\\ \end{cases} $$ where $ \alpha = -0.5(L_\ell - \mu_f)^2/(\sigma_f^{asc})^2 $ and $ \beta = -0.5(L_\ell - \mu_f)^2/(\sigma_f^{des})^2 $

Age selectivity (calc_fsel_age)

The equivalent selectivity at age is converted from the length values (sel_len) as $$ s_a = \sum_\ell s_\ell \times \textrm{Prob}(L_{\ell}|a) $$

If selectivity is explicitly in age units, then the values are directly calculated from parameters in sel_par.

Vector sel_block assigns the output selectivity from a different column of the input matrix and facilitates time-varying selectivity in time blocks. For example, sel_block[1] <- 2 means that selectivity values in the first column of the output is based on the second column of the input matrices (sel_len[, 2] or sel_par[, 2]).