Calculate index at age — calc

For indices of abundance, the function calculates the numbers vulnerable to the survey.

Usage

calc_index(
  N,
  Z,
  sel,
  na = dim(N)[1],
  nr = dim(N)[2],
  ns = dim(N)[3],
  ni = dim(sel)[2],
  samp = array(1, c(ni, nr, ns)),
  delta = rep(0, ni)
)

Arguments

N: Stock abundance at the beginning of the time step. Array [a, r, s]
Z: Instantaneous total mortality. Array [a, r, s]
sel: Index selectivity. Array [a, i, s]
na: Integer, number of age classes
nr: Integer, number of regions
ns: Integer, number of stocks
ni: Integer, number of indices
samp: Boolean indicates which regions and stocks are sampled by the index. Array [i, r, s]
delta: Fraction of time step when the index samples the population. Vector by i. Set to a negative number (-1) to sample the average population over the course of the time step, i.e. N * (1 - exp(-Z))/Z.

Value

Index at age. Array [a, i, s]

Details

The index is calculated as $$ I_{a,i,s} = v_{a,i,s} \sum_r N_{a,r,s} d_{a,r,s} \times \mathbb{1}(r \in R_i) \mathbb{1}(s \in S_i) $$

If the survey samples at a moment in time, then $$ d_{a,r,s} = \exp(-\delta_i Z_{a,r,s}) $$

Otherwise, if the index samples the population over the duration of the time step, then $$ d_{a,r,s} = (1 - \exp(-Z_{a,r,s}))/Z_{a,r,s} $$

where $R_i$ and $S_i$ denote the regions and stocks, respectively, sampled by index $i$. For example, $R_2 = 1$ denotes that the second index of abundance only samples region 1. These are informed by array samp where samp[i, r, s] = 1 indicates that stock s in region r is sampled by index i.