calc_index: Calculate index at age

In multiSA: Multi-Stock Assessment

Calculate index at age

Description

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.

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.

Value

Index at age. Array ⁠[a, i, s]⁠

multiSA documentation built on March 21, 2026, 1:06 a.m.