Glossary

Definitions of mathematical symbols used in FIMS equations.

Population and Recruitment

• \(N_{a,y}\) — Numbers at age \(a\) in year \(y\) (fished)
• \(N^U_{a,y}\) — Unfished numbers at age \(a\) in year \(y\)
• \(N_{a,0}\) — Numbers at age \(a\) in the initial year 0
• \(N^U_{a,0}\) — Unfished numbers at age \(a\) in the initial year 0
• \(R_0\) — Unfished equilibrium recruitment
• \(R_y\) — Recruitment in year \(y\)
• \(\log R_0\) — Natural log of unfished equilibrium recruitment
• \(\log devs\) — Natural log recruitment deviations (see log_devs.hpp)

Mortality

• \(M\) — Natural mortality rate (yr \(^{-1}\))
• \(F_{f,y}\) — Fishing mortality for fleet \(f\) in year \(y\) (yr \(^{-1}\))
• \(F_{f,a,y}\) — Fishing mortality for fleet \(f\) at age \(a\) in year \(y\) (yr \(^{-1}\))
• \(Z_{a,y}\) — Total mortality at age \(a\) in year \(y\), \(Z = M + F\) (yr \(^{-1}\))
• \(S_f(a)\) — Selectivity for fleet \(f\) at age \(a\)
• \(f_y\) — F multiplier in year \(y\)

Biomass

• \(B_y\) — Total biomass in year \(y\)
• \(B^U_y\) — Unfished biomass in year \(y\)
• \(SB_y\) — Spawning biomass in year \(y\)
• \(SB^U_y\) — Unfished spawning biomass in year \(y\)
• \(SB^U_0\) — Unfished spawning biomass in the initial year 0
• \(\text{ratio}_y = SB_y / SB^U_0\) — Spawning biomass ratio in year \(y\)

Stock–Recruitment (Beverton–Holt)

• \(h\) — Steepness, recruitment relative to \(R_0\) at 20% of \(SB^U_0\); range (0.2, 1.0]
• \(\phi_0\) — Spawning biomass per recruit in the initial year 0
• \(SB_{y-1}\) — Spawning biomass in the previous year

Growth

• \(w_a\) — Weight at age \(a\) (mt)

Catch and Landings

• \(C_{f,a,y}\) — Catch in numbers for fleet \(f\) at age \(a\) in year \(y\)
• \(CW_{f,y}\) — Catch weight for fleet \(f\) in year \(y\) (mt)
• \(CW_{f,a,y}\) — Catch weight for fleet \(f\) at age \(a\) in year \(y\) (mt)
• \(q_{f,y}\) — Catchability coefficient for fleet \(f\) in year \(y\)

Index of Abundance

• \(IN_{f,y}\) — Index numbers for fleet \(f\) in year \(y\)
• \(IN_{f,a,y}\) — Index numbers for fleet \(f\) at age \(a\) in year \(y\)
• \(IW_{f,y}\) — Index weight for fleet \(f\) in year \(y\) (mt)
• \(IWAA_{a,y}\) — Index weight at age \(a\) in year \(y\)
• \(INAA_{a,y}\) — Index numbers at age \(a\) in year \(y\)

Index Variables

• \(a\) — Age
• \(y\) — Year
• \(t\) — Time step (sometimes used interchangeably with \(y\))
• \(f\) — Fleet

Statistical

• \(\sigma\) — Standard deviation; sd

Common Abbreviations

• NAA — Numbers at age
• SSB — Spawning stock biomass
• SBPR — Spawning biomass per recruit
• EWAA — Empirical weight at age
• BH — Beverton–Holt
• LPDF — Log probability density function
• LPMF — Log probability mass function