08-3_meanbio-weighted-fmort.qmd

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## Fishing Mortality Weighted by Mean Biomass {.unnumbered}

Fishing mortality weighted by mean biomass $F_{\overline{B}}(t)$ in year $t$ is the mean-biomass weighted sum of fishing mortality at age over the age range of $A_L$ to $A_U$ (see [Mean Biomass](#mean-biomass) above). This quantity may be useful for equilibrium comparisons with fishing mortality reference points developed from surplus production models. The computational formula for fishing mortality weighted by mean biomass is

$$
\begin{split}
& F_{\overline{B}}(t) = \frac{\sum\limits_{a=A_L}^{A_u} \overline{B}_a(t) \cdot F_a(t) }{\overline{B}(t)}\\
& \\
& where\ \overline{B}_a(t) = W_{midyear,a}(t)\cdot N_a(t) \cdot  \frac{\bigl(1-\exp(-M_a(t)-F_a(t))\bigr)}{\bigl(M_a(t)+F_a(t)\bigr)}\\
\end{split}
\tag{49}\label{eq:49}
$$

where $F_a(t)$ is the total fishing mortality on age-$a$ fish calculated across all fleets.