Population Harvest Options

The annual harvest level is determined by a user-specified harvest index \(H(t)\), which selects between two control types:

1. Fishing Mortality Control (Effort-Based) – The user specifies fishing mortality \(F_{a,v}(t)\) by fleet and age in year \(t\).
2. Quota Control (Catch-Based) – The user specifies a total annual landings quota \(Q_v(t)\) by fleet (metric tons) in year \(t\).

A mixed harvest strategy may combine both controls within the same projection, allowing quota control in early years and effort-based control in later years. The binary index \(H(t)\) indicates which rule applies in year \(t\):

• \(H(t) = 1 \rightarrow\) quota-based
• \(H(t) = 0 \rightarrow\) fishing-mortality-based.

Effort-Based Harvest

When effort-based management is used, the fishing mortality rate on age-\(a\) fish by fleet \(v\) in year \(t\) is

\[ F_{a,v}(t) = F_v(t) \cdot S_{a,v}(t) \tag{9}\label{eq:9} \] Here \(F_v(t)\) is the fully selected fishing mortality rate for fleet \(v\) and \(S_{a,v(t)}\) is the age-specific selectivity. Landings and discards are then calculated using equations (7) and (8).

Quota-Based Harvest

Under quota control, the fully selected fishing mortality rate that yields the user-specified landings quota \(Q_v(t)\) by fleet must be determined numerically. Ignoring fleet and time subscripts for simplicity, the catch and landings functions are

\[ C_a(F) = \frac{F \cdot S_a}{M_a+F \cdot S_a}{\Bigl[ 1 - e^{-M_a-F \cdot S_a}\Bigr]} \cdot N_a \tag{10}\label{eq:10} \]

As a result, landings can also be expressed as a function of \(F\)

\[ L(F) = \sum\nolimits_{a=1}^{A}{\Bigl[ 1-d_{a}(t) \Bigr]} \cdot C_{a}(F)w_{L,a} \tag{11}\label{eq:11} \]

The value of \(F\) that satisfies \(Q = L(F)\) is found using a robust root-finding algorithm. AGEPRO applies the bisection method, replacing Newton’s method used in earlier versions. Total annual quotas exceeding the exploitable biomass are flagged as infeasible.