Catch, Landings, and Discards

AGEPRO calculates catch at age for each fleet using the Baranov catch equation (Quinn II and Deriso 1999). Catch represents the portion of the population vulnerable to harvest as determined by selectivity and mortality at age. The catch of age-\(a\) fish by fleet \(v\) in year \(t\) is

\[ C_{a,v}(t)= \frac{F_{a,v}(t)}{M_a(t)+F_{a,v}(t)}{\Bigl[ 1-e^{-M_a(t)-F_{a,v}(t)}\Bigr]} \cdot N_a(t) \tag{6}\label{eq:6} \]

To account for discards, let \(d_{a,v}(t)\) be the proportion of age-\(a\) fish discarded by fleet \(v\) in year \(t\); \(w_{L,a,v}(t)\) and \(w_{D,a,v}(t)\) are the mean landed and discarded weights at age. Then the total landed and discarded weights by fleet \(v\) in year \(t\) are

\[ L_v(t)=\sum\nolimits_{a=1}^{A} {\Bigl[ 1 - d_{a,v}(t) \Bigr]} \cdot C_{a,v}(t) \cdot w_{L,a,v}(t) \tag{7}\label{eq:7} \]

\[ D_v(t) = \sum\nolimits_{a=1}^{A}d_{a,v}(t) \cdot C_{a,v}(t) \cdot w_{D,a,v}(t) \tag{8}\label{eq:8} \]

Quinn II, Terrance J, and Richard B Deriso. 1999. Quantitative Fish Dynamics. Oxford University Press, New York, NY. https://doi.org/10.1093/oso/9780195076318.001.0001.