Population dynamics
The sbt model tracks the number of individual SBT in the
population by year (\(y\)), season
(\(s\)), and age (\(a\))
\[ N_{y,s,a} \]
The initial numbers are defined as
\[ N_{y=1,s=1,a} = M_a \]
Recruitment
Recruitment to the model is defined as
\[ R_y = \frac{\alpha B_y}{\beta B_y} \left( 1 - \exp \left( \log (0.5) \frac{B_y}{D B_0} \right) \right) \exp \left( \delta_y - 0.5 \sigma_R^2 \right) \] where \[ R_0 = \frac{B_0}{\sum_a N_{y=1,s=1,a} \phi_{y,a}} \\ \alpha = \frac{4 h R_0}{5 h - 1} \\ \beta = \frac{B_0 (1-h)}{5 h - 1} \\ \delta_y \sim N \left( 0, \sigma_R^2 \right) \]