\begin {defn}
\textbf{Notation for stock and catch equations}:\\
$N_t $ = Number of fish in a year-class at time $t$, where $t$ is $0 \leq t \leq 1$\\
$N_0$=Number of fish at the start of the year\\
$N_1$=Number of fish at the end of the year\\
$(t_1, t_2)$=Time interval such that $t_1$ is the start of the time interval and $t_2$ is the end of the time interval\\
${\Delta t}$=Change in time between $t_1$ and $t_2$\\
${\Delta N}$=Change in stock size between $t_1$ and $t_2$
\end {defn}

\begin{xmpl}
The following table lists the averages from indices of different year-classes for cod from 1985-1993:\\

\begin {tabular}{r| r r r r r r r r r |r}
Age&2&3&4&5&6&7&8&9&10&Ave 5-10 \\
\hline
Index&904.0&659.2&370.8&121.9&57.0&16.3&5.4&3.0&1.2& \\
Log&6.81&6.49&5.92&4.80&4.04&2.79&1.69&1.09&0.21& \\
\hline
Diff.&&0.32&0.58&1.11&0.76&1.25&1.10&0.59&0.88&0.95 \\\\
\end {tabular}

The conclusion that might be drawn from this is that the total mortality of cod had been about 0.6-1.2 during the period in
question. As will be indicated later, there are, however, reasons for checking thoroughly whether the summations of these
compilations are valid and whether a sensible average is being estimated. The reason, among other things, is that two strong
year-classes appear in some of these numbers but not all of them and have a distorting effect on the overall picture. There is also immigration from Greenland during this period. Therefore, the composition of the year-classes needs to be considered in
addition to the age composition.
\end{xmpl}