Translation Series No.1211

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strength of the stock N pertain to a certain time t. If, however, the
density of population is specified as the mean value for a fishing period
U,thenthe Z-values are not quite correct. The average annual number of
fish amounts to (Beverton and Holt 1957):
= _E_ ( 1 _ e t).
• Here N is the number of fish at the beginning of the period t.
For the years 0 and 1 one obtains; •
° ' '112 ( 1 - e - Z0)
Zo
= -1 (1 - e1)
Z1
The division of the two equations, whereby, according t
•
one sets N 1 = No e. Zo, results in
. --
e—Z)
zn — In + ln
Z1 (1--e-zo) and . on account of (5),
No•, (cfo + M + T)(1,—e--(cf, +M . 11')).
,= In
In (cf t + M + T) (1 — e-(cr.0 m +T))
( 1 ) ,
In order to çalculate Z the second 'term at first approximation
is set equal to 0 and we obtain
cf o + (M+T) = Zo. = In
iNt
. .
One can now calculate c and (M + T) with the values for Z and
1 • Inserting these into (6), one obtains new results for Z, which are
b. 352]
used once more td -obtain improved results for c and (M + T). The three-
to four-fold repetition of this procedure leaàsto constant results (iter •
àtive method).
Beverion and Holt (1957) used the iterative method to calculate
F. If one uses this•equation for the values Of Z and f in Table 54, one
obtains a négativaresult for (M + T). The failure'of the method can have
two causes. Eiiher the changes in Z are not caused or not caused solely '
(6)
. •