The principal factors contributing to fishing effectiveness of a long-line gear during the fishing period may be the soaking duration of the individual hook, the bait loss due to stealing by tuna or other fish, failing by dropping off from hook and shark-damage. The present paper deals with a theoretical treatment regarding the fishing mechanism under some assumptions.
The results are as follows: Letting
C be the numbers of catch per unit gear (basket) at soaking duration
t, then we assume the following equations
dC/
dt=α
Nh-
k1C (1)
and
h=h
0-C-k
1∫
t0Cdt-g(t), (2)
where α is the catchability of the gear, h the number of available hooks for catch per one basket, h
0 the number of hooks per one basket, k
1 the coefficient of failing by dropping off from hook and
g(
t)(=
g0ek2t) the number of bait-loss. We obtain te following solution from Eq. (1) and Eq. (2) in the case of negligibly small value of
k1.
C=
h0[1-exp(-α
Nt)]-
g0/α
N+
k2exp(
k2t) (3)
Further, Eq. (3) is modified by adapting records of fishing effort and catches as follows,
C=h
0[1-exp(-α
Nt)]. (4)
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