318
with
14. Dynamics of Multiple Fish Species
tlx;
;=1 j=l
' Y =
k
lllX;
3
10
k
;=1 j=l
(9)
Second , we assume that the effort E
k directed to each population in a rej
gion is proportional to the relative size of that population in the ecosystem,
(0)
with
(1)
;= 1 j = l
as the fraction of population i in spawning stock biomass in region k.
Third, age cohorts are affected similarly by their relative size. Harvest
from large age classes is proportionally larger than harvest from small cohorts with a proportionality of
(12)
Consequently, effort directed to cohort j in population i of region k, E/ , is
j
(3)
This three-stage allocation of effort assumes that fishermen know the relative sizes of spawning stock biomass in each region . However, it does not
require that fishermen have knowledge of the relative sizes of individual
populations in a region or each population's age distribution. The assumption of knowledge about relative population sizes of regions can be justified, in that fishermen typically closely observe the relative sizes of catch of
their competitors fishing in other regions. Throughout the year, the spatial
distribution of fishing effort is based on those observations and fishermen 's
expectations. Expectations of catch are not explicitly dealt with in this
model. Changes in expectations, however, may result in complex spatial
patterns of allocation of effort and catch within the fishery (Allen &
McGlade 1987).
Catch from age class j in population i is calculated as