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the losses of the zooplankton biomass due to unconsumed food, expenditures on
respiration and mortality, respectively. Let us describe the latter three parameters by
relationships
H
Z
¼ h
Z
R
Z
;
T
Z
¼ t
Z
Z
;
M
Z
¼
ðl
Z
þ l
Z
;
1
Z
Þ
Z
;
ð
4
:
30
Þ
ʼ
Z
, and
ʼ
Z,1
are determined empirically for a concrete
where the coef
cients h
Z
,t
Z
,
species of zooplankton.
As seen from (
4.29
), zooplankton is considered as a passive element of the
ecosystem subject to physical processes of transference in space with the motion of
water masses. However, zooplankton is known to migrate mainly in the vertical
direction. In the given model a simple mechanism can be used to simulate the
process of the vertical migration of zooplankton. For this purpose, let us divide the
whole water thickness into two layers: 0
H. The zooplankton
migration between these layers is supposed to depend on food availability. Hence,
some part of zooplankton from the layer [z
0
, H] can satisfy its needs of food in the
layer [0, z
0
]. So, the whole vertical pro
≤
z
≤
z
0
and z
0
< z
≤
le B(
φ
,
ʻ
, z, t) is considered, having taken
into account B
min
.
The coef
cients C
as
(a = p, Z) in the formulas (
4.25
) and (
4.29
) are determined
on the supposition that the consumption of various kinds of food in the s-th trophic
level is proportional to their ef
cient biomasses:
"
#
1
C
as
¼ k
sa
B
a
X
a
2
S
s
k
sa
B
a
;
ð
4
:
31
Þ
where B
a
is an ef
cient biomass of the a-th food, S
s
is the set of trophic subordi-
nation of the s-th component, k
sa
is the proportion coef
cient that determines the
signi
cance of the s-th constituent in the food ration of the a-th element.
According to the scheme in Fig.
4.3
, the equations which describe the dynamics
of the biomass of nekton, detritus feeders, detritus, dissolved organic matter, and
nutrient salts will be
@
r
=@
t ¼ R
r
H
r
T
r
M
r
X
s
2C
r
C
rs
R
s
ð
4
:
32
Þ
t ¼ R
D
H
D
T
D
M
D
X
s
2C
D
@
D
=@
C
Ds
R
s
ð
4
:
33
Þ
@
d
=@
t
þ
V
u
=@u þ
V
k
@
z ¼ M
b
þ
M
D
þ
M
r
þ
M
p
þ
M
Z
þ
H
Z
þ
H
r
þ
H
D
l
d
d
C
dD
R
D
þ
k
2
;u
@
d
=@k þ
V
z
@
d
=@
2
d
=@u
2
2
d
=@k
2
2
d
=@
z
2
ð
4
þ
k
2
;k
@
þ
k
2
;
z
@
:
34
Þ
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