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environment, M
p
is the dying-off of the phytoplankton cells. The latter parameters
are determined by the following relationships:
; l
p
ð
p
p
Þ
h
g
M
p
¼ max
f
0
ð
4
:
26
Þ
T
p
¼ t
p
p
;
ð
4
:
27
Þ
where t
p
is the speci
c expenditure on respiration of the phytoplankton cells,
ʼ
p
is
the coef
cient of the phytoplankton dying-off,
p
and
ʸ
are the coef
cients charac-
terizing the dependence of the rate of the phytoplankton cells
'
dying-off on their
concentration.
Zooplankton is an important trophic element in the ocean ecosystem. In the
scheme of Fig.
4.3
it is presented by an integral level Z, which implies the presence
of a large number of sub-levels with the intersecting trophic bonds. Zooplankton
consumes phyto- and bacterioplankton. Zooplankton itself feeds a lot of animals, in
the scheme of Fig.
4.3
denoted as nekton r and detritofugs D.
Describe the zooplankton ration by the Ivlev formula:
R
Z
¼ k
Z
1
exp
m
B
;
ð
4
:
28
Þ
;
where B is the biomass of the accessible food B ¼ max 0
f
;
B
B
min
g
k
Z
is a
maximum of the ration with an excess of food,
cient characterizing the
level of starvation. The ration maximum is assumed to be equal to the needs of
food, which
ʽ
is the coef
are determined by the exchange intensity T
1
and a maxi-
mum possible increment P
1
at a given intensity of exchange. Both latter parameters
are related to the coef
—
in turn
—
cient q
2
= P
1
/(P
1
+ T
1
), so that we obtain:
;
k
Z
¼ T
1
u 1
q
2
;
max
where 1/u is the food assimilation, q
2,max
= max q
2
.
The formula (
4.28
) implies that with a small amount of food the ration of zoo-
plankton grows in proportion to the amount of food, but as the ration approaches to a
maximum of k
Z
, its dependence on B diminishes. Since in fact one trophic level never
eats out the other, there is a limitation in (
4.28
) that establishes R
Z
= 0atB
B
min
,
where B
min
is a minimum of the unconsumed food biomass. In (
4.26
) the p parameter
plays the same role, but in the process of the phytoplankton cells
'
mortality.
Thus, a change of the zooplankton biomass follows the law described by the
following differential equation:
≤
@
Z
=@
t
þ
V
u
@
Z
=@u þ
V
k
@
Z
=@k þ
V
z
@
Z
=@
z ¼ R
Z
T
Z
M
Z
H
Z
X
2
Z
@u
2
Z
@k
2
Z
@
ð
4
:
29
Þ
2
2
z
2
C
Zs
R
s
þ
k
2
;u
@
þ
k
2
;k
@
þ
k
2
;
z
@
s
2C
Z
where
ʤ
Z
is a set of the trophic subordination of zooplankton, C
Zs
is the share of the
zooplankton biomass in the food ration of the s-th trophic level, H
Z
, T
Z
, and M
Z
are
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