スイッチング捕食と天敵特異的防御がもたらす食物網

Maximal yields from
multispecies fisheries systems:
Rules for systems with multiple
trophic levels
Hiroyuki Matsuda (Yokohama Nat’l Univ.)
Peter A. Abrams (Univ. Toronto)
1
Kyoto Declaration and Plan of Action on the
Sustainable Contribution of Fisheries to Food
Security in 1992 (FAO)
• Article 14 “When and where
appropriate, consider harvesting
multiple trophic levels in a manner
consistent with sustainable
development of these resources”.
http://www.fao.org/fi/agreem/kyoto/kyoe.asp
2
Prey-predator model for
“sardine” x and “tuna” y
• dx/dt = (r - a x - b y - f) x
• dy/dt = (-d + e b x - g) y
• Maximize total yield
fx+pgy at the equilibrium
3
• Optimal
solution is either
• to catch sardine
after tuna goes
extinct; or
• to catch tuna
only.
Fishing effort on predator fy
Paradox of Kyoto Declaration
Fishing effort on prey 4fx
Examples of biological community at
MSY (Matsuda & Abrams in review)
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
5
Examples of biological community at
MSY (Matsuda & Abrams in review)
Solution maximizing total yield from community
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
6
Examples of biological community at
MSY (Matsuda & Abrams in review)
Solution maximizing total yield from community
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
7
Examples of biological community at
MSY (Matsuda & Abrams in review)
Solution maximizing total yield from community
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
8
Examples of biological community at
MSY (Matsuda & Abrams in review)
Solution maximizing total yield from community
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
9
Examples of biological community at
MSY (Matsuda & Abrams in review)
Solution maximizing total yield from community
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
10
Examples of biological community at
MSY (Matsuda & Abrams in review)
Solution maximizing total yield from community
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
11
Examples of biological community at
MSY (Matsuda & Abrams in review)
Solution maximizing total yield from community
MSY solution often reduces species and links;
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
12
Examples of biological community at MSY
(Matsuda & Abrams in review)
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
13
Examples of biological community at MSY
(Matsuda & Abrams in review)
Constrained MSY that guarantee coexistence
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
14
Examples of biological community at MSY
(Matsuda & Abrams in review)
Constrained MSY that guarantee coexistence
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
15
Examples of biological community at MSY
(Matsuda & Abrams in review)
Constrained MSY that guarantee coexistence
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
16
Examples of biological community at MSY
(Matsuda & Abrams in review)
Constrained MSY that guarantee coexistence
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
17
Examples of biological community at MSY
(Matsuda & Abrams in review)
Constrained MSY that guarantee coexistence
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
18
Examples of biological community at MSY
(Matsuda & Abrams in review)
Constrained MSY that guarantee coexistence
exploit more species, more trophic levels.
5
5
4
1
5
4 5 6
4
4
3
2
6
5
4
3
(e)
6
6
6
(d)
(c)
(b)
(a)
3
3
1
2
1
3
2
1
2
1
2
19
Examples of biological community at MSY
(Matsuda & Abrams in review)
Constrained MSY that guarantee coexistence
exploit more species, more trophic levels.
(d)
(c)
(b)
(a)
6
6
6
5
5
4
1
100%
5
4 5 6
4
4
3
2
6
5
4
3
(e)
3
3
1
92%
2
3
1
2
61%
1
2
12%
1
2
6% 20
Conclusion of story 2
• MSY theory does not guarantee
species coexistence
• Fisheries must take care of
biodiversity conservation explicitly
= Foodweb constraint to reconciling
fisheries with conservation
21
Requiem to Maximum
Sustainable Yield Theory
surplus production
• Ecosystems are uncertain, nonequilibrium and complex.
• MSY theory ignores all the three.
• Does MSY theory
guarantee species
persistence?
- No!!
22
Stock abundance
Feedback control in fishing effort
is powerful...
dE U N  N *


dt
A straw man says;
• Even though the MSY
level is unknown, the
feedback control
stabilizes a broad
range of target stock
level.
f(N)
dN  f ( N )  qEN
dt
Stock size N
23
Feedback control in fishing effort
is powerful...
dE U N  N *


dt
dN  f ( N )  qEN
dt
N*
f(N)
A straw man says;
• Even though the MSY
level is unknown, the
feedback control
stabilizes a broad
range of target stock
level.
Stock size N
24
Feedback control in fishing effort
is powerful...
dE U N  N *


dt
dN  f ( N )  qEN
dt
N*
f(N)
A straw man says;
• Even though the MSY
level is unknown, the
feedback control
stabilizes a broad
range of target stock
level.
Stock size N
25
Feedback control in fishing effort
is powerful...
dE U N  N *


dt
dN  f ( N )  qEN
dt
N*
f(N)
A straw man says;
• Even though the MSY
level is unknown, the
feedback control
stabilizes a broad
range of target stock
level.
Stock size N
26
Feedback control with community interactions also
result in undesired outcomes.
(M & A in preparation)

dNi 
  ri   a ji N j  qei  Ni
dt 
j

9
10
8
r = (0.454,1.059,1.186,0.247,-0.006,-0.028,-0.059,-0.704,-0.308,-0.238)
A = (aji) =
1.
0.74
0.19
0.31
0.
0.
0.
0.
0.7
0.46
0.74
1.
0.87
0.08
0.46
0.66
0.48
0.73
0.84
0.
0.19
0.87
1.
0.96
0.08
0.14
0.83
0.
0.
0.68
7
0.31
0.08
0.96
1.
0.
0.
0.
0.28
0.
0.88
0.
0.46
0.08
0.
0.1
0.
0.
0.92
0.15
0.84
0.
0.66
0.14
0.
0.
0.1
0.01
0.
0.5
0.69
0.
0.48
0.83
0.
0.
0.01
0.1
0.56
0.
0.
e9 = 0.1, ei = 0
0.
0.73
0.
0.28
0.92
0.
0.56
0.1
0.28
0.
0.7
0.84
0.
0.
0.15
0.5
0.
0.28
0.1
0.
0.46
0.
0.68
0.88
0.84
0.69
0.
0.
0.
0.1
5
6
1
4
2
3
27
Feedback control may result in
extinction of other species (sp. 6).
ratio
de9/dt = u(N9-N9*)
28
Conclusion of story 3
• Single stock monitoring is dangerous
• Target stock level is much more
sensitive than we have considered in
single stock models.
• We must monitor not only stock level of
target species, but also the “entire”
ecosystem.
29

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