http://risk.kan.ynu.ac.jp/matsuda/2005/050330Osaka.ppt
多種系におけるフィードバック管理の問
題点
松田裕之（横浜国大・環境情報・リスクマネ
ジメントコース ＆ 高知大・黒潮圏科
学）
Peter A. Abrams（U. of Toronto, Dept. of Zool.)
2003/12/12
1
最大持続生産量理論の幻想
Fallacy of MSY theory
• Ecosystem is fluctuating, uncertain & complex
– MSY theory ignores all of these 3 factors
• fluctuation→adaptive management, public
involvement
• uncertainty→risk management & communication
• complex→ecosystem-based management
資源回復確率
2003/12/12
70-80 年代の漁獲圧なら
90 年代の未成魚乱獲
を続けると
2
二つの制御規則
1. F = f(B) 漁獲係数は資源量の関数
（≒現行のABC決定ルール）
2. dF/dt = f(B) 積分型：資源量が多けれ
ば漁獲係数を上げ、少なければ下げ
る
2003/12/12
3
Feedback control in fishing effort is
powerful...
dE U N  N *


dt
dN  f ( N )  qEN
dt
N*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.
N*
Stock size N
2003/12/12
4
Harvest of prey
(Matsuda & Abrams in press)
dN  r(1 N ) N  fN P  qEN
dt
K
1 hN










dP  d  P  bfN P
1 hN
dt
Catch of prey will
decrease predator,
rather than prey
dP/dt=0
dN/dt=0
In the case of feedback control,
dE
 U (N  S )
dt
2003/12/12
5
If prey is exploited and fishing effort is feedback
control, ...(M & A in preparation)
dP/dt=0
dN/dt=0
dN  r 1 N  N  fCN P  qCEN

dt
K 
1 hCN







bfCN

dP  d  gP 
P
1 hCN 
dt
no adaptation (C is constant)
dE/dt = U(N-N*)
predator P
fishery E
sardine N
2003/12/12
6
Feedback 制御がうまくいくのはごく狭い領域
Prey
Fishing effort
Predator
(b)
(a) (c)
2003/12/12
7
Feedback制御は長
期禁漁や不規則な
挙動をもたらす
(d)(e) (f)
• Feedback control may result in
extinction of either fishery or
predator. Prey
Fishing effort
Predator
2003/12/12
8
Total Allowable Catch rule
乱獲
BF=0
PP
2003/12/12
9
If fishing effort is a function of stock abundance,
• １種系な
らある程
度うまく
いく
2003/12/12
10
Harvest of prey
• 捕食者が絶滅
するまで
Feedback制御
は利かない
Prey
Predator
2003/12/12
11
Notice on feedback control
• 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 species that
interacts with the target species.
2003/12/12
12
２つの食物網
被食者－捕食者系
Prey-predator system
多種系
multi-species system
9
10
P
8
7
N
5
6
1
2003/12/12
4
2
3
13
Feedback control with community
interactions also result in undesired
outcomes. (M & A unpublished)

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)
7
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
2003/12/12
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
14
Feedback control may result in extinction of other
species (sp. 6).
ratio
de9/dt = u(N9-N9*)
2003/12/12
15
Cycle increases average yield.
Stock
Yield
Prey
Predator
2003/12/12
16

資源の非定常性と適応的変化を考慮した最適漁獲モデル