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2006/8/28 1
Effects of predator-prey interactions and adaptive change on sustainable
yield
Hiroyuki Matsuda
Yokohama National University
http://risk.kan.ynu.ac.jp/matsuda/2006/060918Fuku.ppt
(Matsuda & Abrams 2004 Can J Fish Aq Sci 61:175-184)
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2006/8/28 2
Can we say goodbye to the MSY theory and a pessimistic view of the state of the world
fisheries?
• FAO suggested that the total world landings do not increase any more.
• The Maximum Sustainable Yield theory always guarantees the stock persistence;
• The adaptive management is one of the best ways against uncertain ecosystems.
• I say the adaptive management sometimes results in undesired outcomes;
• I say the MSY theory does not guarantee coexistence of species = food web constraint;
• 4WFC organizer gave us the title of “getting more fish and reconciling fisheries with conservation”;
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Whales consume fish more than human(Tamura & Ohsumi 1997)
0
50
100
150
200
250
300
Fisherieslanding
Biomass ofWhales
Consumptionby whales
Mill
ion
tonn
es
Tooth whalesBaleen whales
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2006/8/28 4
Wasp-waist is a classic dream...
• Anyway, we need to investigate how to fluctuate the total biomass of small pelagics.
birds seals tunas
copepods krill ....
, is this illusion?
pelagic
sardine/anchovy lantern fish
deep sea
Only 5 to 10 percent of us succeed of the weight-loss industry
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2006/8/28 5
What traits are frequency-dependent?
Freq.-dep. selection may compensate overfishing;
Freq.-indep. selction might accelerate extinctions
Adaptation of any type of bet-hedging ???
• age and size at maturetion
• reproductive effort
• growth rate
• morphology and behavior
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2006/8/28 6
The age and size at maturity of a salmonAre recent smaller & older maturation
phenotypic plasticity?
K. Morita, S. Morita & H. MatsudaCan J Fish Aq Sce
年
体長
5yr old
4yr old
3yr old
69 cm 3.7yr old64 cm 4.2yr old
Kaeriyama 1994
(mm)
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Rule for maturity
Age-dep.
Size dep maturation
mixture
Low growth
High growth
age
Body
length
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0
50
100
300 400 500 600 700 800 900 10000
50
100
0
50
100
0
50
100
0
50
100
0
50
100
体長( mm )
成熟率%個体数
50% 成熟体長平均成熟体長
3 歳
4 歳
5 歳
50% 成熟率
0 1 2 3 4 5 6 70
100
200
300
400
500
600
700
800
年齢
体長
・平均成熟体長 は、 年齢とともに増加
・ 50 %成熟体長 は、 年齢とともに低下
・成長の悪い個体は、 高齢かつ小型で成 熟を開始する
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2006/8/28 10
What age and season should we catch fish?
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2006/8/28 11
Constrained optimiation
0
)()()(0 tdssVsLsFNY
000
)()( NdssLsENPt
• =Y+(P-N0), /F(t)=0,
L(s)/F(t)=-L (s>t) or 0 (s<t)
tdsMsFtL
0))((exp)(
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2006/8/28 12
子供と産卵親魚は大切に•マサバの 1980年代の漁獲圧
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2006/8/28 13
Fisher(1930)Reprodutive value
• ある齢の魚を 泳がせた ときに、将来「 」成長して次世代に貢献する期待産卵量
生存率 × 産卵数(体重)
t
dstL
sLsEtRV
)(
)()()(
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2006/8/28 14
Harvest value• ある齢の魚を 泳がせた ときに、「 」
将来成長して漁獲に貢献する期待漁獲量– (Matsuda et al. 1999 Env. Econ. Pol. St. 2:129-146)
漁獲係数 × 生存率 × 魚価(体重)
t
dssVtL
sLsFtH )(
)(
)()()(
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2006/8/28 15
ミナミマグロは回復するか?Mori et al. Pop.Ecol. 2001
逆ベビーブーム現象
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2006/8/28 16
MSY (Maximum sustainable yield) theory
dN/dt = r(1 – N/K)N – CIf C<Kr2/4, two positive equilibria exist.Kr2/4 is MSY.
MSYOver-fishing will lose future yield.
Stock abundance N
Pro
duct
ion
dN/d
t
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2006/8/28 17
Requiem to Maximum Sustainable Yield Theory
• Ecosystems are uncertain, non-equilibrium and complex.
• MSY theory ignores all the three.
• Does MSY theory guarantee species persistence?- No!!
Stock abundance
surp
lus p
rodu
ctio
n
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2006/8/28 18
Effects of predator-prey interactions on sustainable yield
Sto
ck &
yie
ld
(1 )1
dN r N Pdt
fNNK hN
Prey abundance
PqCEhN
bfCN
C
dPENW
dt
dP m
11),(
C
WV
dt
dC
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2006/8/28 19
Sto
ck &
yie
ld
Fishing effort
Y
P
The effort that The effort that achieves MSY achieves MSY can be close to can be close to
the effort at the effort at which the stock which the stock
collapses. collapses.
Non-Standard relationship betStandard relationship between effort and yieldween effort and yield
Non-Standard relationship between effort and yield
Stock may increase Stock may increase in population size in population size with increasing with increasing fishing effortfishing effort
25min
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Odd MSY curves(M & A 2004)
Fishery may increase its resource abundance.
“Classic” MSY
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Prey-predator cycles decreases average
predator abundance
Prey abundance N Prey abundance N
YieldYield
Yield
Stock P Stock P
Stock P
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2006/8/28 22
Maximal yields from multi-species fisheries systems: rules
for systems with multiple trophic levels.
Matsuda & Abrams 2006 Ecol Appl 16:225-237
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2006/8/28 23
Unconstrained MSY that maximizes the total yield from the community
• We choose fishing effort ei independently;
• 6-species systems including 2 prey
• random matrix with 50% probabilities;
• we seek r having a positive equilibrium;
• price p is 0-1 for prey, 0-10 for predators
• unconstrained MSY that may result in extinction;
• Constrained MSY that satisfies coexistence of all species
1 2
3
5
6
4
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2
54
3
5
3
6
4
4
Some resultant biological communities at MSY (Matsuda & Abrams 2006)
1 2
3
5
6
(b)
1 2
3
5
6
4
(a)
1 2
5
(c)
3
6
4
Solution maximizing total yield from community
MSY solution often reduces species and links;
1 2
6
4
(d)
1
3
6
(e)
2
54
3
54
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2
4 5
3
5
Examples of biological community at MSY (Matsuda & Abrams 2006)
1 2
3
5
6
(b)
1 2
3
5
6
4
(a)
1 2
5
(c)
100% 92% 61% 12% 6%
4
3
6
4
…often exploit more species, more trophic levels.
1 2
6
4
(d)
1
3
6
(e)
Constrained MSY that guarantee coexistence
2
4 5
4
3
6
4
3
5
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2006/8/28 26
Result of (1) unconstrained and (2) constrained MSY
# # extant species at (1)
# exploited sp at (1)
# exploited sp. at (2)
1 4 875 282
2 279 123 244
3 432 2 268
4 198 0 94
5 77 0 60
≧6 10 0 42
mean 3.1 1.1 2.634min
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2006/8/28 27
Conclusion (Matsuda & Abrams 2006 Ecol Appl)
• MSY theory does not guarantee species coexistence
• Fisheries must take care of biodiversity conservation explicitly
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2006/8/28 28
Management of small pelagics
• Kawai H, Yatsu A, Watanabe C, Mitani T, Katsukawa T, Matsuda H (2002) Recovery policy for chub mackerel stock using recruitment-per-spawning. Fish Sci 68:961-969.
• Matsuda H, Katsukawa T (2002) Fisheries Management Based on Ecosystem Dynamics and Feedback Control. Fish Oceanogr 11: 366-370
• Matsuda H, Kishida T, Kidachi, T (1992) Optimal harvesting policy for chub mackerel in Japan under a fluctuating environment. Can J Fish Aq Sci 49:1796-1800.
• Matsuda H, Wada T, Takeuchi Y, Matsumiya Y (1992) Model analysis of the effect of environmental fluctuation on the species replacement pattern of pelagic fishes under interspecific competition. Res Pop Ecol 34:309-319.
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Species Replacement of Pelagic FishesC
atch
in J
apan
(10
00 m
t) AnchovyHorse mackerelsPacific sauryChub mackerelSardine
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Target switching of multispecies fisheries (Katsukawa & Matsuda, Fish.Res. 2002)
Policy 1 (no switching; NSF)Fishing effort Ei= ei/3 (constant)Or Ei = Ei(xi) (independent of xj)
Policy 2 (switching; SF)Ei= ei xi/(xi) (∝stock abundance)Fishers focus on relatively abundant fish species.
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Switching increases & stabilizes total catch, save it at low levels
0
0.1
0.2
0.3
0.4
0.5
900 910 920 930 940 950 960 970 980 990
Time
Cat
ch
Switching
No Switching
0
0.1
0.2
0.3
0.4
0.5
900 910 920 930 940 950 960 970 980 990
Time
Cat
ch
Switching
• If stock fluctuations of alternative fish are negatively correlated or independent
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Cyclic Advantage Hypothesis based on ecosystem approach (species interaction)
The next dominant to sardine is anchovy –Yes! As I predicted
The second next is chub mackerelMany people agree now
anchovy, Pacific saury, jack mackerel
mackrelsardine
Matsuda et al. (1992) Res. Pop. Ecol. 34:309-319
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Large fluctuation of recruitmentin chub mackerel (Kuroshio stock)
Strong year classes appeared twice
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Immatures were heavily caught before the age at maturity
1970s 1980s 1990s 1993-
%immatures 65.0% 60.0% 87.0% 90.6%
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Future of Pelagic Fish Populations in the north-western Pacific:
• If overfishing of immatures continues,
• If cyclic replacement hypothesis is true,
• Do not catch immatures too much!
–chub mackerel will not recover forever.–Fishers did not agree to my recommendation.
–sardine will not recover forever either.
–The overfishing is an experiment for my hypothesis. (adaptive mismanagement)
–In 2003, fishers agreed to stock recovery plan!
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Difficulties & hopelessness in ecosystem modeling
• We need many unverified assumptions and intuitive understanding is usually difficult
• “Ecosystem models without errors” often overfit observed data and predict a unique future.
• Indirect effects via the third species or adaptive change in traits is often counterintuitive and not negligible in the long-term effect (see Abrams, Polis…);
• Indeterminacy (Yodzis 1988): Results (+/-) vary with small change in parameter values
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Catch of top predators may decrease its prey fish.
1 2
3
5
6
4
Time
Pop
ulat
ion
size
• Myth #3 Trophic cascade: decrease of predator always increases its prey.
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Shiretoko World Nature Heritage (2005)
•We need evidence of sustainable fisheries in Shiretoko;
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漁業
トド
植物プランクトン
動物プランクトン
ホッケタラ サケ科
ヒグマ
カレイ類
海藻
さんま イワシ類
かに類
にしん
さめ類
さば
二枚貝類
まぐろ
あいなめ
えび類
オキアミ類
髭クジラ類
イルカ類
栄養塩
デトリタス
多毛類
イカナゴ
ぶり
巻貝
小型甲殻類
イカ類
タコ類
ソイ類 スケトウダラ
鰭脚類
死肉
海鷲類 海鳥類
なまこ
ウニ
赤字はキーストン種
桃地は非利用対象種
知床の海域生態系(部分図)
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Fisheries
Sealion
phytoplankton
zooplankton
Pleurogrammus Cod
Salmonids
Bear
Flatfishes
seaweed
Pacific saury Sardine & ancohvy
crabs
herring
Sharks
mackerel
bibalves
tunas
Fat greenling
shrimps
krill
Baleen whales
Dolphins
detritus
lugworms
Sand lance
Yellowtail
snails
Crustacea
squids
octopi
rockfish
Walleye pollack
Seals
Dead body
Eagles Seabirds
Sea-cucamber
Sea-urchins
Keystone species
Fisheries resources
Draft Foodweb in Shiretoko World Heritage
jellyfish