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)

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”;

2006/8/28 3

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

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

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

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)

2006/8/28 7

Rule for maturity

Age-dep.

Size dep maturation

mixture

Low growth

High growth

age

Body

length

2006/8/28 8

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

2006/8/28 9

2006/8/28 10

What age and season should we catch fish?

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)(

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

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

)(

)()()(

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 )(

)(

)()()(

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

　

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

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

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

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

2006/8/28 20

Odd MSY curves(M & A 2004)

Fishery may increase its resource abundance.

“Classic” MSY

2006/8/28 21

Prey-predator cycles decreases average

predator abundance

Prey abundance N Prey abundance N

YieldYield

Yield

Stock P Stock P

Stock P

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

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

2006/8/28 24

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

2006/8/28 25

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

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

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

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.

2006/8/28 29

Species Replacement of Pelagic FishesC

atch

in J

apan

(10

00 m

t) AnchovyHorse mackerelsPacific sauryChub mackerelSardine

2006/8/28 30

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.

2006/8/28 31

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

2006/8/28 32

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

2006/8/28 33

Large fluctuation of recruitmentin chub mackerel (Kuroshio stock)

Strong year classes appeared twice

2006/8/28 34

Immatures were heavily caught before the age at maturity

1970s 1980s 1990s 1993-

%immatures 65.0% 60.0% 87.0% 90.6%

2006/8/28 35

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!

2006/8/28 36

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

2006/8/28 37

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.

2006/8/28 38

Shiretoko World Nature Heritage (2005)

•We need evidence of sustainable fisheries in Shiretoko;

2006/8/28 39

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）

2006/8/28 40

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