Topological constraints on the dynamicsof wasp-waist ecosystems

Ferenc JORDÁN

Institute of Ecology and Botany,Hungarian Academy of Sciences, Vácrátót,

andCollegium Budapest, Institute for Advanced Study,

Budapest, Hungary;

jordanf@freemail.hu, http://falco.elte.hu/~jordanf

Varna, 14 June 2005 UNESCO Regime shifts workshop

Wasp-waistarchitecture(simplified)

B

H

B C

D E F

G

HI

J

Jordán, F., Liu, W.C. and Wyatt, T. Topological constraints on the dynamics of wasp-waist ecosystems. Journal of Marine Systems, in press.

A

Model food webs N = 10L = 12equal complexity

B C

D E F

G

HI

J

A

Wasp-waist species:

D > 3

Din = 0

Dout = 0

B C

D E F

G

HI

J

A

Wasp-waist species:

D > 3

Din = 0

Dout = 0

G

G5

G5 on G1, G3, G4, G7 and G8:direct plus indirect

G5 on G2, G9 and G10:only indirect

G5 on G5:self-regulatory effect

G5 on G6:effect on another wasp-waist

G4G3G1 G2

G6

G7 G8 G9 G10

SardineAnchovy

Shared predators

Apparent competition

SardineAnchovy

Shared prey

Exploitative competition

Marine mammals

SardineAnchovy

Trophic cascade

SardineAnchovy

Horse mackerel

Shared prey

Keystone predation

Marine mammals

SardineAnchovy

Horse mackerel

Shared predators

Shared prey

Peruvian upwelling

Rich interaction structure:network context,multispecies management

Jarre-Teichmann A. (1998). The potential role of mass balance models for themanagement of upwelling ecosystems. Ecological Applications 8, S93-S103.

Topological importance index: TI

TIi;j = kn (k;j / l

m k;l) (i;k / kn i;k)

Jordán F., Liu W-C, and Wyatt T. Topological constraints on the dynamics of wasp-waistecosystems. Journal of Marine Systems, in press.

D

CPCD = 1/DC

AA

D

BB

C C

PBA * PCB + PDA * PCD = PCA

PCD

PDA

PCB

PBA

PCB

PBA

PBA * PCB = PCA

additive multiplicative

1 2 3 4 5 6 7 8 9 10

1 0,08 0,04 0,04 0,08 0,22 0,28 0,08 0,08 0,04 0,04

2 0,08 0,05 0,03 0,08 0,13 0,37 0,08 0,08 0,05 0,05

3 0,09 0,03 0,06 0,09 0,31 0,19 0,09 0,09 0,03 0,03

4 0,08 0,04 0,04 0,08 0,22 0,28 0,08 0,08 0,04 0,04

5 0,09 0,03 0,06 0,09 0,24 0,26 0,09 0,09 0,03 0,03

6 0,08 0,05 0,03 0,08 0,18 0,32 0,08 0,08 0,05 0,05

7 0,08 0,04 0,04 0,08 0,22 0,28 0,08 0,08 0,04 0,04

8 0,08 0,04 0,04 0,08 0,22 0,28 0,08 0,08 0,04 0,04

9 0,08 0,05 0,03 0,08 0,13 0,37 0,08 0,08 0,05 0,05

10 0,08 0,05 0,03 0,08 0,13 0,37 0,08 0,08 0,05 0,05

0,83 0,42 0,41 0,83 2,03 2,97 0,83 0,83 0,42 0,42

The interaction matrix of web G for n = 8.G

Relative strength of effects spreading out from G5

Relative strength of effects reaching G5

G

0,00

1,00

2,00

3,00

4,00

5,00

6,00

1 2 3 4 5 6 7 8 9 10

species

impo

rtanc

e one

three

eight

The effect spectrum of web G for n = 1, 3 and 8.

Regime shifts:topological constraints on the sardine-anchovy interaction

web G: sardine - anchovy effects

0,000,050,100,150,200,250,300,350,40

interaction rank

stre

ngth

othersinterWW

G

Regime shifts:topological constraints on the sardine-anchovy interaction

web F: sardine - anchovy effects

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

interaction rank

stre

ngthF

Indirect vs mixed control regimes

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

1 13 25 37 49 61 73 85 97

interaction rank

stre

ngth indirect

mixed

Purely indirect is stronger in many cases than mixed (direct plus indirect)

Self-regulation

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

1 9 17 25 33 41 49 57 65 73 81 89 97

species rank

self-

regu

latio

n st

reng

th

othersWWs

Self-regulatory feedback loops are extremely strong for wasp-waist species

OverfishingIn fished down food webs the probability of mixed interction is reduced,while positive feedback increases leading to alternating states.

+

--

-

Both – and + loops Only + loops

-

InvasionRegime shift: jellyfish invades into a second wasp-waistposition and replaces anchovy – topology predicts high invadibility

Shiganova T. A. (1998). Invasion of the Black Sea by the ctenophore Mnemiopsis leidyiand recent changes in pelagic community structure. Fisheries Oceanography 7, 305-310.

33

1

3

5

4

6

2

9

8

7

1112

13

21

22

23 19

14

15

25

18

26

16

27

28

17

2930

31

32

34

Top-down, KTD

Striped bass, #33

Indirect one-step, TI1also in the KPP-1k=3 set

Bay anchovy, #22

,11 1

1

1

1tef

m

ebcd

n

cx KKK

ec

TIi;j = kn (k;j / l

m k;l) (i;k / kn i;k)

Chesapeake Bay –important fishes?

Conclusions:

• System topology (architecture) constraints dynamics

• Certain behaviours are more probable (canalised trajectory)

• Regime shifts caused biotically are more expected in wasp-waist ecosystems

• Overfishing increases this effect• Vulnerable if invader enters the wasp-

waist

Acknowledgements:

Tim WyattCSIC Instituto de Investigaciones Marinas, Vigo, Spain

Wei-chung LiuDepartment of Tropical Veterinary Medicine,University of Edinburgh, UK

Vera Vasas and Zsófi BenedekEötvös University, Budapest

The Branco Weiss Fellowship,Society in Science, ETH Zürich

The Organisers for the invitation