Topological constraints on the dynamics of wasp-waist ecosystems Ferenc JORDÁN

1. Varna, 14 June 2005 UNESCO Regime shifts workshop Topological constraints on the dynamics of wasp-waist ecosystems Ferenc JORDÁN Institute of Ecology and Botany, Hungarian Academy of Sciences, Vácrátót, and Collegium Budapest, Institute for Advanced Study, Budapest, Hungary; jordanf@freemail.hu, http://falco.elte.hu/~jordanf

3. Wasp-waist architecture (simplified)

4. B H

5. Model food webs N = 10 L = 12 equal complexity A B C D F E G J I H Jordán, F., Liu, W.C. and Wyatt, T. Topological constraints on the dynamics of wasp-waist ecosystems.Journal of Marine Systems, in press.

6. Wasp-waist species: D> 3 Din = 0 Dout = 0 A B C D F E G J I H

7. Wasp-waist species: D> 3 Din = 0 Dout = 0 A B C D F E G J I H

8. G 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 G1 G2 G3 G4 G5 G6 G10 G7 G8 G9

9. Shared predators Anchovy Sardine Apparent competition

10. Anchovy Sardine Shared prey Exploitative competition

11. Marine mammals Anchovy Sardine Trophic cascade

12. Horse mackerel Anchovy Sardine Shared prey Keystone predation

13. Peruvian upwelling Marine mammals Shared predators Horse mackerel Anchovy Sardine Rich interaction structure: network context, multispecies management Shared prey Jarre-Teichmann A. (1998). The potential role of mass balance models for the management of upwelling ecosystems. Ecological Applications8, S93-S103.

14. Topological importance index: TI TIi;j = kn (k;j / lm k;l) (i;k / kn i;k) C PCD = 1/DC D Jordán F., Liu W-C, and Wyatt T. Topological constraints on the dynamics of wasp-waist ecosystems. Journal of Marine Systems, in press.

15. additive multiplicative PBA * PCB + PDA * PCD = PCA PBA * PCB = PCA C C PCD PCB D PCB PDA B B PBA PBA A A

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

18. Relative strength of effects spreading out from G5

19. Relative strength of effects reaching G5

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

21. Regime shifts:topological constraints on the sardine-anchovy interaction G

22. Regime shifts:topological constraints on the sardine-anchovy interaction F

23. Indirect vs mixed control regimes Purely indirect is stronger in many cases than mixed (direct plus indirect)

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

25. Overfishing In fished down food webs the probability of mixed interction is reduced, while positive feedback increases leading to alternating states. + - - - - Only + loops Both – and + loops

26. Invasion Regime shift: jellyfish invades into a second wasp-waist position and replaces anchovy – topology predicts high invadibility Shiganova T. A. (1998). Invasion of the Black Sea by the ctenophore Mnemiopsis leidyi and recent changes in pelagic community structure. Fisheries Oceanography7, 305-310.

27. 25 29 32 30 28 26 33 31 19 9 27 23 21 17 13 16 15 18 22 8 12 11 14 7 6 3 5 2 34 1 4 Chesapeake Bay –important fishes? Top-down, KTD Striped bass, #33 Indirect one-step, TI1 also in the KPP-1k=3 set Bay anchovy, #22 TIi;j = kn (k;j / lm k;l) (i;k / kn i;k)

28. 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

29. Acknowledgements: Tim Wyatt CSIC Instituto de Investigaciones Marinas, Vigo, Spain Wei-chung Liu Department of Tropical Veterinary Medicine, University of Edinburgh, UK Vera Vasas and Zsófi Benedek Eötvös University, Budapest The Branco Weiss Fellowship, Society in Science, ETH Zürich The Organisers for the invitation