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Ecole Normale Supérieure , Paris December 9-13, 2013

ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS. 10. Branching scenarios in prey -predator communities (P. Landi)

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Ecole Normale Supérieure , Paris December 9-13, 2013

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  1. ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS 10. Branching scenarios in prey-predator communities (P. Landi) Overview of branching scenarios in coevolvingcommunities with differenttypes of ecologicalinteractions. Classification of branching scenarios. Full catalog of branching scenarios in prey-predator coevolvingcommunitiesthrough the numericalcontinuationof branching bifurcations. Furtherreading SIAM J. Appl. Math (2013) 73:1634-1658 Ecole Normale Supérieure, Paris December 9-13, 2013

  2. Branching

  3. Coevolution

  4. Bifurcationanalysis

  5. BRANCHING SCENARIOS No Branching 1 Single 2 1 Branching Unilateral 2 Alternate Multiple A Doebeli, Dieckmann, AmNat 2000 B Ferrièreet al., PRSB 2002 C Ito, Ikegami, JTB 2006 D Best et al.,AmNat 2010 Bilateral Non Alternate

  6. No Branching: Ferrièreet al. (2002) (mutalism)

  7. BRANCHING SCENARIOS No Branching (B) 1 Single 2 1 Branching Unilateral 2 Alternate Multiple A Doebeli, Dieckmann, AmNat 2000 B Ferrièreet al., PRSB 2002 C Ito, Ikegami, JTB 2006 D Best et al.,AmNat 2010 Bilateral Non Alternate

  8. Single Branching: Doebeli, Dieckmann (2000) (prey-predator)

  9. BRANCHING SCENARIOS No Branching (B) 1 (A) Single 2 1 Branching Unilateral 2 Alternate Multiple A Doebeli, Dieckmann, AmNat 2000 B Ferrièreet al., PRSB 2002 C Ito, Ikegami, JTB 2006 D Best et al.,AmNat 2010 Bilateral Non Alternate

  10. Unilateral Branching: Ferrièreet al. (2002) (mutualism)

  11. BRANCHING SCENARIOS No Branching (B) 1 (A) Single 2 1 (B) Branching Unilateral 2 (B) Alternate Multiple A Doebeli, Dieckmann, AmNat 2000 B Ferrièreet al., PRSB 2002 C Ito, Ikegami, JTB 2006 D Best et al.,AmNat 2010 Bilateral Non Alternate

  12. Alternate Branching: Doebeli, Dieckmann (2000) (prey-predator) 1 2

  13. Alternate Branching: Ferrièreet al. (2002) (mutualism) 11 9 7 5 3 1 12 10 8 6 4 2

  14. Alternate Branching: Best et al. (2010) (host-parasite) 7 6 5 4 3 2 1

  15. BRANCHING SCENARIOS No Branching (B) 1 (A) Single 2 1 (B) Branching Unilateral 2 (B) Alternate (A,B,D) Multiple A Doebeli, Dieckmann, AmNat 2000 B Ferrièreet al., PRSB 2002 C Ito, Ikegami, JTB 2006 D Best et al.,AmNat 2010 Bilateral Non Alternate

  16. Non Alternate Branching: Ito, Ikegami (2006) (cannibalism)

  17. BRANCHING SCENARIOS No Branching (B) 1 (A) Single 2 1 (B) Branching Unilateral 2 (B) Alternate (A,B,D) Multiple A Doebeli, Dieckmann, AmNat 2000 B Ferrièreet al., PRSB 2002 C Ito, Ikegami, JTB 2006 D Best et al.,AmNat 2010 Bilateral Non Alternate (C)

  18. No BR BR p2 p1

  19. No BR S BR 1 S BR 2 Multiple BR p2 p1

  20. No BR S BR 1 S BR 2 U BR 1 U BR 2 Bilateral BR p2 p1

  21. No BR S BR 1 S BR 2 U BR 1 U BR 2 Alt BR Alt BR Non Alternate BR p2 p1

  22. B A B B A,B,D C A Doebeli, Dieckmann (2000) B Ferrièreet al. (2002) C Ito, Ikegami (2006) D Best et al. (2010)

  23. How can weobtain branching scenarios? General principles (i.e. competitive exclusion, environmentalfeedbacks) Simulation Continuation

  24. Continuation p2 p1

  25. Continuation: first iteration No BR p2 p1

  26. Continuation On the boundary: 2 solutions 2 1 5 equations and 6 unknowns

  27. Continuation p2 0 1 4 2 3 p1

  28. Case study: prey-predator coevolution Resident model

  29. Case study: prey-predator coevolution (Prey) Resident-mutant model Competitionmortality Competitionfunction Symmetriccompetition (Gaussianbell)

  30. Case study: first iteration

  31. Case study: seconditeration

  32. Case study: thirditeration

  33. Case study: fourthiteration

  34. Case study: successive iterations

  35. No BR S BR 1 U BR 1 Alt BR Non Alternate BR p2 p1

  36. Flexibilityand power of continuation

  37. Flexibilityand power of continuation

  38. Leptokurtic vs. Platykurtic

  39. Conclusions An iterative methodbased on continuationhasbeenproposed for obtaining the full catalog of branching scenarios. The full cataloghasbeenderived for a prey-predator system. Continuation can be used to discussprobability vs richness of branching scenarios. Influence of otherparameters can be easilyobtained. Itwould be interesting to apply the method to varioustypicaltwo-speciessystems.

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