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ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS

ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS. 11. Evolution of biological networks toward the edge of biochaos and synchronization (S. Rinaldi)

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ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS

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  1. ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS 11. Evolution of biological networks toward the edge of biochaosand synchronization (S. Rinaldi) Field and laboratory data support the conjecture that biological networks evolve toward the edge of chaos and synchronization. Models of networks of interconnected communities. Biochaos, synchronization, Moran effect, and evolution of dispersal. Formal support to the conjecture. Furtherreadings Am. Nat. (2008) 171:430-442 Am. Nat. (1996) 148:709-718 Int. J. Bifurcat. Chaos (2007) 17:2435-2446 Ecole Normale Supérieure, Paris December 9-13, 2013

  2. EVOLUTION OF BIOLOGICAL NETWORKS EVOLUTION BIOCHAOS AND SYNCHRONIZATION Evidence of chaos Conjecture S. Rinaldi, Plenarylecture, NOLTA, 2006 Evidence of synchronization Theoreticalsupport (main part) Conclusions

  3. CANADIAN LYNX MACKENZIE RIVER BASIN Elton & Nicholson, JAE, 1942

  4. DUNGENESS CRAB Higgins et al., Science, 1997

  5. RED GROUSE ENGLAND Middleton, JAE, 1934

  6. LEMMING ALASKA

  7. GREAT TIT ENGLAND

  8. Ellner & Turchin, Am. Nat., 1995

  9. Ellner & Turchin, Am. Nat., 1995

  10. CANADIAN LYNX

  11. DUNGENESS CRAB

  12. Liebhold et al., AREES, 2004

  13. General model of a single community environment community dimension dimension triangularstucture

  14. Chaos and Liapunovexponents of a single community For chaos and Liapunovexponents(L.E.) seeStrogatz, Addison-Wesley, 1994. L.E. of are L.E. of and : envir. L.E. biolog. L.E. conditioned to largestbiolog. L.E. largestenvir. L.E. The community ischaoticif and/or is positive

  15. The fourpossiblecases Chaos isexclusively due to environment 0 Chaos isexclusively due to biology 0 Chaos isprevalently due to environment 0 Chaos isprevalently due to biology 0 Thereis a hugeliterature on chaos

  16. Pioneeringcontributions on chaos Constantenvironment Discrete time single population [May, Science, 1974] predation [Beddington et al, Nature, 1975] competition [Hassel & Connings, TPB, 1976] stucturedpopulations [Guekenheimer et al, JMP, 1977] Continuous time predation [Gilpin, AmNat, 1979] Lotka-Volterra [Arneodo et al, PhysLett, 1980] foodchain [Hastings & Powell, Ecology, 1991] plankton dynamics [Scheffer, JPR, 1991] Periodicenvironment Discrete time single population [Kot & Schaffer, TPB, 1984] Continuous time predation [Inone & Kamifukumoto, ProgTheorPhys, 1984] epidemics [Schaffer & Kot, JTB, 1985] plankton dynamics [Doveri et al, TPB, 1993] Chaoticenvironment predation [Colombo et al, AmNat, 2008]

  17. Biochaos environment community Definition: Biochaos biochaos

  18. Example environment prey-predator Rosenzweig-MacArthur model Rössler model (Colombo et al. AmNat 2008)

  19. Evolutiontoward the edge of biochaos biochaos biochaos Hansen TPB 1992 Ferrière & Clobert JTB 1992 Ferrière & Gatto PRSB 1993 . . . Doebeli & Koella PRSB 1995 . . . biochaos

  20. Sliding on the edge of biochaos biochaos Dercole et al. PRSB 2006

  21. Models of disconnectedcommunities

  22. Models of disconnectedcommunities 2 1 i P

  23. Synchronization of disconnectedcommunities Empiricalevidence: pathches are oftensynchronized Monet, 1873 Monet, 1873 Monet, 1873 Grenfell et al., Nature, 1998

  24. Biochaos and synchronization of disconnectedcommunities Modernformulation of Moraneffect (Colombo et al., AmNat, 2008) Disconnectedcommunitiessynchronizeif and onlyif i.e., if and onlyifthereis no biochaos biochaos Bc S S sync Bc

  25. Connectedcommunities 2 1 i j if and are notconnected if and are connected # connections to P The eigenvalues of importanttopologicalindicator Moreover, populations can disperse atdifferentrates,

  26. Models of connectedcommunities 2 1 i j For the environment P For each patch where

  27. Synchronization of connectedcommunities Master StabilityFunction[Pecora & Carrol, PRL, 1998; Jansen & Lloyd, JMB, 2000] If (i.e., ifthereisbiochaos) thenpatchessynchronizeprovideddispersals are sufficiently high. In particular, ifdispersals are balanced (), patchessynchronizeprovided sync

  28. Example environment prey-predator Rosenzweig-MacArthur model Rössler model (Colombo et al. AmNat 2008)

  29. Summary Bc S S Bc S S Bc Bc

  30. Evolution of dispersal Dispersal can evolve Assumption are threeadaptive traits Dispersalisoftenassociated to costs Obvious consequence: evolutionreduceswhenpatches are synchronous Lessobviousconsequence: evolutionincreaseswhenpatches are notsynchronous [Holt & McPeek, AmNat, 1996] S predator dispersal, Dercole et al., IJBC, 2007 control parameter

  31. The conjecture There are threepossibleancestralconditions S S S S S S S S S Bc Bc Bc Bc Bc Bc Bc Bc Bc

  32. Conclusions S S Bc Bc Metapopulations evolve toward the edge of biochaos and synchronization Evolutionmakes patch behaviorcomplexbutsimplifies network behavior Genericallyweshouldexpectpopulations to be almostchaotic and almostsynchronous Whenevolutionis over dispersalisabsent (or verylow)

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