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ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS

ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS. 1. Introduction (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 1. Introduction (S. Rinaldi) Behavioral, ecological, and evolutionarytime-scales. Variouskinds of interactions. Time series and state portraits. Asymptoticbehaviors of interactingpopulations. ODE ecologicalmodels. The influence of parameters on asymptoticbehaviors. Furtherreadings Encyclopedia of TheoreticalEcology, Univ. California Press, 2012, pp. 88-95 Ecole Normale Supérieure, Paris December 9-13, 2013

  2. Population time-scales Population= similarindividuals (cells, plants, animals) living in the same habitat Behavioral: from seconds to hours Time-scales Ecological: from hours to decades Evolutionary: up to millionyears

  3. Interactions Intraspecific Interspecific Environmental Economic

  4. Time series -thpopulationnumber of individualsat time Zeiraphera diniana in Oberengadin Valley - Switzerland

  5. Interactingpopulations Two populations: Trajectory Question: Do initialconditionsmatter in the long run? Answer: Next slide

  6. State Portraits Here the initialconditions do notmatter Here the initialconditionsmatter

  7. Asymptoticbehaviors What happens for Where do we come from? What happens for Where do wego? Gauguin 1897-1898 Boston Museum of Art

  8. Asymptoticbehaviors stableequilibrium [stationary regime] stablecycle [periodic regime] stabletorus [quasi-periodic regime] strange attractor [chaotic regime]

  9. Asymptoticbehaviors stableequilibrium [stationary regime] stablecycle [periodic regime] stabletorus [quasi-periodic regime] strange attractor [chaotic regime]

  10. Asymptoticbehaviors stableequilibrium [stationary regime] stablecycle [periodic regime] stabletorus [quasi-periodic regime] strange attractor [chaotic regime]

  11. Asymptoticbehaviors stableequilibrium [stationary regime] stablecycle [periodic regime] stabletorus [quasi-periodic regime] strange attractor [chaotic regime]

  12. Asymptoticbehaviors stableequilibrium [stationary regime] stablecycle [periodic regime] stabletorus [quasi-periodic regime] strange attractor [chaotic regime]

  13. Reppellers () unstableequilibrium unstablecycle unstabletorus strange repeller

  14. Saddles () Saddleshavestable(1) and unstable (2) manifolds (1) (1) (1) (2) (2) (2) In higherdimensionalsystemswe can alsohavesaddle tori and strange saddles

  15. Asymptoticbehaviors of twopopulations Equilibria Stablenode Stable focus Unstablenode Saddle Unstable focus Cycles Stablecycle Unstablecycle

  16. State portraits State portraits can be obtained • By interpolatingfield or laboratory data • Through intuitive arguments • Throughmodels

  17. ODE models Model mass conservation law for eachpopulation Inflows birth immigration stocking inflows Outflows death intraspecificcompetition intraspecificpredation (cannibalism) interspecificcompetition interspecificpredation outflows Shortly or where =parameters

  18. Bifurcationdiagrams How equilibria and cyclesdepend on parameters? TRC2 SN TRC1 H H h1 SN h2 SN TRC

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