1 / 22

ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS

ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS. 1. Introduction (S. Rinaldi)

kaycee
Download Presentation

ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related