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ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS

ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS. 9. Prey-predator coevolution and the Red Queen (F. Dercole ) The Red Queen hypothesis. Empirical and modeling perspectives. Prey-predator Red Queen cycles. Chaotic Red Queen coevolution in three-species food chains.

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ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS

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  1. ANALYSIS OF MULTI-SPECIES ECOLOGICALAND EVOLUTIONARY DYNAMICS 9. Prey-predator coevolution and the Red Queen(F. Dercole) The Red Queen hypothesis. Empirical and modeling perspectives. Prey-predator Red Queen cycles. Chaotic Red Queen coevolution in three-species food chains. Furtherreadings SIAM J. Appl. Math. (2003) 63:1378-1391 Proc. Roy. Soc. Lond. B (2010) 277:2321-2330 Int. J. Bifurcat. Chaos (2010) 20:3473-3485 Ecole Normale Supérieure, Paris December 9-13, 2013

  2. The Red Queen hypothesis Question: Can the interaction between species drive a never-ending evolutionary change even in an isolated, uniform, and constant (abiotic) environment? The Red Queen hypothesis: Yes (see Van Valen L., Evol. Theory 1, 1-30, 1973) Why the Red Queen? In her adventures in wonderland Alice says: “Well, in our country, you’d generally get to somewhere else — if you ran very fast for a long time as we’ve been doing” And the Queen replies: “A slow sort of country! Now, here, you see, it takes all the running you can do, to keep in the same place” Empirical perspective: Evolutionary data support the hypothesis, though the climatic conditions have been far from constant over evolutionary time Modeling perspective: Yes, the evolutionary cycles of the AD canonical equation (Dieckmann et al., J. Math. Biol. 176, 91-102)

  3. Prey-predator coevolution model The resident model (see f.r. 1) The resident ecological equilibrium The evolution set is defined by

  4. The prey resident-mutant model The prey invasion fitness The competition function symmetric competition

  5. The predator resident-mutant model The predator invasion fitness

  6. The prey and predator invasion fitnesses The AD canonical equation

  7. Coevolution of a three-species food chain The resident model (see f.r. 2 and 3) Question: Can the Red Queen become chaotic with the addition of a super-predator? The invasion fitnesses The resident ecological equilibrium The evolution set is defined by

  8. The AD canonical equation A sequence of evolutionary state portraits for increasing or decreasing () (with the Feigenbaum cascade of period doubling bifurcations)

  9. The chaotic evolutionary attractor Evolutionary chaos… makes evolutionary dynamics intrinsically unpredictable drives the ecological equilibrium chaotically on the evolutionary time-scale possibly explaining the week forms of chaos observed in the ecological fluctuations helps maintaining genetic diversity even between identical and isolated environments

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