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ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS

ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS. 8. Evolutionary extinction in prey-predator and mutualistic communities (F. Dercole )

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ANALYSIS OF MULTI-SPECIES ECOLOGICAL AND EVOLUTIONARY DYNAMICS

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  1. ANALYSIS OF MULTI-SPECIES ECOLOGICALAND EVOLUTIONARY DYNAMICS 8. Evolutionary extinction in prey-predator and mutualistic communities(F. Dercole) Evolutionary vs ecological extinctions. Evolutionary murder and suicide in the coevolution of prey-predator and mutualistic communities. Ecological attractor switching, evolutionary reversals, and branching-extinction evolutionary cycles. Furtherreadings Analysis of EvolutionaryProcesses, Princeton Univ. Press, 2008, Chap. 3 and Appx. A SIAM J. Appl. Math. (2003) 63:1378-1391 Int. J. Bifurcat. Chaos (2005) 15:2179-2190 Ecole Normale Supérieure, Paris December 9-13, 2013

  2. Evolutionary extinction in prey-predator and mutualistic communities Two evolutionary state portraits prey-predator coevolution (see f.r. 2) coevolution of mutualism (see f.r. 3) ( and are per-capita rates of commodities trading) ( and are scaled prey and predator body sizes)

  3. Prey-predator coevolution Predator evolution slows down while approaching the boundary, so it is the evolution of the prey trait that drives the predator to extinction This is naively called evolutionary murder The boundary of the evolution set is a transcritical bifurcation at which (the predator goes extinct) A transcritical boundary allows boundary evolutionary equilibria at which only the prey selection derivative vanishes at The evolutionary trajectories close to the boundary are almost horizontal ( )

  4. Coevolution of mutualism When the boundary is reached, an ecological transient brings both resident populations to extinction This is naively called evolutionary suicide The boundary of the evolution set is a saddle-node bifurcation at which the resident equilibrium disappears The resident densities and are far from zero up to the bifurcation, so that both species coevolve (with nonvanishing and ) to self-destruction

  5. Ecological attractor switching Evolutionary reversal In general, the ecological transient leads to another attractor (an equilibrium?) of the resident model, where only some (or none) of the populations may be extinct. A switch of the ecological attractor (with or without extinction of some of the populations) can reverse the selection pressure on the traits of the surviving populations (Dercole F. et al., Evolution 56, 1081-1090, 2002)

  6. After an evolutionary extinction we must derive a lower-dimensional canonical equation

  7. The AD working scheme

  8. After an evolutionary extinction we must derive a lower-dimensional canonical equation Evolutionary branching and extinction can concatenate forming, e.g., Branching-extinction evolutionary cycles (DercoleF., J. Math. Biol. 47, 569-580, 2003)

  9. … and extinction bifurcations (boundary collisions, see f.r. 1 Appx. A) Back to our examples On the contrary, the evolutionary persistence of an obligate mutualism crucially depend on evolutionary extinction Evolutionary persistence is possible only if there is asymmetry in the competition for commodities, with a premium for good mutualists (see f.r. 3) Evolutionary extinction does not play a relevant role in prey-predator coevolution, at least in the modeling literature

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