The branching bifurcation of Adaptive Dynamics

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Della_Rossa_et_al_IJBC.pdf

accepted 77105 2 213090 document 77105 lightbox.jpg image/png 0dd37def4be08c85c5f8abb3ee0bcbb2 MD5 24799 2017-04-25 08:43:10 https://pure.iiasa.ac.at/id/eprint/11413/2/lightbox.jpg 11413 2 2 image/png other Thumbnails conversion from text to thumbnail_lightbox en public

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/77104 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/77104 http://eprints.org/relation/isIndexCodesVersionOf https://pure.iiasa.ac.at/id/document/77104 archive 351 disk0/00/01/14/13 2016-01-15 08:53:11 2021-08-27 17:39:52 2016-01-15 08:53:11 article show Della Rossa F. Dercole F. 7808 Landi P. 8869 The branching bifurcation of Adaptive Dynamics pub iis_ecl prog_eep Adaptive dynamics; bifurcation; evolutionary branching; evolutionary stability; invasion fitness; singular strategy We unfold the bifurcation involving the loss of evolutionary stability of an equilibrium of the canoncal equation of Adaptive Dynamics (AD). The equation deterministically describes the expected long-term evolution of inheritable traits phenotypes or strategies-of coevolving populations, in the limit of rare and small mutations. In the vicinity of a stable equilibium of the AD canonical equation, a mutant type can invade and coexist with the present-resident-types, whereas the fittest always win far from equilibrium. After coexistence, residents and mutants effectively diversify, according to the enlarged canonical equation, only if natural selection favors outer rather than intermediate traits-the equilibrium being evolutionarily unstable, rather than stable. Though the conditions for evolutionary branching-the joint effect of resident-mutant coexistence and evolutionary instability- have been known for long, the unfolding of the bifurcation has remained a missing tile of AD, the reason being related to the nonsmoothness of the mutant invasion fitness after branching. In this paper, we develop a methodology that allows the approximation of the invasion fitness after branching in terms of the expansion of the (smooth) fitness before branching. We then derive a canonical model or the branching bifurcation and perform its unfolding around the loss of evolutionary stability. We cast our analysis in the simplest (but classical) setting of asexual, unstructured populations living in an isolated, homogeneous, and constant abiotic environment; individual traits are one-dimensional; intra-as well as inter-specific ecological interactions are described in the vicinity of a stationary regime. 2015-06 published World Scientific Publishing 10.1142/S0218127415400015 XJ-15-149 International Journal of Bifurcation and Chaos; 25(7):1540001 (June 2015) [doi:10.1142/S0218127415400015] 1208 1404 public International Journal of Bifurcation and Chaos 25 7 1540001 1540001 TRUE 0218-1274 FALSE info:eu-repo/semantics/article