The transition from evolutionary stability to branching : a catastrophic evolutionary shift
Date
2016-05-14
Journal Title
Journal ISSN
Volume Title
Publisher
Nature Publishing Group
Abstract
Evolutionary branching—resident-mutant coexistence under disruptive selection—is one of the main contributions of Adaptive Dynamics (AD), the mathematical framework introduced by S.A.H. Geritz, J.A.J. Metz, and coauthors to model the long-term evolution of coevolving multi-species communities. It has been shown to be the basic mechanism for sympatric and parapatric speciation, despite the essential asexual nature of AD. After 20 years from its introduction, we unfold the transition from evolutionary stability (ESS) to branching, along with gradual change in environmental, control, or exploitation parameters. The transition is a catastrophic evolutionary shift, the branching dynamics driving the system to a nonlocal evolutionary attractor that is viable before the transition, but unreachable from the ESS. Weak evolutionary stability hence qualifies as an early-warning signal for branching and a testable measure of the community’s resilience against biodiversity. We clarify a controversial theoretical question about the smoothness of the mutant invasion fitness at incipient branching. While a supposed nonsmoothness at third order long prevented the analysis of the ESSbranching transition, we argue that smoothness is generally expected and derive a local canonical model in terms of the geometry of the invasion fitness before branching. Any generic AD model
undergoing the transition qualitatively behaves like our canonical model.
Description
CITATION: Dercole, F., Rossa, F. & Landi, P. 2016. The transition from evolutionary stability to branching : a catastrophic evolutionary shift. Scientific Reports, 6:26310, doi:10.1038/srep26310.
The original publication is available at http://www.nature.com
Publication of this article was funded by the Stellenbosch University Open Access Fund.
The original publication is available at http://www.nature.com
Publication of this article was funded by the Stellenbosch University Open Access Fund.
Keywords
Evolutionary stability, Evolutionary branching, Transition, Evolution (Biology) -- Mathematical models, Mutation (Biology) -- Mathematical models, Adaptive Dynamics, Coevolution
Citation
Dercole, F., Rossa, F. & Landi, P. 2016. The transition from evolutionary stability to branching : a catastrophic evolutionary shift. Scientific Reports, 6:26310, doi:10.1038/srep26310