Evol Ecol Res 11: 489-515 (2009)     Full PDF if your library subscribes.

Evolutionary game theory: ESS, convergence stability, and NIS

Joseph Apaloo¹, Joel S. Brown² and Thomas L. Vincent³

¹Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, Nova Scotia, Canada,  ²Department of Biological Sciences, University of Illinois, Chicago, Illinois, USA and  ³Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona, USA

Correspondence: J. Apaloo, Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, PO Box 5000, Antigonish, Nova Scotia B2G 2W5, Canada.
e-mail: japaloo@stfx.ca

ABSTRACT

Question: How are the three main stability concepts from evolutionary game theory – evolutionarily stable strategy (ESS), convergence stability, and neighbourhood invader strategy (NIS) – related to each other? Do they form a basis for the many other definitions proposed in the literature?

Mathematical methods: Ecological and evolutionary dynamics of population sizes and heritable strategies respectively, and adaptive and NIS landscapes.

Results: Only six of the eight combinations of ESS, convergence stability, and NIS are possible. An ESS that is NIS must also be convergence stable; and a non-ESS, non-NIS cannot be convergence stable. A simple example shows how a single model can easily generate solutions with all six combinations of stability properties and explains in part the proliferation of jargon, terminology, and apparent complexity that has appeared in the literature. A tabulation of most of the evolutionary stability acronyms, definitions, and terminologies is provided for comparison.

Key conclusions: The tabulated list of definitions related to evolutionary stability are variants or combinations of the three main stability concepts.

Keywords: adaptive landscape, convergence stability, Darwinian dynamics, evolutionary game stabilities, evolutionarily stable strategy, neighbourhood invader strategy, strategy dynamics.

DOWNLOAD A FREE, FULL PDF COPY
IF you are connected using the IP of a subscribing institution (library, laboratory, etc.)
or through its VPN.

 

        © 2009 Joseph Apaloo. All EER articles are copyrighted by their authors. All authors endorse, permit and license Evolutionary Ecology Ltd. to grant its subscribing institutions/libraries the copying privileges specified below without additional consideration or payment to them or to Evolutionary Ecology, Ltd. These endorsements, in writing, are on file in the office of Evolutionary Ecology, Ltd. Consult authors for permission to use any portion of their work in derivative works, compilations or to distribute their work in any commercial manner.

       Subscribing institutions/libraries may grant individuals the privilege of making a single copy of an EER article for non-commercial educational or non-commercial research purposes. Subscribing institutions/libraries may also use articles for non-commercial educational purposes by making any number of copies for course packs or course reserve collections. Subscribing institutions/libraries may also loan single copies of articles to non-commercial libraries for educational purposes.

       All copies of abstracts and articles must preserve their copyright notice without modification.