Premium
ESS, NIS and GIS for matrix games in n ‐species systems
Author(s) -
Ding Zhanwen,
Peng Yanxiang,
Yang Honglin
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1386
Subject(s) - stability (learning theory) , geographic information system , evolutionarily stable strategy , mathematics , ecology , computer science , mathematical economics , game theory , geography , biology , remote sensing , machine learning
In this paper, we discuss the concepts of evolutionarily stable strategy (ESS), neighborhood invader strategy (NIS) and global invader strategy (GIS) in n ‐species systems. We give their definitions both on system level and species level. Although the definition on system level and that on species level are apparently different, it is found that they are equivalent to one another. About the relationships among an ESS, an NIS and a GIS for n ‐species systems, we obtain the results similar to the ones for single species models: a GIS must be an NIS; an NIS must be an ESS; an ESS may not be a GIS; a GIS must be unique. The stability in the frequency dynamics with two phenotypes is also considered and the global stability of a GIS is shown. Copyright © 2010 John Wiley & Sons, Ltd.