Format

Send to

Choose Destination
See comment in PubMed Commons below
J Theor Biol. 2007 Nov 21;249(2):289-95. Epub 2007 Jul 18.

The one-third law of evolutionary dynamics.

Author information

1
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA. ohtsuki@fas.harvard.edu

Abstract

Evolutionary game dynamics in finite populations provide a new framework for studying selection of traits with frequency-dependent fitness. Recently, a "one-third law" of evolutionary dynamics has been described, which states that strategy A fixates in a B-population with selective advantage if the fitness of A is greater than that of B when A has a frequency 13. This relationship holds for all evolutionary processes examined so far, from the Moran process to games on graphs. However, the origin of the "number"13 is not understood. In this paper we provide an intuitive explanation by studying the underlying stochastic processes. We find that in one invasion attempt, an individual interacts on average with B-players twice as often as with A-players, which yields the one-third law. We also show that the one-third law implies that the average Malthusian fitness of A is positive.

PMID:
17826798
PMCID:
PMC2430062
DOI:
10.1016/j.jtbi.2007.07.005
[Indexed for MEDLINE]
Free PMC Article
PubMed Commons home

PubMed Commons

0 comments
How to join PubMed Commons

    Supplemental Content

    Full text links

    Icon for Elsevier Science Icon for PubMed Central
    Loading ...
    Support Center