The one-third law of evolutionary dynamics

[摘要] 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 1/3.. This relationship holds for all evolutionary processes examined so far, from the Moran process to games on graphs. However, the origin of the number 1/3 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. (C) 2007 Elsevier Ltd. All rights reserved.

[发布日期] 2007-11-21

[关键词] evolutionary dynamics;evolutionary game theory;finite population;fixation probability;sojourn time