منابع مشابه
Asymptotically Optimal Amplifiers for the Moran Process
We study the Moran process as adapted by Lieberman, Hauert and Nowak. A family of directed graphs is said to be strongly amplifying if the extinction probability tends to 0 when the Moran process is run on graphs in this family. The most-amplifying known family of directed graphs is the family of megastars of Galanis et al. We show that this family is optimal, up to logarithmic factors, since e...
متن کاملAmplifiers and Suppressors of Selection for the Moran Process on Undirected Graphs
We consider the classic Moran process modeling the spread of genetic mutations, as extended to structured populations by Lieberman et al. (Nature, 2005). In this process, individuals are the vertices of a connected graph G. Initially, there is a single mutant vertex, chosen uniformly at random. In each step, a random vertex is selected for reproduction with a probability proportional to its fit...
متن کاملAbsorption Time of the Moran Process
The Moran process models the spread of mutations in populations on graphs. We investigate the absorption time of the process, which is the time taken for a mutation introduced at a randomly chosen vertex to either spread to the whole population, or to become extinct. It is known that the expected absorption time for an advantageous mutation is O(n) on an n-vertex undirected graph, which allows ...
متن کاملStochastic Evolution as a Generalized Moran Process
This paper proposes and analyzes a model of stochastic evolution in finite populations. The expected motion in our model resembles the standard replicator dynamic when the population is large, but is qualitatively different when the population size is small, due to the difference between maximizing payoff and maximizing relative payoff. Moreover, even in large populations the asymptotic behavio...
متن کاملPhase Transitions of the Moran Process and Algorithmic Consequences
The Moran process is a randomised algorithm that models the spread of genetic mutations through graphs. If the graph is connected, the process eventually reaches “fixation”, where every vertex is a mutant, or “extinction”, where no vertex is a mutant. Our main result is an almost-tight bound on the expected running time of the algorithm. For all ε > 0, we show that the expected running time on ...
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ژورنال
عنوان ژورنال: Journal of the ACM
سال: 2017
ISSN: 0004-5411,1557-735X
DOI: 10.1145/3019609