Abstract
We study the Moran process as adapted by Lieberman. Hauert and Nowak. This is a model of an evolving population on a graph or digraph where certain individuals, called "mutants" have fitness r and other individuals, called "non-mutants" have fitness 1. We focus on the situation where the mutation is advantageous, in the sense that r > 1. A family of digraphs is said to be strongly amplifying if the extinction probability tends to 0 when the Moran process is run on digraphs in this family. The most-amplifying known family of digraphs is the family of megastars of Galanis et al. We show that this family is optimal, up to logarithmic factors, since every strongly-connected n-vertex digraph has extinction probability Omega(n(-1/2)). Next, we show that there is an infinite family of undirected graphs, called dense incubators, whose extinction probability is O(n(-1/3)). We show that this is optimal, up to constant factors. Finally, we introduce sparse incubators, for varying edge density, and show that the extinction probability of these graphs is O(n/m), where m is the number of edges. Again, we show that this is optimal, up to constant factors. (C) 2018 Elsevier B.V. All rights reserved.
Item Type: | Journal article |
---|---|
Faculties: | Mathematics, Computer Science and Statistics > Mathematics |
Subjects: | 500 Science > 510 Mathematics |
ISSN: | 0304-3975 |
Language: | English |
Item ID: | 82393 |
Date Deposited: | 15. Dec 2021, 15:01 |
Last Modified: | 13. Aug 2024, 12:43 |