Phase Transitions of the Moran Process and Algorithmic Consequences

Autor:	Goldberg, Leslie Ann, Lapinskas, John, Richerby, David
Rok vydání:	2018
Předmět:	Mathematics - Probability Computer Science - Discrete Mathematics Computer Science - Social and Information Networks Mathematics - Combinatorics Quantitative Biology - Populations and Evolution
Druh dokumentu:	Working Paper
Popis:	The Moran process is a random process 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 expected absorption time. For all epsilon > 0, we show that the expected absorption time on an n-vertex graph is o(n^(3+epsilon)). In fact, we show that it is at most n^3 * exp(O((log log n)^3)) and that there is a family of graphs where it is Omega(n^3). In the course of proving our main result, we also establish a phase transition in the probability of fixation, depending on the fitness parameter r of the mutation. We show that no similar phase transition occurs for digraphs, where it is already known that the expected absorption time can also be exponential. Finally, we give an improved FPRAS for approximating the probability of fixation. Its running time is independent of the size of the graph when the maximum degree is bounded and some basic properties of the graph are given. Comment: To appear in Random Structures and Algorithms
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1804.02293 Zobrazit plný text záznamu View this record from Arxiv