2018
DOI: 10.1007/978-3-319-77404-6_57
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Mutants and Residents with Different Connection Graphs in the Moran Process

Abstract: The Moran process, as studied by Lieberman, Hauert and Nowak [10], is a stochastic process modeling the spread of genetic mutations in populations. In this process, agents of a two-type population (i.e. mutants and residents) are associated with the vertices of a graph. Initially, only one vertex chosen uniformly at random (u.a.r.) is a mutant, with fitness r > 0, while all other individuals are residents, with fitness 1. In every step, an individual is chosen with probability proportional to its fitness, and … Show more

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Cited by 3 publications
(8 citation statements)
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“…As it is apparent by the Markov chain abstraction, the fixation probability f (X) starting from a mutant set X is the absorption probability for the absorbing state V [22]. This absorption probability can be calculated from the set of equations ( 1), or after eliminating self-loops, from the equations (2). For ease of presentation, let us focus on the latter, and also denote by p X+j X and p X−i X the transition probabilities which are coefficients of f (X + j) and f (X − i) in (2).…”
Section: Markov Chain Abstraction and The Generalized Isothermal Theoremmentioning
confidence: 99%
See 1 more Smart Citation
“…As it is apparent by the Markov chain abstraction, the fixation probability f (X) starting from a mutant set X is the absorption probability for the absorbing state V [22]. This absorption probability can be calculated from the set of equations ( 1), or after eliminating self-loops, from the equations (2). For ease of presentation, let us focus on the latter, and also denote by p X+j X and p X−i X the transition probabilities which are coefficients of f (X + j) and f (X − i) in (2).…”
Section: Markov Chain Abstraction and The Generalized Isothermal Theoremmentioning
confidence: 99%
“…This absorption probability can be calculated from the set of equations ( 1), or after eliminating self-loops, from the equations (2). For ease of presentation, let us focus on the latter, and also denote by p X+j X and p X−i X the transition probabilities which are coefficients of f (X + j) and f (X − i) in (2). Let M = (M (t)) t≥0 be a Moran process, and for each k ∈ {0, 1, .…”
Section: Markov Chain Abstraction and The Generalized Isothermal Theoremmentioning
confidence: 99%
“…Proof. Let U = V, so that s = (log r n) 1∕3 and the quantity C(log n) 1∕3 , from the failure probability in the statement of the theorem, is equal to C(log r) 1∕3 s. We will choose C to be small enough (as a function of r) so that, when n is sufficiently large, the final inequalities of (20) and (21)…”
Section: Applications Of Lemmas 39 and 40mentioning
confidence: 99%
“…Some versions of the process allow edge weights, which is equivalent to allowing multiple edges in the graph, and others determine the fitness of a vertex partly or fully by game payoffs with its neighbors. More recently, a variant has been proposed in which the mutants and nonmutants interact along different graphs. In this paper, we consider the original process of Lieberman et al , with a single, simple, unweighted graph and mutants with fixed fitness r .…”
Section: Introductionmentioning
confidence: 99%
“…Some versions of the process allow edge weights, which is equivalent to allowing multiple edges in the graph, and others determine the fitness of a vertex partly or fully by game payoffs with its neighbours. More recently, a variant has been proposed [20] in which the mutants and non-mutants interact along different graphs. In this paper, we consider the original process of Lieberman et al [18], with a single, simple, unweighted graph and mutants with fixed fitness r.…”
Section: Related Workmentioning
confidence: 99%