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Incentive Processes in Finite Populations [article]

Marc Harper, Dashiell Fryer
2013 arXiv   pre-print
We define the incentive process, a natural generalization of the Moran process incorporating evolutionary updating mechanisms corresponding to well-known evolutionary dynamics, such as the logit, projection  ...  We show that the behaviors of the incentive process can deviate significantly from the analogous properties of deterministic evolutionary dynamics in some ways but are similar in others.  ...  This research was partially supported by the Office of Science (BER), U. S. Department of Energy, Cooperative Agreement No. DE-FC02-02ER63421.  ... 
arXiv:1306.2389v2 fatcat:cxgigih5pbe77l4vtdtlnlhaze

Moran process and Wright-Fisher process favor low variability

Jan Rychtář, ,Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, 1015 Floyd Avenue, Richmond, VA 23284-2014, USA, Dewey T. Taylor
2017 Discrete and continuous dynamical systems. Series B  
We focus on two frequency-independent stochastic processes: (1) Wright-Fisher process and (2) Moran process.  ...  In both processes, the selection favors A replacing B and opposes B replacing A if the fitness variance for A is smaller than the fitness variance for B.  ...  The authors would like to thank the handling editor and two anonymous reviewers for their suggestions and comments that helped to improve the manuscript.  ... 
doi:10.3934/dcdsb.2020242 fatcat:hxsohskinbgoxbthdleldmcqei

Fixation Maximization in the Positional Moran Process [article]

Joachim Brendborg, Panagiotis Karras, Andreas Pavlogiannis, Asger Ullersted Rasmussen, Josef Tkadlec
2022 arXiv   pre-print
In this paper we introduce the positional Moran process, a natural generalization in which the mutant fitness advantage is only realized on specific nodes called active nodes.  ...  The Moran process is a classic stochastic process that models invasion dynamics on graphs.  ...  Conversely, it can be viewed a special case of the Moran process with two environments (Kaveh, McAvoy, and Nowak 2019) .  ... 
arXiv:2201.02248v3 fatcat:wlbb3jnoofgkhm4mau7xo7m6py

Amplifiers for the Moran Process

Andreas Galanis, Andreas Göbel, Leslie Ann Goldberg, John Lapinskas, David Richerby
2017 Journal of the ACM  
The Moran process, as studied by Lieberman, Hauert and Nowak, is a randomised algorithm modelling the spread of genetic mutations in populations.  ...  If the underlying graph is strongly connected then the algorithm will eventually reach fixation, in which all individuals are mutants, or extinction, in which no individuals are mutants.  ...  The continuous-time Moran process as defined in [8] can be recovered as a function of the times at which these clocks trigger.  ... 
doi:10.1145/3019609 fatcat:ch5fpwywv5bkbcktsj2xux2j74

Amplifiers for the Moran Process [article]

Andreas Galanis, Andreas Göbel, Leslie Ann Goldberg, John Lapinskas, David Richerby
2016 arXiv   pre-print
The Moran process, as studied by Lieberman, Hauert and Nowak, is a randomised algorithm modelling the spread of genetic mutations in populations.  ...  If the underlying graph is strongly connected then the algorithm will eventually reach fixation, in which all individuals are mutants, or extinction, in which no individuals are mutants.  ...  In order to deal with conditioning in the proofs we will in fact define several general stochastic processes, all of which depend on G and r -one of these will be equivalent to the continuous-time Moran  ... 
arXiv:1512.05632v2 fatcat:q6tgfz5iafgbrh5w7er65i4kdu

Phase Transitions of the Moran Process and Algorithmic Consequences [article]

Leslie Ann Goldberg, John Lapinskas, David Richerby
2019 arXiv   pre-print
The Moran process is a random process that models the spread of genetic mutations through graphs.  ...  We show that no similar phase transition occurs for digraphs, where it is already known that the expected absorption time can also be exponential.  ...  [4] have already shown that a T -step run of an active Moran process can be simulated in O(∆T ) time with O(nd) preprocessing time.  ... 
arXiv:1804.02293v4 fatcat:lyxlzd77ivchdidjwblzanla2q

Fixation probabilities for the Moran process with three or more strategies: general and coupling results [article]

Eliza M. Ferreira, Armando G. M. Neves
2018 arXiv   pre-print
Other results are upper and lower bounds for the fixation probabilities obtained by coupling the Moran process with three strategies with birth-death processes with only two strategies.  ...  We study fixation probabilities for the Moran stochastic process for the evolution of a population with three or more types of individuals and frequency-dependent fitnesses.  ...  Acknowledgements This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brasil (CAPES) -Finance Code 001.  ... 
arXiv:1811.09552v1 fatcat:2bdvcgkezzba3pmbz6hypvhche

Invasion Dynamics in the Biased Voter Process [article]

Loke Durocher, Panagiotis Karras, Andreas Pavlogiannis, Josef Tkadlec
2022 arXiv   pre-print
On the positive side, we show that when r>1, the optimization function is submodular and thus can be greedily approximated within a factor 1-1/e.  ...  The voter process is a classic stochastic process that models the invasion of a mutant trait A (e.g., a new opinion, belief, legend, genetic mutation, magnetic spin) in a population of agents (e.g., people  ...  We can thus compute the fixation probability of S by summing over each execution that ends in the fixation of at least one of A, B. This "extended" process is instrumental in proving submodularity.  ... 
arXiv:2201.08207v2 fatcat:6a6ogshqljd2fo7dzmw2flwj6a

Assortment and the evolution of cooperation in a Moran process with exponential fitness [article]

Daniel Cooney, Benjamin Allen, Carl Veller
2016 arXiv   pre-print
Evolution proceeds as a Moran process, and payoffs from the underlying cooperator-defector game are translated to positive fitnesses by an exponential transformation.  ...  These evolutionary dynamics can arise, for example, in a nest-structured population with rare migration.  ...  As noted by Traulsen et al. (2008) , the ratio of fixation probabilities ρ C /ρ D in the frequency-dependent Moran process simplifies significantly with the exponential fitness transformation (3) : ρ  ... 
arXiv:1509.05757v2 fatcat:xhqcvpxo2bgaboj5u5slddlwce

Amplifiers and Suppressors of Selection for the Moran Process on Undirected Graphs [article]

George Giakkoupis
2016 arXiv   pre-print
We consider the classic Moran process modeling the spread of genetic mutations, as extended to structured populations by Lieberman et al. (Nature, 2005).  ...  The process ends when the mutation either reaches fixation (i.e., all vertices are mutants), or gets extinct.  ...  Acknowledgements I would like to thank Christoforos Raptopoulos and George Mertzios for bringing to my attention the question about the existence of undirected strong amplifiers and suppressors, during  ... 
arXiv:1611.01585v1 fatcat:gi5hha7fnfbo5dfh4f7vnkpdu4

Asymptotically Optimal Amplifiers for the Moran Process [article]

Leslie Ann Goldberg, John Lapinskas, Johannes Lengler, Florian Meier, Konstantinos Panagiotou, Pascal Pfister
2018 arXiv   pre-print
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.  ...  We study the Moran process as adapted by Lieberman, Hauert and Nowak.  ...  Acknowledgements We thank an anonymous referee of an earlier version for suggesting a simplification that shortened the proof of Lemma 37.  ... 
arXiv:1611.04209v4 fatcat:no36pwvcrrflnej75qmlqecks4

Immigration-induced phase transition in a regulated multispecies birth-death process

Song Xu, Tom Chou
2018 Journal of Physics A: Mathematical and Theoretical  
We find an accurate estimate for the expected distribution 〈 c_k 〉 by mapping the problem to a lower-dimensional Moran process, allowing us to also straightforwardly calculate the covariances 〈 c_k c_ℓ  ...  Finally, we exploit the concepts associated with energy landscapes to explain the failure of the mean-field assumption by identifying a phase transition in the quasi-steady-state species counts triggered  ...  However, they find that fluctuations in the total population do not affect fixation times of neutral species which is consistent with our finding that a fixed-population Moran process can be used to accurately  ... 
doi:10.1088/1751-8121/aadcb4 fatcat:rjmrgts7njgonfokanwb76iczq

Replicative senescense as a consequence of stochastic processes [article]

Alejandro José Fendrik, Lilia Romanelli, Ernesto Rotondo
2018 bioRxiv   pre-print
One of the remarkable features of aging is that is accompanied by the decrease in the rate of cell replication in tissue regeneration processes (replicative senescence).  ...  cells.This effect is due to the inherent characteristics of the renewal dynamics and as time goes by it leads to a quiescence state for stem cells due to the recurrent fixation of such altered cell.  ...  Acknowledgments 280 We are in debt to A. Braunstein and M.V.Reale for helpful discussions. AJF and LR thanks the hospitality of the Italian Institute of Genomic Medicine at Torino.  ... 
doi:10.1101/490433 fatcat:eg2nch2egbayjcwro2tgexwmda

The Common Ancestor Process Revisited

Sandra Kluth, Thiemo Hustedt, Ellen Baake
2013 Bulletin of Mathematical Biology  
We consider the Moran model in continuous time with two types, mutation, and selection. We concentrate on the ancestral line and its stationary type distribution. Building on work by Fearnhead (J.  ...  Probab. 12 (2007), 808-847), we characterise this distribution via the fixation probability of the offspring of all individuals of favourable type (regardless of the offspring's types).  ...  We are grateful to Jay Taylor for valuable comments on the manuscript. This project received financial support by Deutsche Forschungsgemeinschaft (SPP 1590), grant no. BA2469/5-1.  ... 
doi:10.1007/s11538-013-9871-0 pmid:24045892 fatcat:momrqrebvjas3o45zpmlqvddfq

The continuous limit of the Moran process and the diffusion of mutant genes in infinite populations [article]

Fabio A. C. C. Chalub, Max O. Souza
2006 arXiv   pre-print
We consider the so called Moran process with frequency dependent fitness given by a certain pay-off matrix.  ...  For finite populations, we show that the final state must be homogeneous, and show how to compute the fixation probabilities.  ...  The coefficients can be adjusted from the basic discrete process. In particular, we can choose Ψ such that Equation (38) 0) ).  ... 
arXiv:math/0602530v1 fatcat:msshenvbxvb6db2vx4qthqhpj4
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