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Moran process: Difference between revisions
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{{InCharge|author1=Christoph Hauert}} | {{InCharge|author1=Christoph Hauert}}__NOTOC__ | ||
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The Moran process was named after its inventor, the geneticist P. A. P. Moran, who proposed in 1962 this stochastic process to model evolution in a finite, unstructured (well-mixed) population of constant size \(N\). | The Moran process was named after its inventor, the geneticist [[#References | P. A. P. Moran]], who proposed in 1962 this stochastic process to model evolution in a finite, unstructured (well-mixed) population of constant size \(N\). | ||
==Evolutionary dynamics== | ==Evolutionary dynamics== | ||
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Assuming that mutations are rare events \(\rho_1\) is of particular interest. It is easy to see that a neutral mutant (\(r=1\)) has a fixation probability of \(\rho_1=1/N\): eventually the entire population will have a single common ancestor but in terms of fitness mutants and residents are indistinguishable and so every member of the population has equal chances to be the chosen one. Evolution is said to favor a mutant if the fixation probability of the mutant exceeds the fixation probability of a neutral mutant, \(\rho_1 >1/N\). | Assuming that mutations are rare events \(\rho_1\) is of particular interest. It is easy to see that a neutral mutant (\(r=1\)) has a fixation probability of \(\rho_1=1/N\): eventually the entire population will have a single common ancestor but in terms of fitness mutants and residents are indistinguishable and so every member of the population has equal chances to be the chosen one. Evolution is said to favor a mutant if the fixation probability of the mutant exceeds the fixation probability of a neutral mutant, \(\rho_1 >1/N\). | ||
Celebrated results by the population geneticists Maruyama (1970) and Slatkin (1981) conjecture that fixation probabilities are unaffected by population structures, see [[Spatial Moran process]]. Indeed this turns out to be true for a large class of population structures, the [[Moran graphs]] but not in general. Instead, some population structures exhibit the intriguing properties that they act as [[Evolutionary amplifiers]], which amplify selection and suppress random drift such that beneficial mutants have a higher chance to fixate as compared to the original Moran process, or as [[Evolutionary suppressors]], which suppress selection and enhance random drift such that beneficial mutants have a lower chance to fixate, again compared to the original Moran process. | Celebrated results by the population geneticists [[#References|Maruyama (1970)]] and [[#References|Slatkin (1981)]] conjecture that fixation probabilities are unaffected by population structures, see [[Spatial Moran process]]. Indeed this turns out to be true for a large class of population structures, the [[Moran graphs]] but not in general. Instead, some population structures exhibit the intriguing properties that they act as [[Evolutionary amplifiers]], which amplify selection and suppress random drift such that beneficial mutants have a higher chance to fixate as compared to the original Moran process, or as [[Evolutionary suppressors]], which suppress selection and enhance random drift such that beneficial mutants have a lower chance to fixate, again compared to the original Moran process. | ||
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# Maruyama, T. (1974) A Simple Proof that Certain Quantities are Independent of the Geographical Structure of Population ''Theor. Pop. Biol.'' '''5''' 148-154. | # Maruyama, T. (1974) A Simple Proof that Certain Quantities are Independent of the Geographical Structure of Population ''Theor. Pop. Biol.'' '''5''' 148-154. | ||
# Slatkin, M. (1981) Fixation probabilities and fixation times in a subdivided population ''Evolution'' '''35''' 477-488. | # Slatkin, M. (1981) Fixation probabilities and fixation times in a subdivided population ''Evolution'' '''35''' 477-488. | ||
[[Category:Evolutionary processes]] | |||
