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Moran process: Difference between revisions
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{{InCharge|author1=Christoph Hauert}} | {{InCharge|author1=Christoph Hauert}} | ||
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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 P. A. P. Moran, who proposed in 1962 this stochastic process to model evolution in a finite, unstructured (well-mixed) population of constant size \(N\). | ||
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In the simplest case, the population is composed of residents (blue) and mutants (orange): | In the simplest case, the population is composed of residents (blue) and mutants (orange): | ||
[[Image:Moran - step 0 (setup).svg|left| | [[Image:Moran - step 0 (setup).svg|left|200px]] ''Setup:'' The state of the population is given by the number of residents (blue, fitness \(1\)) and mutants (orange, fitness \(r\)). | ||
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[[Image:Moran - step 1 (birth).svg|left| | [[Image:Moran - step 1 (birth).svg|left|200px]] ''Step 1:'' At each time step a focal individual is chosen for reproduction with a probability proportional to its fitness (here, a mutant is selected for reproduction). | ||
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[[Image:Moran - step 2 (death).svg|left| | [[Image:Moran - step 2 (death).svg|left|200px]] ''Step 2:'' A randomly chosen individual is eliminated (here, a resident is selected for death). | ||
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[[Image:Moran - step 3 (replace).svg|left| | [[Image:Moran - step 3 (replace).svg|left|200px]] ''Step 3:'' The offspring replaces the eliminated individual. | ||
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