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- Moran_process abstract "A Moran process or Moran model is a simple stochastic process used in biology to describe finite populations named after Patrick Moran who first proposed the model in 1958.It can be used to model variety-increasing processes such as mutation as well as variety-reducing effects such as genetic drift and natural selection. The process can describe the probabilistic dynamics in a finite population of constant size N in which two alleles A and B are competing for dominance. The two alleles are considered to be true replicators (i.e. entities that make copies of themselves). In each time step a random individual (which is of either type A or B) is chosen for reproduction and a random individual is chosen for death; thus ensuring that the population size remains constant. To model selection, one type has to have a higher fitness and is thus more likely to be chosen for reproduction.The same individual can be chosen for death and for reproduction in the same step.".
- Moran_process wikiPageExternalLink Moran.
- Moran_process wikiPageID "21700432".
- Moran_process wikiPageRevisionID "601595768".
- Moran_process bg "#f2dfce;".
- Moran_process content "Also in this case, fixation probabilities can be computed, but the transition probabilities are not symmetric. The notation , , and is used. The fixation probability can be defined recursively and a new variable is introduced. : Now two properties from the definition of the variable can be used to find a closed form solution for the fixation probabilities: : From and the knowledge follows : ----".
- Moran_process content "For the expected value the calculation runs as follows : For the variance the calculation runs as follows, using the variance of a single step : ----".
- Moran_process content "For the expected value the calculation runs as follows. Writing : Writing and , and applying the law of total expectation, Applying the argument repeatedly gives or For the variance the calculation runs as follows. Writing we have : For all t, and are identically distributed, so their variances are equal. Writing as before and , and applying the law of total variance, : If , we obtain . Rewriting this equation as : yields : as desired. ----".
- Moran_process content "The mean time spent in state j when starting in state i which is given by : Here denotes the Kroenecker delta. This recursive equation can be solved using a new variable so that and thus and rewritten : The variable is used and the equation becomes : Now can be calculated, knowing that and : Therefore : with . Now , the total time until fixation starting from state i, can be calculated : ----".
- Moran_process contentcss "border:1px #C4C3D0solid;".
- Moran_process hasPhotoCollection Moran_process.
- Moran_process header "For a mathematical derivation of the equation above, click on "show" to reveal".
- Moran_process headercss "color:black;".
- Moran_process subject Category:Evolutionary_dynamics.
- Moran_process subject Category:Population_genetics.
- Moran_process subject Category:Stochastic_processes.
- Moran_process type Abstraction100002137.
- Moran_process type Cognition100023271.
- Moran_process type Concept105835747.
- Moran_process type Content105809192.
- Moran_process type Hypothesis105888929.
- Moran_process type Idea105833840.
- Moran_process type Model105890249.
- Moran_process type PsychologicalFeature100023100.
- Moran_process type StochasticProcess113561896.
- Moran_process type StochasticProcesses.
- Moran_process comment "A Moran process or Moran model is a simple stochastic process used in biology to describe finite populations named after Patrick Moran who first proposed the model in 1958.It can be used to model variety-increasing processes such as mutation as well as variety-reducing effects such as genetic drift and natural selection. The process can describe the probabilistic dynamics in a finite population of constant size N in which two alleles A and B are competing for dominance.".
- Moran_process label "Moran process".
- Moran_process sameAs m.05zs6ry.
- Moran_process sameAs Q17157279.
- Moran_process sameAs Q17157279.
- Moran_process sameAs Moran_process.
- Moran_process wasDerivedFrom Moran_process?oldid=601595768.
- Moran_process isPrimaryTopicOf Moran_process.