The spatial Moran process models stochastic evolution in structured populations. Population structure
The essential difference to the original [[Moran process]] that arises through the population structure is that the offspring of the
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title=Evolutionary dynamics on the complete graph|
...tex is connected to its two neighbours on the left and right. The invasion process of a mutant can then be easily illustrated over time by stacking subsequent
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...ies are a highly robust quantity and naturally an important determinant of evolutionary processes.
[[Image:Frucht graph.svg|left|200px|link=EvoLudoLab: Moran process on the Frucht graph]]
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...mutants (\(r<1\)) have an increased fixation probability, \(\rho>\rho_1\). Evolutionary suppressors are also characterized by hierarchical population structures bu
The simplest and most extreme case of an evolutionary suppressor is given by a linear chain where the offspring of each individua
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...ns are sensitive to subtle differences in selective values. Traditionally, evolutionary dynamics was studied in the context of well-mixed or spatially extended pop
...odel evolutionary processes in structured populations, the [[spatial Moran process]].
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...ist [[#References | P. A. P. Moran]], who proposed in 1962 this stochastic process to model evolution in a finite, unstructured (well-mixed) population of con
==Evolutionary dynamics==
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Traditionally in both classical as well as evolutionary game theory a finite set of discrete strategies is assumed ''a priori''. Wh
...r, to justify these ''a priori'' assumptions. Since evolution is a gradual process, it is important to consider continuous variants of game theoretical metaph
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title=Evolutionary dynamics on the complete graph|
...mutants can spread to any part of the graph in a single step, the invasion process progresses quickly and does not exhibit any characteristic patterns.
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title=Evolutionary dynamics on the complete graph|
...from any other one in relatively few steps. Consequentially, the invasion process of mutants is similar to the complete graph (or even unstructured populatio
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title=Evolutionary dynamics on the star graph|
...nificant increase when compared to a \(50\%\) chance in the original Moran process. Typically it takes between \(4'500-6'500\) generations for the mutant to r
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...ence a mutant has the same fixation probability as in the original [[Moran process]] for unstructured populations.]]
...probabilities of a mutant unchanged and identical to the original [[Moran process]] in unstructured, well-mixed populations. Rather surprisingly it turns out
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...n into two phenotypic clusters of high and low investing individuals. This process provides a quite natural explanation for the emergence of discrete strategi
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title=Evolutionary dynamics on the superstar graph|
...emendous increase when compared to a \(50\%\) chance in the original Moran process. Interestingly, the typical time to reach fixation is less than on the star
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...es have the same fixation times. The fixation times for the original Moran process are shown as a dark red line for reference.
...raph of equal size - even though the superstar acts as a slightly stronger evolutionary amplifier despite the stronger finite size effects.}}
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...us mutants (\(r<1\)) have a smaller fixation probability, \(\rho<\rho_1\). Evolutionary amplifiers are also characterized by hierarchical population structures wit
...undirected (bi-directional) links. The hub represents a bottleneck for the evolutionary progression because if one leaf vertex is occupied by a mutant it needs to
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...again two branches evolve. But in contrast to evolutionary branching, this process is not generic as it requires a particular preparation of the initial confi
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...d decrease and vanish, as predicted by classical models for cooperation in evolutionary game theory, such as the [[Prisoner's Dilemma]] and [[Public Goods Games]].
...the interacting individuals. Here we incorporate ecological dynamics into evolutionary games and reveal a new mechanism for maintaining cooperation whenever the p
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10 KB (1,591 words) - 08:47, 13 October 2023
Traditionally in both classical as well as evolutionary game theory a finite set of discrete strategies is assumed ''a priori''. Wh
...er to justify these ''a priori'' assumptions. Since evolution is a gradual process, it is important to consider continuous variants of game theoretical metaph
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== Death-birth process ==
...ncy is the same for all individuals. This is in contrast to [[#Birth-death process|birth-death updating]] where competition occurs globally and individuals wi
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26 KB (4,790 words) - 10:54, 7 March 2025
...elfish individuals. Cooperation has long established as a central topic in evolutionary biology because, at least at a first glance, such behavior seems to contrad
...re \(A\)'s can invade a resident population of \(B\)'s and vice versa. The evolutionary end state of the population is a mixture both \(A\) and \(B\) types. The mo
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