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Stochastic dynamics in finite populations: Difference between revisions
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Stochastic dynamics in finite populations (view source)
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In infinite, well-mixed population, the fraction of players can change continuously, as described by the replicator dynamics in [[2×2 Games / Well-mixed populations|well-mixed populations]]. But in finite populations of size <math>N</math>, the fraction must change at least by <math>1/N</math>. | In infinite, well-mixed population, the fraction of players can change continuously, as described by the replicator dynamics in [[2×2 Games / Well-mixed populations|well-mixed populations]]. But in finite populations of size <math>N</math>, the fraction must change at least by <math>1/N</math>. | ||
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This result holds for many evolutionary processes under weak selection. Using tools from population genetics, it can be proven that it holds for all processes within the domain of Kingman’s coalescence. | This result holds for many evolutionary processes under weak selection. Using tools from population genetics, it can be proven that it holds for all processes within the domain of Kingman’s coalescence. | ||
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==From finite to infinite populations== | |||
[[Image:Stochastic dynamics - noise term Cxx, no mutation.png|200px|thumb|Blabla.]] | |||
<!-- <math> | |||
\bordermatrix{ | |||
& R & S & P \cr | |||
R & 0 & \frac{s}{2} & -1 \cr | |||
S & -1 & 0 & 2+s \cr | |||
P & \frac{1+s}{3} & -1 & 0 \cr | |||
}, | |||
</math> --> | |||
{{-}} | |||
===Deterministic Dynamics=== | |||
<div class="lab_description SDE"> | |||
[[Image:RSP - ODE.svg|left|200px]] | |||
==== [[EvoLudoLab: Rock-Paper-Scissors - ODE|Replicator dynamics]]==== | |||
{{-}} | |||
</div> | |||
<div class="lab_description SDE"> | |||
[[Image:RSP - ODE Mutations.svg|left|200px]] | |||
==== [[EvoLudoLab: Rock-Paper-Scissors - ODE|Replicator-Mutator dynamics]]==== | |||
{{-}} | |||
</div> | |||
===Stochastic Dynamics=== | |||
<div class="lab_description SDE"> | |||
[[Image:RSP - SDE.svg|left|200px]] | |||
==== [[EvoLudoLab: Rock-Paper-Scissors - ODE|Stochastic differential equations]]==== | |||
{{-}} | |||
</div> | |||
<div class="lab_description SDE"> | |||
[[Image:RSP - SDE.svg|left|200px]] | |||
==== [[EvoLudoLab: Rock-Paper-Scissors - ODE|Stochastic differential equations, with mutations]]==== | |||
{{-}} | |||
</div> | |||
===Individual Based Simulations=== | |||
<div class="lab_description SDE"> | |||
[[Image:RSP - IBS.svg|left|200px]] | |||
==== [[EvoLudoLab: Rock-Paper-Scissors - ODE|Individual based simulations]]==== | |||
{{-}} | |||
</div> | |||
<div class="lab_description SDE"> | |||
[[Image:RSP - IBS.svg|left|200px]] | |||
==== [[EvoLudoLab: Rock-Paper-Scissors - ODE|Individual based simulations, with mutations]]==== | |||
{{-}} | |||
</div> | |||
==References== | ==References== | ||
