Stochastic dynamics in finite populations: Difference between revisions
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===Deterministic Dynamics=== | ===Deterministic Dynamics=== | ||
<div class="lab_description SDE"> | <div class="lab_description SDE"> | ||
[[Image:RSP - ODE.svg|left|200px]] | [[Image:RSP - ODE.svg|left|200px|link=EvoLudoLab: Rock-Paper-Scissors - ODE]] | ||
====[[EvoLudoLab: Rock-Paper-Scissors - ODE|Replicator dynamics]]==== | ====[[EvoLudoLab: Rock-Paper-Scissors - ODE|Replicator dynamics]]==== | ||
In the limit <math>N\to\infty</math> with <math>s=1.4</math> and without mutations, <math>\mu=0</math>, <math>\hat x</math> is an attractor of the replicator dynamics. The figure shows a sample trajectory that spirals towards the interior fixed point <math>\hat x</math>. | In the limit <math>N\to\infty</math> with <math>s=1.4</math> and without mutations, <math>\mu=0</math>, <math>\hat x</math> is an attractor of the replicator dynamics. The figure shows a sample trajectory that spirals towards the interior fixed point <math>\hat x</math>. | ||
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<div class="lab_description SDE"> | <div class="lab_description SDE"> | ||
[[Image:RSP - ODE Mutations.svg|left|200px]] | [[Image:RSP - ODE Mutations.svg|left|200px|link=EvoLudoLab: Rock-Paper-Scissors - ODE with Mutations]] | ||
==== [[EvoLudoLab: Rock-Paper-Scissors - ODE with Mutations|Replicator-Mutator dynamics]]==== | ==== [[EvoLudoLab: Rock-Paper-Scissors - ODE with Mutations|Replicator-Mutator dynamics]]==== | ||
Including mutations in the replicator dynamics gives rise to the replicator-mutator dynamics. Mutations destabilizes the interior fixed point <math>\hat x</math> an can give rise to stable limit cycles. The image shows a sample trajectory for <math>\mu=0.002</math>. | Including mutations in the replicator dynamics gives rise to the replicator-mutator dynamics. Mutations destabilizes the interior fixed point <math>\hat x</math> an can give rise to stable limit cycles. The image shows a sample trajectory for <math>\mu=0.002</math>. | ||
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===Stochastic Dynamics=== | ===Stochastic Dynamics=== | ||
<div class="lab_description SDE"> | <div class="lab_description SDE"> | ||
[[Image:RSP - SDE.svg|left|200px]] | [[Image:RSP - SDE.svg|left|200px|link=EvoLudoLab: Rock-Paper-Scissors - SDE]] | ||
==== [[EvoLudoLab: Rock-Paper-Scissors - SDE|Stochastic differential equations]]==== | ==== [[EvoLudoLab: Rock-Paper-Scissors - SDE|Stochastic differential equations]]==== | ||
{{-}} | {{-}} | ||
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<div class="lab_description SDE"> | <div class="lab_description SDE"> | ||
[[Image:RSP - SDE Mutations.svg|left|200px]] | [[Image:RSP - SDE Mutations.svg|left|200px|link=EvoLudoLab: Rock-Paper-Scissors - SDE with Mutations]] | ||
==== [[EvoLudoLab: Rock-Paper-Scissors - SDE with Mutations|Stochastic differential equations, with mutations]]==== | ==== [[EvoLudoLab: Rock-Paper-Scissors - SDE with Mutations|Stochastic differential equations, with mutations]]==== | ||
{{-}} | {{-}} | ||
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===Individual Based Simulations=== | ===Individual Based Simulations=== | ||
<div class="lab_description SDE"> | <div class="lab_description SDE"> | ||
[[Image:RSP - IBS.svg|left|200px]] | [[Image:RSP - IBS.svg|left|200px|link=EvoLudoLab: Rock-Paper-Scissors - IBS]] | ||
==== [[EvoLudoLab: Rock-Paper-Scissors - IBS|Individual based simulations]]==== | ==== [[EvoLudoLab: Rock-Paper-Scissors - IBS|Individual based simulations]]==== | ||
{{-}} | {{-}} | ||
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<div class="lab_description SDE"> | <div class="lab_description SDE"> | ||
[[Image:RSP - IBS Mutations.svg|left|200px]] | [[Image:RSP - IBS Mutations.svg|left|200px|link=EvoLudoLab: Rock-Paper-Scissors - IBS with Mutations]] | ||
==== [[EvoLudoLab: Rock-Paper-Scissors - IBS with Mutations|Individual based simulations, with mutations]]==== | ==== [[EvoLudoLab: Rock-Paper-Scissors - IBS with Mutations|Individual based simulations, with mutations]]==== | ||
{{-}} | {{-}} | ||
