EvoLudoLab: Mutualisms - Asymmetric cooperation - Revision history

Hauert at 07:40, 19 February 2026

2026-02-19T07:40:38Z

← Older revision		Revision as of 00:40, 19 February 2026
Line 1:		Line 1:
	{{EvoLudoLab:Mutualism\|		{{EvoLudoLab:Mutualism\|
	options="--module ~~Mut~~ --geometry n --init frequency 1,1:2,8 --payhost 0,1;-0.0015,0~~.9985~~ --paymutualist 0,1;-0.0015,0~~.9985~~ --playerupdate thermal 0.1 --accuscores --resetscores ephemeral --references random 1 --popsize 100x --popupdate async --timestep 2 --run --size 820,620"\|		options="--module Mutual --geometry n --init frequency 1,1:8,2 --payhost 0.9985,-0.0015;1,0 --paymutualist 0.9985,-0.0015;1,0 --playerupdate thermal 0.1 --accuscores --resetscores ephemeral --references random 1 --popsize 100x --popupdate async --timestep 2 --run --size 820,620"\|
	title=Inter-species donation game on lattices\|		title=Inter-species donation game on lattices\|
	doc=Lowering the cost-to-benefit ratio results in spontaneous symmetry breaking of cooperation in the two layers. The distribution of cooperators and defectors in each layer is almost complementary. Clusters, or regions of cooperators, in one layer are matched by defectors in the other. As a consequence, the lattices consist mostly of \(CD\) and \(DC\) pairs. Because of the distinctly different frequencies of cooperation in each lattice, either \(CD\) or \(DC\) pairs dominate. However, note that which pair dominates is of no consequence, because species interactions are symmetric, and hence it is merely a consequence of which species is labelled \(X\) and which \(Y\).		doc=Lowering the cost-to-benefit ratio results in spontaneous symmetry breaking of cooperation in the two layers. The distribution of cooperators and defectors in each layer is almost complementary. Clusters, or regions of cooperators, in one layer are matched by defectors in the other. As a consequence, the lattices consist mostly of \(CD\) and \(DC\) pairs. Because of the distinctly different frequencies of cooperation in each lattice, either \(CD\) or \(DC\) pairs dominate. However, note that which pair dominates is of no consequence, because species interactions are symmetric, and hence it is merely a consequence of which species is labelled \(X\) and which \(Y\).

	For the simulations, the lattice size is \(N=L\times L\) with \(L=100\), a cost-to-benefit ratio of \(r=0.0015\) and \(K=0.1\). Note, initially the cooperator frequency for the mutualist is \(>50\%\). This helps to break the symmetry and allows the dynamics to equilibrate faster. However, this also means that the final asymmetry is almost certainly benefitting the hosts.}}		For the simulations, the lattice size is \(N=L\times L\) with \(L=100\), a cost-to-benefit ratio of \(r=0.0015\) and \(K=0.1\). Note, initially the cooperator frequency for the mutualist is \(>50\%\). This helps to break the symmetry and allows the dynamics to equilibrate faster. However, this also means that the final asymmetry is almost certainly benefitting the hosts.}}

Hauert at 15:53, 31 January 2025

2025-01-31T15:53:54Z

← Older revision		Revision as of 08:53, 31 January 2025
Line 1:		Line 1:
	{{EvoLudoLab:Mutualism\|		{{EvoLudoLab:Mutualism\|
	options="--module Mut --geometry n --init frequency 1,1:2,8 --payhost 0,1;-0.0015,0.9985 --paymutualist 0,1;-0.0015,0.9985 --playerupdate thermal 0.1 --accuscores --references random 1 --popsize 100x --popupdate async --timestep 2 --run --size 820,620"\|		options="--module Mut --geometry n --init frequency 1,1:2,8 --payhost 0,1;-0.0015,0.9985 --paymutualist 0,1;-0.0015,0.9985 --playerupdate thermal 0.1 --accuscores --resetscores ephemeral --references random 1 --popsize 100x --popupdate async --timestep 2 --run --size 820,620"\|
	title=Inter-species donation game on lattices\|		title=Inter-species donation game on lattices\|
	doc=Lowering the cost-to-benefit ratio results in spontaneous symmetry breaking of cooperation in the two layers. The distribution of cooperators and defectors in each layer is almost complementary. Clusters, or regions of cooperators, in one layer are matched by defectors in the other. As a consequence, the lattices consist mostly of \(CD\) and \(DC\) pairs. Because of the distinctly different frequencies of cooperation in each lattice, either \(CD\) or \(DC\) pairs dominate. However, note that which pair dominates is of no consequence, because species interactions are symmetric, and hence it is merely a consequence of which species is labelled \(X\) and which \(Y\).		doc=Lowering the cost-to-benefit ratio results in spontaneous symmetry breaking of cooperation in the two layers. The distribution of cooperators and defectors in each layer is almost complementary. Clusters, or regions of cooperators, in one layer are matched by defectors in the other. As a consequence, the lattices consist mostly of \(CD\) and \(DC\) pairs. Because of the distinctly different frequencies of cooperation in each lattice, either \(CD\) or \(DC\) pairs dominate. However, note that which pair dominates is of no consequence, because species interactions are symmetric, and hence it is merely a consequence of which species is labelled \(X\) and which \(Y\).

	For the simulations, the lattice size is \(N=L\times L\) with \(L=100\), a cost-to-benefit ratio of \(r=0.0015\) and \(K=0.1\). Note, initially the cooperator frequency for the mutualist is \(>50\%\). This helps to break the symmetry and allows the dynamics to equilibrate faster. However, this also means that the final asymmetry is almost certainly benefitting the hosts.}}		For the simulations, the lattice size is \(N=L\times L\) with \(L=100\), a cost-to-benefit ratio of \(r=0.0015\) and \(K=0.1\). Note, initially the cooperator frequency for the mutualist is \(>50\%\). This helps to break the symmetry and allows the dynamics to equilibrate faster. However, this also means that the final asymmetry is almost certainly benefitting the hosts.}}

Hauert at 23:34, 12 August 2024

2024-08-12T23:34:57Z

← Older revision		Revision as of 16:34, 12 August 2024
Line 1:		Line 1:
	{{EvoLudoLab:Mutualism\|		{{EvoLudoLab:Mutualism\|
	options="--module Mut --geometry n --~~inittype~~ frequency 1,1:2,8 --payhost 0,1;-0.0015,0.9985 --paymutualist 0,1;-0.0015,0.9985 --playerupdate thermal 0.1 --accuscores --references random 1 --popsize 100x --popupdate async --timestep 2 --run --size 820,620"\|		options="--module Mut --geometry n --init frequency 1,1:2,8 --payhost 0,1;-0.0015,0.9985 --paymutualist 0,1;-0.0015,0.9985 --playerupdate thermal 0.1 --accuscores --references random 1 --popsize 100x --popupdate async --timestep 2 --run --size 820,620"\|
	title=Inter-species donation game on lattices\|		title=Inter-species donation game on lattices\|
	doc=Lowering the cost-to-benefit ratio results in spontaneous symmetry breaking of cooperation in the two layers. The distribution of cooperators and defectors in each layer is almost complementary. Clusters, or regions of cooperators, in one layer are matched by defectors in the other. As a consequence, the lattices consist mostly of \(CD\) and \(DC\) pairs. Because of the distinctly different frequencies of cooperation in each lattice, either \(CD\) or \(DC\) pairs dominate. However, note that which pair dominates is of no consequence, because species interactions are symmetric, and hence it is merely a consequence of which species is labelled \(X\) and which \(Y\).		doc=Lowering the cost-to-benefit ratio results in spontaneous symmetry breaking of cooperation in the two layers. The distribution of cooperators and defectors in each layer is almost complementary. Clusters, or regions of cooperators, in one layer are matched by defectors in the other. As a consequence, the lattices consist mostly of \(CD\) and \(DC\) pairs. Because of the distinctly different frequencies of cooperation in each lattice, either \(CD\) or \(DC\) pairs dominate. However, note that which pair dominates is of no consequence, because species interactions are symmetric, and hence it is merely a consequence of which species is labelled \(X\) and which \(Y\).

	For the simulations, the lattice size is \(N=L\times L\) with \(L=100\), a cost-to-benefit ratio of \(r=0.0015\) and \(K=0.1\). Note, initially the cooperator frequency for the mutualist is \(>50\%\). This helps to break the symmetry and allows the dynamics to equilibrate faster. However, this also means that the final asymmetry is almost certainly benefitting the hosts.}}		For the simulations, the lattice size is \(N=L\times L\) with \(L=100\), a cost-to-benefit ratio of \(r=0.0015\) and \(K=0.1\). Note, initially the cooperator frequency for the mutualist is \(>50\%\). This helps to break the symmetry and allows the dynamics to equilibrate faster. However, this also means that the final asymmetry is almost certainly benefitting the hosts.}}

Hauert: Created page with "{{EvoLudoLab:Mutualism| options="--module Mut --geometry n --inittype frequency 1,1:2,8 --payhost 0,1;-0.0015,0.9985 --paymutualist 0,1;-0.0015,0.9985 --playerupdate thermal 0.1 --accuscores --references random 1 --popsize 100x --popupdate async --timestep 2 --run --size 820,620"| title=Inter-species donation game on lattices| doc=Lowering the cost-to-benefit ratio results in spontaneous symmetry breaking of cooperation in the two layers. The distribution of cooperators..."

2024-08-10T05:55:28Z

Created page with "{{EvoLudoLab:Mutualism| options="--module Mut --geometry n --inittype frequency 1,1:2,8 --payhost 0,1;-0.0015,0.9985 --paymutualist 0,1;-0.0015,0.9985 --playerupdate thermal 0.1 --accuscores --references random 1 --popsize 100x --popupdate async --timestep 2 --run --size 820,620"| title=Inter-species donation game on lattices| doc=Lowering the cost-to-benefit ratio results in spontaneous symmetry breaking of cooperation in the two layers. The distribution of cooperators..."

New page

{{EvoLudoLab:Mutualism|
options="--module Mut --geometry n --inittype frequency 1,1:2,8 --payhost 0,1;-0.0015,0.9985 --paymutualist 0,1;-0.0015,0.9985 --playerupdate thermal 0.1 --accuscores --references random 1 --popsize 100x --popupdate async --timestep 2 --run --size 820,620"|
title=Inter-species donation game on lattices|
doc=Lowering the cost-to-benefit ratio results in spontaneous symmetry breaking of cooperation in the two layers. The distribution of cooperators and defectors in each layer is almost complementary. Clusters, or regions of cooperators, in one layer are matched by defectors in the other. As a consequence, the lattices consist mostly of \(CD\) and \(DC\) pairs. Because of the distinctly different frequencies of cooperation in each lattice, either \(CD\) or \(DC\) pairs dominate. However, note that which pair dominates is of no consequence, because species interactions are symmetric, and hence it is merely a consequence of which species is labelled \(X\) and which \(Y\).

For the simulations, the lattice size is \(N=L\times L\) with \(L=100\), a cost-to-benefit ratio of \(r=0.0015\) and \(K=0.1\). Note, initially the cooperator frequency for the mutualist is \(>50\%\). This helps to break the symmetry and allows the dynamics to equilibrate faster. However, this also means that the final asymmetry is almost certainly benefitting the hosts.}}