EvoLudoLab: Spatial Ecological PGG - Diffusion induced coexistence: Difference between revisions
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{{VirtualLab:EcoPGG| | {{VirtualLab:EcoPGG| | ||
options="--run --delay 100 --popsize 101x --popupdate D --geometry nf --intertype | options="--run --delay 100 --popsize 101x --popupdate D --geometry nf --intertype a --colors black:red:green --reportfreq 2 --diffusion 100:1 --inittype 2 --initfreqs 8:1:1 --basefit 1.0 --selection 1.0 --groupsize 8 --cost 1.0 --interest 2.2 --birthrate 1.0 --deathrate 1.2 --pdedt 0.1 --pdeL 256"| | ||
type=PDE| | type=PDE| | ||
title=Diffusion induced co-existence| | title=Diffusion induced co-existence| | ||
doc=The initial configuration is symmetric and gives rise to a symmetrical evolutionary end state. The competing forces of cooperators (activators) and defectors (inhibitors) gives rise to spatial pattern formation reminiscent of Turing patterns. However, in contrast to Turing's diffusion induced instability, diffusion induced co-existence develops in the vicinity of an unstable fixed point. Hence, in the absence of spatial extension, the population would disappear. Spatially heterogenous distributions enables cooperators and defectors to persist. | doc=The initial configuration is symmetric and gives rise to a symmetrical evolutionary end state. The competing forces of cooperators (activators) and defectors (inhibitors) gives rise to spatial pattern formation reminiscent of Turing patterns. However, in contrast to Turing's diffusion induced instability, diffusion induced co-existence develops in the vicinity of an unstable fixed point. Hence, in the absence of spatial extension, the population would disappear. Spatially heterogenous distributions enables cooperators and defectors to persist. | ||
The parameters are <math>r=2.2</math>, <math>N=8</math>, <math>c=1</math>, <math>b=1</math>, <math>d=1.2</math> using numerical integration of the partial differential equation with the diffusion constants <math>D_C=1</math>, <math>D_D= | The parameters are <math>r=2.2</math>, <math>N=8</math>, <math>c=1</math>, <math>b=1</math>, <math>d=1.2</math> using numerical integration of the partial differential equation with the diffusion constants <math>D_C=1</math>, <math>D_D=100</math>. The initial configuration is a circular disk of equal densities of cooperators and defectors (<math>0.1</math>) in the center of a square lattice with fixed (reflecting) boundary conditions. | ||
Note that in order to exactly reproduce the patterns emerging in the movie, the requires a finer mesh, i.e. smaller <math>dx</math> and hence requires considerably more CPU time.}} | |||
[[Category: Christoph Hauert]] | [[Category: Christoph Hauert]] | ||
