EvoLudoLab: Mutualisms - Symmetry, random walk

Color code:	Cooperators	Defectors
	New cooperator	New defector

Payoffs:	Low High

Note: The gradient of the payoff scale is augmented by pale shades of the strategy colours to mark payoffs that are achieved in homogeneous populations of the corresponding type.

Inter-species donation game on lattices

Under harsh conditions (large \(r\)) small, isolated clusters of cooperators, \(\blacksquare\), form in both species embedded in a sea of defectors, \(\blacksquare\). The isolated clusters of cooperators perform a branching and annihilating random walk with almost perfect correlations between lattices.

For the simulations, the lattice size is \(N=L\times L\) with \(L=100\), a cost-to-benefit ratio of \(r=0.0225\) and \(K=0.1\). Note that \(r\) is close to the extinction threshold and hence often simulations may actually end up in an absorbing state with all defectors in both lattices. To prevent such accidental extinctions large lattice sizes are required.

Data views

Strategies - Structure	Snapshot of the spatial arrangement of strategies.
Strategies - Structure 3D	3D view of snapshot of the spatial arrangement of strategies.
Strategies - Mean	Time evolution of the strategy frequencies.
Fitness - Structure	Snapshot of the spatial distribution of payoffs.
Fitness - Structure 3D	3D view of snapshot of the spatial distribution of payoffs.
Fitness - Mean	Time evolution of average population payoff bounded by the minimum and maximum individual payoff.
Fitness - Histogram	Snapshot of payoff distribution in population.
Structure - Degree	Degree distribution in structured populations.
Stationary distribution	Statistics of the stationary distribution of the numbers of each strategic type. Note, only available for non-zero mutation rates.
Console log	Message log from engine.

Module parameters

The list below describes only the few parameters related to specifying the evolutionary dynamics of two species, say hosts and mutualists, with payoffs solely based on inter-species interactions. Numerous other parameters are available to set population structures or update rules on the player as well as population level.

--payhost <a,b;c,d>

payoff matrix for the host species. This indicates the payoffs when cooperator or defector hosts interact with cooperator or defector mutualists. For example a cooperator host obtains b against a defecting mutualist. This is the complement to --paymutualist <a,b;c,d>.

--paymutualist <a,b;c,d>

payoff matrix for the mutualist species. This indicates the payoffs when cooperator or defector mutualists interact with cooperator or defector hosts. For example a defector mutualist obtains c against a cooperating mutualist. This is the complement to --paymutualist <a,b;c,d>.

--inittype <type>

type of initial configuration:

frequency <f0>,<f1>...

random distribution with given trait frequencies, f0, f1,.... Note, only available for frequency based modules and models.

density <d0>,<d1>...

initial trait densities <d1,...,dn>. Note, only available for density based modules and models.

uniform

uniform random distribution, equal frequencies of all traits.

monomorphic <t>[,<v>]

monomorphic initialization with trait t. Note, for modules with variable population densities, the optional parameter v indicates the initial frequency of vacant sites. If omitted the monomorphic trait is initialized at its (estimated) carrying capacity.

mutant <m>,<r>[,<v>]

single mutant with trait m in homogeneous resident population of type r. The mutant is placed in a location selected uniformly at random (mutants arising through cosmic rays). Note, for modules with variable population densities, the optional parameter v indicates the initial frequency of vacant sites. If omitted the resident trait is initialized at its (estimated) carrying capacity.

temperature <m>,<r>[,<v>]

single mutant with trait m in homogeneous resident population of type r. The mutant is placed in a location selected proportional to the in-degree of nodes (temperature initialization, mutants arising through errors in reproduction). Note, for modules with variable population densities, the optional parameter v indicates the initial frequency of vacant sites. If omitted the resident trait is initialized at its (estimated) carrying capacity.

stripes

stripes of traits. Note, only available for 2D lattices.

kaleidoscopes

configurations that produce evolutionary kaleidoscopes for deterministic updates (players and population). Note, only available for some modules.

Note, for modules that admit multiple species, the initialization types for each species can be specified as an array separated by ;. With more species than initialization types, they are assigned in a cyclical manner.