EvoLudoLab: Mutualisms - Asymmetric cooperation
| 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
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.
Data views
| Snapshot of the spatial arrangement of strategies. | |
| 3D view of snapshot of the spatial arrangement of strategies. | |
| Time evolution of the strategy frequencies. | |
| Snapshot of the spatial distribution of payoffs. | |
| 3D view of snapshot of the spatial distribution of payoffs. | |
| Time evolution of average population payoff bounded by the minimum and maximum individual payoff. | |
| Snapshot of payoff distribution in population. | |
| Degree distribution in structured populations. | |
| Statistics of the stationary distribution of the numbers of each strategic type. Note, only available for non-zero mutation rates. | |
| 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.