# Data views of *VirtualLabs*

#### by Christoph Hauert, Version 0.9, February 2005.

## Discrete set of strategies

## Structure - Strategy | |
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## Strategies in well-mixed populationsIn well-mixed or unstructured populations individuals are drawn as colored dots arranged on a circle. The location of the dots has no implications as interactions are equally likely to occur between any members of the population. The color of each site denotes its strategy. The number of strategies depends on the game presently studied. Intermediate or lighter shades of color indicate sites that have just reassessed and changed their strategy. This is a very useful indicator for the activity in the system. For larger population sizes, it may not be possible to display this view because the dot size becomes less than a pixel on the screen. | |

## Strategies on a linear chainIndividuals can be arranged on a linear chain and interact with their neighbors on both or just one side. The number of interaction partners is determined by the neighborhood size. Subsequent states of the population are added as a new line to the bottom of the display area such that time runs from top to bottom. The sample snapshot to the left shows an asymmetric population structure with fixed boundary conditions where individuals interact only with one neighbor to the right. | |

## Strategies on rectangular latticesSetting the geometry to von Neumann and Moore neighborhood but larger neighborhoods covering individuals in a 5×5, 7×7 etc. area are also possible.Note that this view is not accessible for all types of geometries. It can be displayed only population structures corresponding to a regular lattice. | |

## Strategies on honeycomb latticesThe | |

## Strategies on triangular latticesThe third and last possibility of regular lattices in two dimensions is the | |

## Strategies on a star structureIn a star-structured population, all nodes (leafs) are connected to a central hub. Thus, the hub has denotes the population size.N | |

## Strategies on a super-star structureThe super-stars are star-like structures but have directed links where the central hub is connected to all nodes arranged in different 'petals'. Each of the nodes in one petal feeds into a chain of nodes that is connected back to the hub. The number of links (i.e. the length of the chain) that separate any two petal-nodes determines a so-called amplification factor On the left two examples are shown: the top panel shows the links and their direction for a super-star with 5 petals and and 13 petals as it is displayed by the virtuallabs.K=4 | |

## Strategies on arbitrary structuresThe default representation of the population structure is to draw colored dots arranged in a circle (just as for well-mixed populations) but then to draw the links between interacting individuals. While it may not be possible to identify all connections of one individual it still gives an impression of the connection density and of features of the algorithm used to initialize the population structure. | |

## Mean - Strategy | |

## Mean frequencies of strategiesMean frequencies of all strategies in the population as a function of time. The line colors distinguish the different strategies and the three horizontal black ;lines indicate the 25%, 50% and 75% levels. The actual time scale along the | |

## 2D Phase plane - Strategy | |

## Strategy frequencies in 2D Phase planeMean frequencies of strategies shown in a 2D phase plane. In the case of voluntary participation in public goods games and population dynamics a convenient transformation exists that maps the simplex The example on the left illustrates a stable limit cycle that is produced by the the feedback mechanism between public goods games and population sizes. | |

## Simplex _{3} | |

## Strategy frequencies on
_{3} | |

## Simplex _{4} | |

## Strategy frequencies on
_{4} | |

## Structure - Fitness | |

## Payoffs in structured populationsThe gray shade of each site indicates the payoff achieved. White sites have achieved the maximum payoff and black ones the minimum. In addition, sites earning payoffs of a homogenous population of a particular strategy are colored in light shades of that strategies' color. For example, on the square lattice depicted to the left, pale blue indicates sites that obtain payoffs of mutual cooperation and the pale red ones of mutual defection. Just as for the strategies above, the different population structures are shown whenever possible. This ranges from well-mixed populations and different kinds of lattices to more general structures such as random regular graphs or scale-free networks. | |

## Mean Fitness | |

## Mean FitnessMean fitness for each strategy type as well as the average population fitness. The fitness of the different strategies are indicated with different colors and the average population payoff is shown in black. The | |

## Histogram - Payoff | |

## Payoff histogramsHistogram of the payoffs for each strategy type. The different strategies are indicated by different colors and the name of the strategy is given in the top left corner of the respective panel. To improve the readability of the histograms, the ordinate is automatically rescaled. The current scale is specified in the top left corner of each panel. For example, a current scale of 25% means that the maximum for this panel is scaled to 25%. In the defector panel the payoff for mutual defection is marked by pale red lines straddling the corresponding bin in the histogram. Similarly, in the cooperator panel the payoff for mutual cooperation is marked by pale blue lines. |

## Continuous range of strategies

## Structure - Strategy | |
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## Continuous strategies on rectangular latticesThe shade of grey of each site denotes its strategy, e.g. the amount of the cooperative investment. Dark shades refer to low and light shades to high investors. Setting the geometry to von Neumann or Moore neighborhood. In addition the geometry can be or hexagonal as before.triangularNote that this view is not accessible for all types of geometries. It can be displayed only population structures corresponding to a regular lattice. | |

## Structure - Fitness | |

## Payoffs on rectangular latticesThe gray shade of each site indicates the payoff achieved. White sites achieve the maximum and black sites the minimum payoff. | |

## Mean - Strategy | |

## Average strategyIn analogy to the mean frequency of the different strategies in the discrete scenario this displays the mean strategy, e.g. the mean propensity to cooperate or the mean investment level as a solid black line. The pale blue and red lines indicate the maximum and minimum investments - to give a rough idea of the variance in the population. Note that the range of strategies may not be bounded. In that case the range is simply chosen large enough - e.g. twice the optimum investment level. | |

## Histogram - Strategy | |

## Strategy distributionIn order to get a better idea of the strategy composition of the population a histogram of the strategy frequencies is available. The range of possible strategies is divided into 100 bins. The sample image on the left shows the strategy distribution shortly after evolutionary branching. The population spontaneously splits into two distinct phenotypic clusters. More on continuous games and evolutionary branching can be found in the tutorial on the Evolutionary Origin of Cooperators and Defectors. | |

## Distribution - Strategy | |

## Strategy density distributionThe density distribution of the strategies is shown as a function of time. The ordinate denotes the trait interval and the abscissa the time axis. The shades of grey indicate the density (frequency) of a particular trait in the population ranging from white (none) to black (1/3), red (2/3) and finally yellow (all). Generally the shades are grey such as in the example to the left depicting the branching process in the Evolutionary Origin of Cooperators and Defectors. | |

## Mean - Payoff | |

## Payoff levelsThis view displays the mean population payoff (black) together with the minimum (pale red) and maximum (pale blue) payoffs for one player. Note that the accessible payoffs may not be bounded. In that case the maximum value is chosen to be sufficiently large e.g. the payoff for strategies investing twice the optimum. | |

## Histogram - Payoff | |

## Payoff distributionIn order to get a better idea of the distribution in the population, a histogram of the strategy payoffs is available. The range of possible payoffs is divided into 100 bins. |