pone-0020474-g003: Legend for gradient maps.The map applies to both analytic and simulated gradient landscapes. The axes represent the average boldness and vengefulness of the population as its strategic characteristics. For each point, we measure the direction and speed of population drift. For analytical landscapes, we will also pinpoint the expected location of the evolutionary stable states. For simulation landscapes, we will be measuring the time that the simulation spends in each of the two key regions: norm emergence and norm collapse zones. Sample maps for different network topologies are shown in Figure 7.

Mentions: Evaluating gradients from Eq. 6 for any network topology and population characteristics leads to gradient maps of predicted population movements. The legend for these maps is described on Figure 3. For any constant value of average degree, the theoretical analysis suggests that the higher the average number of triplets, the more likely a cooperative ESS is to emerge and the bigger the size of its basin of attraction. On the contrary, for a constant average number of triplets, the higher average degree, the less likely a cooperative ESS is to emerge. Moreover, we can numerically calculate the minimum average number of triplets for each average degree in order to have an ESS in the area of norm establishment and compare it with different network topologies (Figure 4).