Table 1 Trend test between time average density of signals 〈ρσ〉t, and normalized apparent cost \(\bar{c}\), and between 〈ρσ〉t and time average payoff of signals \({\langle {w}_{\sigma }^{a}\rangle }_{t}\) in different games. From top to down, Spearman’s rank correlation coefficient between 〈ρσ〉t and \(\bar{c}\), and between 〈ρσ〉t and \({\langle {w}_{\sigma }^{a}\rangle }_{t}\), p value of the Spearman test between 〈ρσ〉t and \(\bar{c}\), and between 〈ρσ〉t and \({\langle {w}_{\sigma }^{a}\rangle }_{t}\), and finally, p value of the Mann-Kendall test between 〈ρσ〉t and \(\bar{c}\), and between 〈ρσ〉t and \({\langle {w}_{\sigma }^{a}\rangle }_{t}\). Here, an average over a window of length 5000 time steps is taken. In all the cases both tests strongly support a trend between payoff and density of signals, but in the case of TTD and SD, fail to establish a trend between the apparent cost and density of signals. In all the cases, the trend between density and fitness is significantly stronger compared to the trend between apparent cost and density.
n | PD | TTD | SD | BS | leader |
|---|---|---|---|---|---|
\(r({\bar{c}}_{\sigma },{\langle {\rho }_{\sigma }\rangle }_{t})\) | −0.46 | −0.13 | −0.37 | −0.52 | −0.59 |
\(r({\langle {w}_{\sigma }^{a}\rangle }_{t},{\langle {\rho }_{\sigma }\rangle }_{t})\) | 0.93 | 0.97 | 0.92 | 0.96 | 0.96 |
\({p}_{r}({\bar{c}}_{\sigma },{\langle {\rho }_{\sigma }\rangle }_{t})\) | 3.7 × 10−2 | 5.7 × 10−1 | 1.0 × 10−1 | 1.6 × 10−2 | 5.8 × 10−3 |
\({p}_{r}({\langle {w}_{\sigma }^{a}\rangle }_{t},{\langle {\rho }_{\sigma }\rangle }_{t})\) | 2.2 × 10−9 | 6.7 × 10−13 | 5.5 × 10−9 | 8.6 × 10−12 | 3.8 × 10−12 |
\({p}_{MK}({\bar{c}}_{\sigma },{\langle {\rho }_{\sigma }\rangle }_{t})\) | 4.7 × 10−2 | 3.4 × 10−1 | 1.2 × 10−1 | 2.1 × 10−2 | 1.2 × 10−2 |
\({p}_{MK}({\langle {w}_{\sigma }^{a}\rangle }_{t},{\langle {\rho }_{\sigma }\rangle }_{t})\) | 6.9 × 10−7 | 4.1 × 10−8 | 9.6 × 10−7 | 1.7 × 10−7 | 6.0 × 10−8 |
