Fig 1.
Illustration of the social drift–diffusion model.
Each individual, represented by a jagged line, must decide whether a signal is present (left panel) or absent (right panel). If the signal is present, the individual can decide correctly (hit) or wrongly (miss). If the signal is absent, the individual can decide correctly (correct rejection; CR) or wrongly (false alarm; FA). An individual’s start point depends on the information it gathered prior to the social phase (δp) and its start point bias (zp). Here the start point bias is towards the decision boundary (i.e., the red horizontal line) of the signal, implying that an individual is more likely to make a correct (wrong) decision when the signal is present (absent). At the start, no individual reached either decision boundary, implying that social information was absent. As individuals diffuse they hit a decision boundary and make a decision. Undecided individuals, in turn, start drifting towards the choice of the individual(s) that already decided, reflecting the process of social information use.
Table 1.
Description of the model parameters.
Underlined parameters evolve in the evolutionary algorithm.
Fig 2.
Outcomes of the evolutionary algorithms per group size and error cost in cooperative groups.
(A) When costs are symmetrical (i.e., error cost asymmetry = 1), no start point bias evolves at any group size. With increasing cost asymmetry, small (but not large) groups evolve a larger bias. (B) Across all error costs, larger groups evolve a higher boundary separation. (C) Across all combinations of group size and error cost, a high social drift evolves. Dots and error bars represent the mean and standard deviation, respectively, across the eight evolved populations. For exemplary evolutionary trajectories see S6 Fig.
Fig 3.
Hit and correct rejection rates (black lines, left axis) and payoff (colored lines, right axis) as a function of start point bias for different group sizes and error costs for cooperative groups.
Across all group sizes, increasing the start point bias towards the decision boundary of the signal leads to an increase in the hit rate, but simultaneously to a decrease of the correct rejection rate. Under symmetrical error costs, individuals across all group sizes maximize their payoff by maximizing the hit and correct rejection rate alike; this occurs at a bias close to 0. Under asymmetric costs, individuals need to ensure a high hit rate in order to avoid costly misses. Small groups achieve this by developing a bias. Large groups achieve a high hit (and correct rejection) rate without a start point bias, and therefore maximize the payoff at a much lower bias. The boundary separation and strength of the social drift were fixed at the endpoints of the evolutionary algorithms for each combination of group size and error cost.
Fig 4.
Payoff analysis with varying start point bias, boundary separation or strength of the social drift.
(A–C) The mean payoff of individuals in different-sized, cooperative groups across the three key parameters under high asymmetric error costs (cost asymmetry: 4). In these simulations, one evolved parameter was varied (x-axis), while the other two were fixed at their evolved level of cooperative groups. Larger groups maximized their payoffs (indicated by dots) at (A) a lower start point bias and (B) higher boundary separation compared to small groups. (C) All group sizes maximized their payoff at the highest level of social drift strength. Dashed horizontal lines show the mean payoff of the first responder. With increasing strength of the social drift, the mean payoff of all group members approximated the payoff of the first responder. (D–F) The benefits of individuals in competitive groups having above-average values in the three key parameters under high asymmetric error costs. Positive (negative) y-values indicate that individuals with above-average (below-average) values in the respective parameter achieved a higher payoff. Competitive groups evolved parameter values at which their members did not profit from having a higher (or lower) parameter value (i.e, where colored lines meet the solid horizontal line at zero), which approximates the outcomes of the evolutionary algorithm. These values partly differed from optimal outcomes in cooperative groups (dots), indicating a social dilemma. At these evolved endpoints of the cooperative groups individuals in competitive groups benefited from having a higher (D) start point bias and (E) boundary separation. (F) Cooperative and competitive groups did not differ in their evolved value of social drift.
Fig 5.
Evolutionary outcomes of cooperative and competitive groups at an error cost ratio of 4.
Across all group sizes, competitive groups evolved (A) a larger start point bias and (B) larger boundary separation, indicating a conflict between individual- and group-level interests. (C) Both cooperative and competitive groups evolved the maximum strength of the social drift. (D) Cooperative groups made, on average, faster choices than competitive groups, and this difference increased with group size. (E) At large, but not small, group sizes, cooperative groups outperformed competitive groups. Dots and error bars represent the mean and standard deviation of the endpoints of the evolutionary simulations, respectively.