Uncertainty about social interactions leads to the evolution of social heuristics

Individuals face many types of social interactions throughout their lives, but they often cannot perfectly assess what the consequences of their actions will be. Although it is known that unpredictable environments can profoundly affect the evolutionary process, it remains unclear how uncertainty about the nature of social interactions shapes the evolution of social behaviour. Here, we present an evolutionary simulation model, showing that even intermediate uncertainty leads to the evolution of simple cooperation strategies that disregard information about the social interaction (‘social heuristics’). Moreover, our results show that the evolution of social heuristics can greatly affect cooperation levels, nearly doubling cooperation rates in our simulations. These results provide new insight into why social behaviour, including cooperation in humans, is often observed to be seemingly suboptimal. More generally, our results show that social behaviour that seems maladaptive when considered in isolation may actually be well-adapted to a heterogeneous and uncertain world.


Supplementary Information
Uncertainty about social interactions leads to the evolution of social heuristics van  anti-conventional, shifts after playing opposite of opponent, otherwise defects 0 0 1 1 inconsistent plays opposite of previous move 0 1 0 0 con-D conventional, stays after playing the opposite of opponent, otherwise defects 0 1 0 1 ATFT anti-tit for tat, plays opposite of opponent's last move 0 1 1 0 APavlov win, shift; lose, stay 0 1 1 1 hopeless only defects after mutual cooperation 1 0 0 0 grim only cooperates after mutual cooperation 1 0 0 1 Pavlov win, stay; lose, shift 1 0 1 0 TFT tit for tat, copies opponent's last move 1 0 1 1 MNG Mr Nice Guy, only defects after 'being cheated' (playing C while other plays D) 1 1 0 0 consistent repeats its own previous move 1 1 0 1 con-C conventional, stays after playing the opposite of opponent, otherwise cooperates 1 1 1 0 willing only defects after mutual defection 1 1 1 1 ALLC always cooperates Supplementary Table 1. An overview of all 16 possible substrategies that condition their behaviour on the previous interaction round. The first column (strategy) shows whether the strategy defects (0) or cooperates (1) after each of the four possible outcomes of the previous round (from left to right: mutual cooperation, having cooperated while the interaction partner defected, having defected while the interaction partner cooperated, and mutual defection).

Supplementary Note 1: Invasion analysis
Supplementary Figure 1 shows the invasion fitness of the most common heuristic (grim) and contextdependent strategies (grim/pavlovsee Fig. 3 in the main text) against each other, for different values of uncertainty. The most common heuristic strategy can invade the most common context-dependent strategy only under high uncertainty (if u ≥ 0.6), whereas the most common context-dependent strategy can never invade the most common heuristic strategy. For most of the range, neither strategy can invade the other. Nonetheless, as might be expected, the invasion fitness of the heuristic strategy increases with uncertainty, whereas the invasion fitness of the context-dependent strategy decreases with uncertainty. Hence, in finite populations (like in our model), the probability of the heuristic strategy invading a population of the context-dependent strategy becomes more likely with increasing uncertainty, whereas opposite is true for invasions of the context-dependent strategy. Of course, the invasion fitnesses of these two strategies against each other only tell a small part of the storythey only comprise a tiny part of the strategy space in our model.
Supplementary Figure 1. Invasion fitness of the most common heuristic strategy (grim with probability to cooperate on the first move of 0.99) and the most common context-dependent strategy (substrategy 1: grim with probability to cooperate on the first move of 0.30; substrategy 2: pavlov with probability to cooperate on the first move of 0.83; threshold between both strategies: c = -0.46) against each other. If the invasion fitness exceeds 1.00 (dotted line), the strategy can invade the other. To obtain these values, we simulated 100,000 interactions of both strategies against each other and against themselves, for each level of uncertainty (from 0 to 1 in steps of 0.1).

Supplementary Note 2: Simulations for fixed values of c
Supplementary Figure 2 shows the cooperation rate at the end of simulations in which all interactions were characterized by a fixed consequence of cooperation (c). The mean cooperation level over the entire range of c equals 0.55 (based on an interpolation of data points in the region between -3.0 and -2.0 and the region between -0.5 and 1.0 when assuming linearity in these regions). This exceeds the cooperation level that we observe in the original model under low uncertainty (0.46) but is far below the observed cooperation level in the original model under high uncertainty (0.87). The average cooperation levels that we observe under high uncertainty in our original model (0.87) are similar to the average cooperation levels that we observe for the model without heterogeneity at c = -1 (0.85). Since c = -1 is the expected consequence of cooperation in our original model, this may lead to the suspicion that individuals are selected to play 'the average game' when uncertainty is maximal. To investigate this, Supplementary Figure 3 shows an overview of the strategies that evolved in both situations. Although the simulation outcomes in the original model under full uncertainty and in the model with fixed c = -1 are not entirely the same, they are very similar. In both cases, the evolution of the strategy grim was by far the most likely outcome of the simulations, and the strategy tit for tat was also relatively likely to evolve. However, there are also some differences. In the model with fixed c, the strategies desperate, alld and pavlov were more likely to evolve than in the original model. In contrast, in the original model some simulations led to the evolution of contextdependent strategies (even though the information on which these strategies condition their behaviour is completely unreliable). Also, simulation outcomes where no single strategy dominated the population (i.e., had a frequency of >0.8) at the end of the simulations occurred relatively frequently in the original model, whereas they never occurred in the model with fixed c.

Supplementary
Supplementary Figure 3. Evolved strategies in the original model under full uncertainty (upper bar) and the model without heterogeneity, for c = -1 (lower bar). Each bar shows the fraction of simulations that led to the evolution of each of the mentioned strategies dominating the population (i.e., reach a frequency > 0.8). Both bars represent a total of 5,000 simulations (50 replicate simulations for each of 100 mutation matrices.