Cultural coevolution of norm adoption and enforcement when punishers are rewarded or non-punishers are punished

A number of studies have shown that social norms can be maintained at a high frequency when norm-violators are punished. However, there remains the problem of how norm-adopters and punishers coevolve within a single group. We develop a recursive system to examine the coevolution of norm-adopters and punishers where the viability of punishers is enhanced by one of two "metanorms": (1) Norm-observers reward punishers for punishing norm-violators (Reward Model); (2) Punishers punish non-punishers (Punishment Model). Both models generate a bistable system and each is characterized in phenotype frequency space by a distinct region of attraction to the equilibrium consisting of only norm-adopting punishers. Using a Monte Carlo simulation, we find that cultural drift may allow norm-adopters and punishers to coevolve from invasion into this region of attraction, resulting in their fixation. This coevolution typically occurs across a wider range of conditions under the reward- than the punishment-based metanorm. We also show that, under appropriate conditions, a large negative statistical association between the two traits may evolve only under the Reward Model. Furthermore, for each metanorm, a population of norm-adopters who always observe the norm can be locally stable over a continuum of punishment frequencies.