common to consider the role of broader ecological interactions on the evolution of various forms of altruism.
Here, we consider the evolution of restraint in communities where ecological interactions generate a type of negative feedback. One of the simplest communities with this property involves three members engaged in nontransitive competition. A simple scenario entails one player incurring a significant cost to harm a second player (e.g., through parasitism or allelopathy) and a third player possessing mildly costly resistance to the harm. Reminiscent of the children’s game rock–paper–scissors, the harmer outcompetes the sensitive player, who outcompetes the resistant player; in turn, the resistant player outcompetes the harmer. Such nontransitivity has been reported in plant systems (Lankau and Strauss, 2007; D. D. Cameron et al., 2009) and as we see below, bacterial systems. More generally, in rock–paper–scissors games, each strategy beats one of the other two and is beaten by the third (e.g., paper covers rock but is cut by scissors). Imagine a nontransitive community in which, for convenience, we call the players Rock, Paper, and Scissors. Each type has a rate at which it displaces its victim (e.g., Rocks crush Scissors at some rate). Next, imagine a less-restrained variant of Rock, called Rock*, that displaces Scissors at a faster rate. In a Rock*–Paper–Scissors community, the abundance of Scissors decreases because of the increased prowess of Rock*. As a consequence, Scissors’ victim (Paper) is liberated, which can displace Rock*. In an ironic twist, the improved Rock* decreases in abundance because of the expansion of its victim’s victim. This form of negative feedback ensures that a higher displacement rate results in decreased abundance (Tainaka, 1993, 1995; Frean and Abraham, 2001; Marsland and Frank, 2001). Thus, more restrained players may be less prone to extinction, a phenomenon termed “survival of the weakest” (Frean and Abraham, 2001). A complication arises when considering a community with multiple variants present simultaneously (e.g., Rock and Rock* with Paper and Scissors). The same traits that allow Rock* to displace Scissors faster may render Rock* a better competitor against Rock. In this case, restraint has a selective disadvantage, despite its positive effects on abundance. How then can restraint evolve in a nontransitive community?
Spatial structure can play a critical role promoting restraint in non-transitive systems. Returning to our Rock–Paper–Scissors community, limitation of dispersal results in a patchwork of the three players. A patch of any one player chases its victim and is chased by its enemy (Durrett and Levin, 1997; Kerr et al., 2002). Within any patch, an unrestrained variant (Rock*) will replace its restrained counterpart (Rock). However, patches of unrestrained variants are more likely to go extinct. This difference in patch viability favors restraint. Limited dispersal ensures a type of posi-