Trading public goods stabilizes interspecific mutualism Marco Archetti a,n , Istva ´ n Scheuring b a Economic Theory, Faculty of Business and Economics, University of Basel, Peter Merian-Weg 6, Basel 4002, Switzerland b Research Group in Theoretical Biology and Evolutionary Ecology, Department of Plant Systematics, Ecology and Theoretical Biology, E¨ otv¨ os University, Pa ´zma ´ny P. s. 1/C, 1117, Budapest, Hungary HIGHLIGHT c Interspecific mutualism raises a collective action problem: why cooperate? c Punishment is not possible when one cannot discriminate cooperators from defectors. c Assume that two groups of individuals trade non-linear goods. c In this case mutualism is maintained by the exchange of these goods alone. c Punishment is only necessary if benefits are linear (the N-person prisoner’s dilemma). article info Article history: Received 13 June 2012 Received in revised form 10 September 2012 Accepted 17 October 2012 Available online 24 October 2012 Keywords: Game theory Cooperation Evolution Collective action Symbiosis abstract The existence of cooperation between species raises a fundamental problem for evolutionary theory. Why provide costly services to another species if the feedback of this provision also happens to benefit intra-specific competitors that provide no service? Rewarding cooperators and punishing defectors can help maintain mutualism; this is not possible, however, when one can only respond to the collective action of one’s partners, which is likely to be the case in many common symbioses. We show how the theory of public goods can explain the stability of mutualism when discrimination between cooperators and defectors is not possible: if two groups of individuals trade goods that are non-linear, increasing functions of the number of contributions, their mutualistic interaction is maintained by the exchange of these public goods, even when it is not possible to punish defectors, which can persist at relatively high frequencies. This provides a theoretical justification and testable predictions for the evolution of mutualism in the absence of discrimination mechanisms. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction 1.1. The collective action problem in mutualistic interactions without dicrimination A host and a symbiont can cooperate if they have a shared interest, for example if the symbiont is transmitted vertically from parent to offspring. Many mutualisms, however, involve multiple, non-clonal symbionts per host, or horizontal transmis- sion of symbionts among unrelated host individuals (Frank, 1996). In this case, a collective action problem (Olson, 1965) arises: while the symbionts as a group could obtain more resources by the prudent exploitation of the host, each symbiont is selected to pursue its own short-term interest to increase its fitness, at the expense of the other symbionts and of the host, a problem analogous to the ‘‘tragedy of the commons’’ (Hardin, 1968) arising in the exploitation of common pool resources (Ostrom, 1990). What prevents an individual symbiont from free-riding on the contributions of the other symbionts? Most of the literature on mutualism has focused on punish- ment as a way to maintain cooperation between species. Punish- ing non-cooperative partners or rewarding cooperative ones can help solve the problem (Clutton-Brock and Parker, 1995) if the behaviour of the partners can be observed (Fig. 1a). The potential for discrimination has been described in certain rhizobia (Kiers et al., 2003) and mycorrhizal fungi (Kiers et al., 2011). While it is difficult to prove the absence of punishment in other systems (but for rhizobia see, for example, Heath and Tiffin, 2009), it stands to reason that in some cases discrimination may not be possible and one may only be able to react to the collective action of its partners (Fig. 1b), either because there is no way to detect the behaviour (or its effects) of individual partners or because the differences between cooperators and non-cooperators are too Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/yjtbi Journal of Theoretical Biology 0022-5193/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jtbi.2012.10.022 n Corresponding author. Tel.: þ41 61 267 28 36. E-mail addresses: marco.archetti@unibas.ch, archetti.marco@gmail.com (M. Archetti), scheurin@caesar.elte.hu (I. Scheuring). Journal of Theoretical Biology 318 (2013) 58–67