Social organisms living in stable groups often engage in aggressive interactions with conspecifics from neighbouring groups over territory, mating opportunities and other resources. The outcome of these interactions can significantly affect both individual fitness and group survival. Examples include border patrols in chimpanzees1 2, raiding parties in spider monkeys3, clan wars in hyenas4 and between-group fights in lions5, free-ranging dogs6, meerkats7, Capuchin monkeys8, blue monkeys9, black howler monkeys10 and ring-tail lemurs11. As in other collective activities that lead to the production of a public good, aggressive between-group interactions result in a collective action problem: if a group member benefits from the action of group-mates and individual effort is costly, then there is an incentive to ‘free ride’, that is, to reduce one’s effort or to withdraw it completely. However, if individuals follow this logic, the public good is not produced and all group members suffer. Overcoming the collective action problem is a major challenge facing social groups across a range of species, including humans12 13 14. Theoretical studies of cooperation have identified several possible solutions for reducing free-riding tendencies, such as altruism, relatedness, direct and indirect reciprocity, and punishment15 16. Although these mechanisms should in general also apply to cooperation in between-group conflict, theoretical and empirical work is limited in scope17. Here we investigate the collective action problem in between-group conflict within an evolutionary context. In particular, we study the effect of within-group inequality on provision of the public good, that is, differences between group-mates in dominance rank, status, motivation, valuation of the reward, costs paid and strength. We identify a mechanism that can overcome the collective action problem in groups of unrelated individuals without recourse to altruism, reciprocity or punishment. Our focus is on the evolution of social instincts. As first argued by Darwin in On the Origins of Species, social instincts—that is, genetically based propensities that govern the behaviour of individuals in social interactions—have evolved by natural and sexual selection. In modern perspective, these instinctive social behaviours are plastic, resulting from the interaction of the genotype with the social environment (including the behaviour of social partners)18. By focusing on the origin of social instincts, the framework we develop here aims to place the debate19 on between-group conflict in human evolution within a broad cross-specific perspective. A crucial evolutionary question, discussed already by Darwin in The Descent of Man, is how important between-group conflict was in shaping the human behavioural repertoire. Existing theoretical work suggests that relatively modest levels of mortality in between-group conflict could have sufficiently large evolutionary effects, driving the emergence of characteristic human abilities, biases and preferences (for example, cooperation, altruism, belligerence, parochialism and ethnocentrism), as well as social and cultural norms and institutions16 20 21 22 23 24. Like Darwin’s account, these theoretical approaches rely on factors that are exclusive to our species, such as cultural transmission aided by language, culturally enforced sharing norms or group decisions and particular within- and between-group interaction patterns (for example, cultural group selection)16 22. Given that our approach does not rely on these factors, our insights may apply to any species with between-group conflict. This body of theoretical work is informed by inferences drawn from comparison with the social systems of other primate species, or from archaeological and ethnographic data16 25 26 27 28 29 30. Many of these inferences are contentious19. For example, the ethnographic data typically pertain to present-day mobile forager groups, which are characterized by an egalitarian social structure31. However, it is not clear to what extent this social system is a good ‘model’ for early human groups. Other types of small-scale societies may also provide clues to early human social systems, but they have been largely neglected in the literature on the evolution of cooperation. This includes semisedentary and sedentary forager groups with varying degrees of hierarchy and other types of inequality. Our work may provide insights into the dynamics of these groups and guide discussions of human cooperation towards a broader conceptual framework. Our models are grounded in contest theory, an approach used widely in economics32. We extend in several important directions existing work on the evolution of cooperation in the context of between-group conflict. First, rather than allowing for only two discrete strategies (for example, cooperate and defect), we use a more general and realistic framework in which individual efforts and costs are treated as continuous variables; this is also more in line with experimental economic games, where subjects can typically vary their contributions continuously. Second, existing models of between-group conflict use standard public goods games, where individual benefit is a linear function of the number of contributors (or of their total effort). However, it is now recognized that this assumption can lead to misleading conclusions32 33. In our approach, benefits are specified by a nonlinear function explicitly capturing the efforts of both focal and competing groups. Third, existing approaches postulate a completely egalitarian division of spoils and disregard any differences between individuals except for the strategy they use. In contrast, as noted above we explicitly aim to capture the effects of differences between individuals on their strategies and the fitness consequences of their actions (for example, differences with respect to their dominance rank, status, motivation, valuation of the reward, costs paid and strength). Finally, compared with related work in the economics literature32 34, our approach adds biological realism by focusing on evolution by small mutations, by explicitly allowing for group extinction and multiplication and by investigating the effects of migration and genetic relatedness. Here we study a series of mathematical models describing competition between groups comprising heterogenous individuals. Our models show that within-group inequality leads dominant individuals (or those with higher strengths or lower costs) to contribute the effort required to produce the public good (that is, to succeed in between-group competition) while the rest of the group free rides12. This is because they can ‘afford’ higher costs of contribution, owing to their larger shares of the public good. Their behaviour is seemingly altruistic, in the sense that they contribute more effort than their group-mates and often have lower fitness as a result. Their contribution is driven by competition with their counterparts in other groups rather than with their own group-mates. This mechanism can overcome the collective action problem in groups of unrelated individuals without resorting to altruism, reciprocity or punishment. Results Basic model We consider a population of individuals living in a large number of groups G of constant size n. The groups engage in competition for resources, which affects their survival and multiplication as well as the reproduction of members of surviving groups. Groups can be egalitarian, so that each individual gets an equal share of the resources that the group obtains, or hierarchical, so that each individual’s share depends on its dominance rank. Each group faces a collective action problem. The amount of resources obtained by each group depends on the total effort of its members towards the group success; at the same time, individuals pay fitness costs that increase with their efforts. Each individual’s effort is controlled genetically and is modelled as a non-negative continuous variable. In the case of hierarchical groups, individual efforts are conditioned on the dominance rank, which is assigned to group members randomly at each generation (for example, based on their strength). There is no coercion. We allow for mutation, recombination, migration and genetic relatedness between individuals. To introduce our approach and results, we start with a simple model. Let P j be a share of the resources obtained by group j in competition with other groups, and x ij the effort of individual i in group j towards the group’s success (i=1,…,n; j=1,…,G). We specify the total group effort as where the sum is taken over all group members, and define the group success probability P j as where the sum is taken over all groups32 35. We assume that the groups survive to leave offspring to the next generation with probabilities equal to P j . For members of such groups, we define individual fertility as where f 0 is a constant baseline fertility (which can be set to 1 without loss of generality), B is the total (normalized) resource contested by the groups, c is the cost parameter and v i is the share of the group’s reward allocated to individual i. We treat valuations v i as constants dependent on the within-group dominance rank (v 1≥v 2≥…≥v n; ∑ v i =1). The groups that do not survive are replaced by the offspring of surviving groups. Generations are discrete and non-overlapping. Specifically, we assume that each group in the current generation descends from a group in the previous generation chosen randomly and independently with probabilities P j . Individuals in each group descend from individuals in their parental group independently with probabilities , where is the average fertility in group j (=Σ i f ij /n). Under these assumptions, the fitness of individual i from group j is In what follows it will be convenient to use parameter b=B/(nG), which is the expected benefit per individual in an egalitarian group if all individuals in the population are identical. Below we describe our key findings. A technical explanation and derivations of our results are given in the Methods. Egalitarian groups Consider first the case when groups are egalitarian so that v i =1/n for all i. Then, the population is predicted to evolve to an equilibrium at which the total group effort is while each individual effort is =X*/n. As expected, both individual and group efforts increase with benefit b and decrease with cost c. Increasing the group size n (while keeping b constant) does not change the total group effort, but it decreases the individual effort as a result of increasing free riding. If the benefit per individual b decreases with group size n, then the total group effort will decrease with increasing n. These results assume that the groups are formed uniformly at random each generation, implying that group members are no more genetically related to one another than they are to members of other groups. The evolution of cooperation in a public goods game as studied here is driven by the overlapping interests of group-mates36 and does not require genetic relatedness (or reciprocity, coercion or punishment)33 37. Genetic relatedness does however increase cooperation15. In the model considered here, with average within-group relatedness r and no between-group relatedness, each individual effort increases by factor For example, let female offspring disperse randomly between groups while male offspring stay in the natal group (as in chimpanzees and, likely, in our ancestors38). This will result in a ~30% increase in the individual and group efforts relative to the case of zero relatedness (assuming that n≥5). Hierarchical groups The results outlined above assume a completely egalitarian division of the spoils. In hierarchical groups, the predicted collective action behaviour is strikingly different. With random group formation, only individuals with valuations v i higher than a certain threshold will make a non-zero effort, while low valuators will free ride contributing nothing. All ranks will contribute only if, for each i, Note that the threshold value v crit is close to 1/n if the group size n and/or benefit b are large. If all ranks do contribute, then the total group effort X*=(1+b)/c, which is the same as in egalitarian groups. Ranks for which v i 1 it is a decreasing, concave-up function of rank. In simulations, we used five values of δ=0.25, 0.5, 1, 2, 4. Figure 2 illustrates the dynamics of individual efforts and fertilities with n=8. In this case, only the top three ranks make substantial contributions. (Note that because of mutation individual contributions always remain positive). Figure 3 shows the average efforts and fertilities for different ranks with n=12. The ranks with the lowest valuations contribute almost nothing and their fertilities increase with valuation. The contributions of the high valuators increases linearly with v i but their fertilities decrease linearly with v i . Figure 4 is a summary graph showing that as within-group inequality increases (measured by δ), the individual efforts of high valuators increase while their shares of reproduction decrease. They also show that the total group effort grows with within-group inequality and benefit b. Generalizations To check the robustness of our conclusions, we have also studied two modifications of the basic model. In the first version, the probability of group success was specified as where β is a positive parameter measuring the ‘decisiveness’ of the group strength: β>1 implies that stronger groups will get disproportionately large shares of the reward32. Increasing β increases both the individual and group efforts (as expected), but it results in no other qualitative differences (Fig. 5). In another modification, we assumed that group-mates share the reward equally (v i =1/n) but differ with respect to the cost coefficient c i . This may be the case if some individuals are stronger than others, so that the same amount of effort can be less costly for them in fitness terms. In our simulations, we used costs c i that increased linearly with rank i. Specifically, we used n equally spaced values of c i from (1−d)/2 to (1+d)/2 with five different values of d: 0.05 (small differences in costs), 0.1, 0.2, 0.4, 0.8 (large differences in costs). Our major conclusions remain qualitatively valid, with low-cost individuals playing the role of high-valuation group members in the basic model (Fig. 6). Note that the model with differences in costs is mathematically equivalent to a model with a constant cost c but with differences in fighting abilities s i and the total group effort defined as In this model, individuals with larger fighting abilities s i will, ceteris paribus, contribute more to X. Therefore, our conclusions are applicable to the case of within-group variation in strengths. That is, lower-cost or higher-strength individuals are predicted to contribute more effort than their group-mates, and they can have lower reproductive success as a result. Discussion We have studied the collective action problem in between-group conflict within an evolutionary context, focusing on the effect of within-group inequality in dominance rank, status, motivation, valuation of the reward, costs paid and strength. We have shown that inequality in rank can lead dominant individuals to act seemingly altruistically towards their group-mates by contributing the effort required to succeed in between-group competition while others free ride. As a result, these individuals have reduced reproductive success compared with their free-riding subordinate group-mates. Analogous reasoning applies when individuals differ in the costs incurred from contributing to the public good or when they differ in strength: lower-cost or higher-strength individuals contribute more effort to the public good, and they have reduced reproductive success compared with their free-riding group-mates as a result. This behaviour may seem altruistic but actually it is not. In the case of hierarchical groups, for example, dominant individuals maximize their fitness by contributing; given the subordinates’ lack of contribution, dominants will not be better off by reducing their contribution or by withholding it completely. Thus, the non-contributors are indeed free riding, but the contributors are not altruistic; paradoxically, they are acting in their own interest by contributing to the public good. What is driving their contribution is that they are essentially competing with their counterparts in other groups rather than with their own group-mates. The outcome of seemingly altruistic behaviour by dominant individuals (or those with lower costs or higher strength) is consistent with Olson’s controversial conclusion that individuals who obtain the greatest share of a public good bear a disproportionate share of the costs, leading to ‘a systematic tendency for ‘exploitation’ of the great by the small!’ [12, (p. 29)]. Olson’s insight relates to the phenomenon of collective action within a single group. Here we have shown that this effect can be even more extreme when the driving force of collective action is between-group conflict coupled with within-group inequality. In this case, groups of unrelated individuals can ‘solve’ the collective action problem without resorting to altruism, reciprocity or punishment. Note that we assumed that individual efforts are only limited by the requirement of non-negative fertility (cx i 0) if for all i Note that increasing the value of the resource b or the group size n moves v crit closer to 1/n, so that individuals with a valuation smaller than the average will not contribute but will free ride. Equation (19) shows that individual efforts increase with valuation v i . In contrast, individual reproductive success at equilibrium is and thus decreases with valuation. That is, the higher costs paid by high-rank individuals negate their larger shares of the reward. If not all group members make a positive effort, then the derivations become more complex. Let there be n e contributors and v be their total valuation (v=∑ v i where the sum is over n e contributors). Then, summing up equation (16) over all contributors, at equilibrium their total effort X satisfies to a quadratic equation Of the two solutions of this quadratic, only the smallest one, X*, is relevant biologically (the other solution leads to negative fertilities). Note that cX*≤n e+bnΣv i
