Cooperation, with friends or with relatives?

Based on a survey of 200 papers, Kay et al. (1) argue that many modeling results on the evolution of helping are likely due to kin selection, although this was not acknowledged by the original authors. Our work (2) on the evolution of indirect reciprocity is one of the papers surveyed and criticized. We agree with many of the conclusions by Kay et al., but we wish to point out that the evolutionary stability of the standing strategy, which we investigated, does not depend on relatedness between donors and recipients of help. We, in fact, showed this analytically. We argued that the evolutionary success of so-called image-scoring strategies, proposed by Nowak and Sigmund (3), depends on genetic drift in small populations, and thus potentially on relatedness, whereas the standing strategy is robust to those effects. We conclude that there are cases where modelers have discovered the evolution of helping without carefully considering whether help is predominantly directed toward relatives, but there are also thoroughly studied strategies for which helping is dependent on social relationships other than relatedness. The standing strategy is one such example.

Fig. 1 illustrates our conclusion. The standing strategy persists at high frequency over the range from very limited (m = 0.01) to full (m = 1) dispersal, corresponding to the range of within-subpopulation relatedness from over 0.25 down to zero (Fig. 1A). A relevant measure of relatedness is Wright's fixation index F_ST, as pointed out by Lehmann and Rousset (4), and it is shown in the figure. The alternatives in the analysis are discriminators, which are a type of image-scoring strategy (2); cooperators; and defectors. The standing strategy can also invade from low frequency in this population. Without the standing strategy present, discriminators can persist in combination with cooperators at low rates of dispersal (Fig. 1B), but, in this example, discriminators cannot invade from low frequency when m > 0.01. It is worth noting that, with only cooperators and defectors present, defectors dominate even for substantial within-population relatedness (triangles in Fig. 1B). The explanation is that benefits of receiving help are counteracted by effects of kin competition (4). Thus, the b in Hamilton's rule, rb − c > 0, is effectively zero for helping a random subpopulation member. For strategies that discriminate within subpopulations, which hold both for standing and image scoring, relatedness can influence the evolutionary outcome. However, as seen in Fig. 1A, this does not undermine the stability of the standing strategy.

Fig. 1.

The evolutionary stability of the standing strategy does not depend on relatedness. (A) In an island model metapopulation, with 100 subpopulations each of size 100, the standing strategy dominates against the alternatives image scoring (IS), always cooperation (C), and always defection (D), irrespective of the rate of dispersal, including for full dispersal (m = 1; the points for IS and C are shifted right and left for clarity). The gray curve shows F_ST. (B) Without the standing strategy, IS persists at intermediate frequency together with C for low rates of dispersal, but D takes over for higher rates of dispersal. The triangles show a situation with only C and D, for which D dominates irrespective of m, as a consequence of kin competition. Individual-based simulations are over 10,000 generations for each of m = 0.01, 0.05, 0.10, 0.20, 0.30, 0.40, 0.50, 0.75, and 1.00. Other parameters are as in figure 4 of ref. 2: 500 rounds of interaction, helping benefit 1.0 and cost 0.25, 5% execution errors, and mutation rate of 0.001.

Overall, we support the reasoning by Kay et al. (1) that much modeling of the evolution of helping would profit from making clear the role of relatedness. This applies to so-called spatial games, as we have emphasized in a comment (5) on a target review by Lehmann and Keller (6), and this would also apply to games on graphs. Nevertheless, even if modelers can be criticized for neglecting to clarify the role of relatedness, it is still the case that other social relationships, such as reciprocity, can independently promote the evolution of helping.