Five Rules for the Evolution of Cooperation

Cooperation is required for new levels of organization like genomes, cells, multicellular organisms, social insects, and human society to emerge. But if cooperation means that individual entities pay some cost c to provide benefit b (both measured in terms of fitness) to some other entity, why should it ever occur in the competitive regime of evolution by natural selection?

Nowak (2006) describes five mechanisms by which natural selection can foster cooperation.

  1. Kin selection. Natural selection can favor cooperation between related individuals, where relatedness r is defined as the probability of sharing a gene. For siblings, r = 1/2; for cousins, r = 1/8, etc. Hamilton’s rule says that cooperation emerges only if r > c/b.
  2. Direct reciprocity. Tit for tat, or I help you if you help me. This requires repeated interactions. More specifically, direct reciprocity can only lead to cooperation if the probability w of another meeting between the same two individuals is greater than the cost-benefit ratio: w > c/b.
  3. Indirect reciprocity. I help you. Somebody helps me.” Indirect reciprocity works via reputation, as your decision to cooperate or defect is observed by others who may gossip about it so that others can use it to decide whether to cooperate with you. It can only support cooperation if the probability q of knowing someone’s reputation is greater than the cost-benefit ratio: q > c/b.
  4. Network reciprocity. Suppose cooperators pay a cost c to benefit each of their neighbors by b. Cooperators can then win out by forming clusters in which they cooperate. The benefit-cost ratio must be greater than the average number of neighbors: b/c > k.
  5. Group selection. Suppose a population is divided into groups, and that cooperators help others in their own group. Individuals reproduce in proportion to their payoff, and offspring are added to the same group. If a group becomes sufficiently large, it can split into two. When this happens, another group goes extinct, so that the total population size is constrained. In the case of weak selection and rare group splitting, we get the following. If n is the maximum group size and m is the number of groups, cooperation can emerge if b/c > 1 + n/m.

These are not all potential mechanisms for the evolution of cooperation. For example, in green beard” models recognize one another via arbitrary markers. Cooperation can also emerge if the game is voluntary: if players can choose cooperate, defect, or walk away, cooperation typically wins out. Punishment can promote cooperation in certain situations, but is not itself a mechanism for the evolution of cooperation. All models of punishment rely on other underlying mechanisms (e.g. indirect reciprocity, group selection, or network reciprocity), but it can increase the rate of cooperation in such models.

May 4, 2023