This article may be too technical for most readers to understand.(April 2015)
Reciprocity in evolutionary biology refers to mechanisms whereby the evolution of cooperative or altruistic behaviour may be favoured by the probability of future mutual interactions. A corollary is how a desire for revenge can harm the collective and therefore be naturally deselected.
Three types of reciprocity have been studied extensively:
- Direct reciprocity
- Network reciprocity
Direct reciprocity was proposed by Robert Trivers as a mechanism for the evolution of cooperation. If there are repeated encounters between the same two players in an evolutionary game in which each of them can choose either to "cooperate" or "defect", then a strategy of mutual cooperation may be favoured even if it pays each player, in the short term, to defect when the other cooperates. Direct reciprocity can lead to the evolution of cooperation only if the probability, w, of another encounter between the same two individuals exceeds the cost-to-benefit ratio of the altruistic act: w > c / b
"In the standard framework of indirect reciprocity, there are randomly chosen pairwise encounters between members of a population; the same two individuals need not meet again. One individual acts as donor, the other as recipient. The donor can decide whether or not to cooperate. The interaction is observed by a subset of the population who might inform others. Reputation allows evolution of cooperation by indirect reciprocity. Natural selection favors strategies that base the decision to help on the reputation of the recipient: studies show that people who are more helpful are more likely to receive help." In many situations cooperation is favoured and it even benefits an individual to forgive an occasional defection but cooperative societies are always unstable because mutants inclined to defect can upset any balance.
The calculations of indirect reciprocity are complicated, but again a simple rule has emerged. Indirect reciprocity can only promote cooperation if the probability, q, of knowing someone’s reputation exceeds the cost-to-benefit ratio of the altruistic act:
- q > c / b
One important problem with this explanation is that individuals may be able to evolve the capacity to obscure their reputation, reducing the probability, q, that it will be known.
Individual acts of indirect reciprocity may be classified as "upstream" or "downstream":
- Upstream reciprocity occurs when an act of altruism causes the recipient to perform a later act of altruism in the benefit of a third party. In other words: A helps B, which then motivates B to help C.
- Downstream reciprocity occurs when the performer of an act of altruism is more likely to be the recipient of a later act of altruism. In other words: A helps B, making it more likely that C will later help A.
Real populations are not well mixed, but have spatial structures or social networks which imply that some individuals interact more often than others. One approach of capturing this effect is evolutionary graph theory, in which individuals occupy the vertices of a graph. The edges determine who interacts with whom. If a cooperator pays a cost, c, for each neighbor to receive a benefit, b, and defectors have no costs, and their neighbors receive no benefits, network reciprocity can favor cooperation. The benefit-to-cost ratio must exceed the average number of people, k, per individual:
- b / c > k (See below, however.)
Recent work  shows that the benefit-to-cost ratio must exceed the mean degree of nearest neighbors, <knn>:
- b / c > <knn>
- R. Trivers, Q. Rev. Biol. 46, 35 (1971).
- A simple rule for the evolution of cooperation on graphs and social networks. Ohtsuki H1, Hauert C, Lieberman E, Nowak MA. Nature. 2006 May 25;441(7092):502-5.
- Nowak, M. A. (2006). "Five rules for the Evolution of Cooperation". Science. 314 (5805): 1560–1563. Bibcode:2006Sci...314.1560N. doi:10.1126/science.1133755. PMC 3279745. PMID 17158317.
- "Does it pay to be nice? – the maths of altruism part i". plus.maths.org. April 24, 2012.
- Nowak, M. A.; Sigmund, K. (1998). "Evolution of indirect reciprocity by image scoring". Nature. 393 (6685): 573–7. Bibcode:1998Natur.393..573N. doi:10.1038/31225. PMID 9634232. S2CID 4395576.
- Fowler, JH (2005). "Second Order Free Riding Problem Solved?". Nature. 437 (7058): E8, discussion E8–9. Bibcode:2005Natur.437E...8F. doi:10.1038/nature04201. PMID 16177738. S2CID 4425399.
- Nowak, M. A.; Roch, S (2007). "Upstream reciprocity and the evolution of gratitude". Proceedings of the Royal Society B: Biological Sciences. 274 (1610): 605–610. doi:10.1098/rspb.2006.0125. PMC 2197219. PMID 17254983.
- Lieberman, E.; Hauert, C.; Nowak, M. A. (2005). "Evolutionary dynamics on graphs" (PDF). Nature. 433 (7023): 312–316. Bibcode:2005Natur.433..312L. CiteSeerX 10.1.1.398.4515. doi:10.1038/nature03204. PMID 15662424. S2CID 4386820.
- Ohtsuki, H.; Hauert, C.; Lieberman, E.; Nowak, M. A. (2006). "A simple rule for the evolution of cooperation on graphs". Nature. 441 (7092): 502–505. Bibcode:2006Natur.441..502O. doi:10.1038/nature04605. PMC 2430087. PMID 16724065.
- Konno, Tomohiko (2011). "A condition for cooperation in a game on complex networks". Journal of Theoretical Biology. 269 (1): 224–233. CiteSeerX 10.1.1.763.2044. doi:10.1016/j.jtbi.2010.10.033. PMID 21044635. S2CID 15555524.
- Martin Nowak Evolutionary Dynamics: Exploring the Equations of Life Harvard 2006
- Martin Nowak Five Rules for the Evolution of Cooperation Science 314, 1560 (2006)
- Panchanathan K. & Boyd, R. (2004). Indirect reciprocity can stabilize cooperation without the second-order free rider problem. Nature 432: 499–502. Full text
- Panchanathan K. & Boyd, R. (2003) A Tale of Two Defectors: The Importance of Standing for the Evolution of Indirect Reciprocity. Journal of Theoretical Biology, 224: 115–126. Full text
- Lindenfors P (2017) For Whose Benefit? The Biological and Cultural Evolution of Cooperation. Springer. ISBN 978-3-319-50873-3.