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Home , Cultural evolution, Martin Nowak

The of altruism and the serial rediscovery of the role of relatedness Tomas Kaya , Laurent Kellera,1 , and Laurent Lehmanna

aDepartment of Ecology and Evolution, University of Lausanne, 1015 Lausanne, Switzerland

Edited by Joan E. Strassmann, Washington University in St. Louis, St. Louis, MO, and approved October 2, 2020 (received for review July 6, 2020)

The genetic evolution of altruism (i.e., a behavior resulting in a understand the genetic evolution of altruism, and more gener- net reduction of the survival and/or reproduction of an actor to ally of any trait, it is crucial to consider the average fitness of benefit a recipient) once perplexed biologists because it seemed all individuals bearing a given allele responsible for producing paradoxical in a Darwinian world. More than half a century ago, a change in that trait. In particular, in a population of homo- W. D. Hamilton explained that when interacting individuals are geneous individuals, an altruism-inducing allele will increase in genetically related, alleles for altruism can be favored by selec- frequency when rb − c > 0, where −c is the average effect of tion because they are carried by individuals more likely to interact the altruism-inducing allele on the fitness of its bearer, b is the with other individuals carrying the alleles for altruism than ran- average effect on the fitness of recipients, and r is the genetic dom individuals in the population (“”). In recent relatedness between the actor and the recipients (7). decades, a substantial number of supposedly alternative path- Relatedness r is a regression coefficient measuring how the ways to altruism have been published, leading to controversies alleles in a particular individual covary in frequency with those surrounding explanations for the evolution of altruism. Here, we of individuals with whom the individual interacts (8, 9). Relat- systematically review the 200 most impactful papers published edness is thus a measure of the extent to which the recipient of on the evolution of altruism and identify 43 evolutionary mod- altruism is more likely than a random individual in the popu- els in which altruism evolves and where the authors attribute lation to carry the altruism-inducing allele present in the actor. the evolution of altruism to a pathway other than kin selection Usually, such assortment results from actor and recipient hav- and/or deny the role of relatedness. An analysis of these models ing inherited identical alleles from a recent common ancestor reveals that in every case the life cycle assumptions entail local (i.e., alleles in actor and recipient are identical by descent; see reproduction and local interactions, thereby leading to interact- Box 1 for more complex situations). For example, family struc- ing individuals being genetically related. Thus, contrary to the ture results in particular relatedness patterns: In diploid species authors’ claims, Hamilton’s relatedness drives the evolution to where mating occurs randomly in the population, siblings have a altruism in their models. The fact that several decades of inves- relatedness of 1/2 (i.e., they have a 50% chance of having inher- tigating the evolution to altruism have resulted in the systematic ited the same allele from their parents at any given locus) and and unwitting rediscovery of the same mechanism is testament the relatedness between aunt and nephew is 1/4. Because the to the fundamental importance of positive relatedness between best-known cases of altruism occur between highly related indi- actor and recipient for explaining the evolution of altruism. viduals, John Maynard Smith coined the term kin selection to describe the operation of in a context where evolution | kin selection | altruism | Hamilton’s rule | rediscovery interactions occur among genetically related individuals (10, 11). Unfortunately, this has sometimes given the incorrect impres- sion that kin selection operates only within structured families. cademic discoveries are often made simultaneously and In reality, kin selection operates as soon as there is limited Aindependently by multiple scientists (1–3). In the 17th cen- genetic mixing and interacting group size is not infinite, as in the tury, Newton and Leibniz independently developed calculus. The “viscous,” “island,” and “stepping-stone” models of spatial pop- theory of evolution by natural selection was discovered inde- ulation structure described in Fig. 1. In these models, dispersal pendently by (1858) and Alfred Wallace (1858). is limited and locally interacting individuals are likely to share There are also instances of the same discovery being made many years apart. The heliocentric solar system was first discovered by the Ancient Greek astronomer Aristarchos of Samos (∼310 to Significance 230 BC), but received little attention until it was independently rediscovered 18 centuries later by the Renaissance mathemati- The canonical explanation for the evolution of altruism (“kin cian Nicolaus Copernicus. Such asynchronous rediscoveries have selection”)—which was mathematically derived in the 1960s become rare in a globalized world of communication between by W. D. Hamilton—emphasizes the importance of genetic distant regions and accessible online information. However, over relatedness. Over the past three decades, numerous authors the past few decades a striking exception has unfolded in the claim to have discovered alternative explanations. We sys- evolutionary sciences, where many researchers have repeatedly tematically analyze the models substantiating these claims rediscovered that interactions between relatives favor the evo- and reveal that in every model the interacting individuals lution of altruistic traits, despite this mechanism having been are genetically related and that the authors have therefore uncovered and mathematically described more than half a cen- unwittingly rediscovered Hamilton’s insight. tury ago by W. D. Hamilton (4–6). What is more, unlike previous cases, this rediscovery does not seem to have resulted from igno- Author contributions: T.K., L.K., and L.L. designed research; T.K. and L.L. analyzed data; rance of the existence of previous work, but from a failure to and T.K., L.K., and L.L. wrote the paper.y recognize the equivalence between the processes underlying the The authors declare no competing interest.y models. This article is a PNAS Direct Submission.y The question of the genetic evolution of altruism—defined Published under the PNAS license.y here as a behavior decreasing the expected survival and/or repro- 1 To whom correspondence may be addressed. Email: [email protected] duction (fitness) of the actor while increasing the fitness of the This article contains supporting information online at https://www.pnas.org/lookup/suppl/ recipient—rose to prominence because altruism seemed para- doi:10.1073/pnas.2013596117/-/DCSupplemental.y doxical in a Darwinian world. In 1963, Hamilton showed that to First published November 2, 2020.

28894–28898 | PNAS | November 17, 2020 | vol. 117 | no. 46 www.pnas.org/cgi/doi/10.1073/pnas.2013596117 Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 uinssadlyepewoflo hsltrtr o believe evo- now of literature circle this larger follow the who relatedness, laypeople of and role the lutionists confident central of remain core the altruism a novelty on about while the working And, biologists about altruism. evolutionary of claims of evolution false the enjoyed driving curbing have mechanism efforts in these success not However, would little (22–27). altruism it that without and particular pos- evolve individuals is of taken interacting relatedness have evolution that among proved itive studies the mathematically previous and for models of account to such number claim to often A mechanisms 1 altruism. new Fig. in found described have structures employ- population models the simulation ing and mathematical dispersal, limited selection. kin this by in shaped even is Yet, evolution 16). phenotypic (13, context, the neighbors of increasing of phenotypes reproduction benefits of and indirect survival evolution the the out prevent sit- and cancel This certain altruism can Under population. competition competition.” the kin “kin of uations, from than occurrence random the other to each at leads against sampled compete selection individuals to kin are likely by related more that shaped hence are mixing and genetic be individuals locally occur limited to interactions Importantly, that likely (15). implies extent also are some most traits least likely hence at social are (14), to populations mixing all genetic all not limited not of if selection if form kin most some for exhibit Since condition to 13). defining (12, deter- the who operate loci is the others to This at actor trait. of the the with survival mining descent and by actor identical reproduction alleles an share by the expressed affect spatial traits evolving same therefore of the dispersal, components in limited genetic Under lived the generations. who previous ancestor in common neighborhood a from alleles a tal. et Kay ept h atta i eeto skont prt under operate to known is selection kin that fact the Despite ormi ntbe(45). unstable tend remain dynamics to evolutionary sig- the be between phenotype, to altruistic association and perfect them nal near expect a would without stable, one interac- more where entail relatives, models unstable beard among generally green tions when is even process are Finally, the requirements (44). that and these shows signal, if modeling that Second, met, of phenotype. to basis altruistic ability the the an on signal, sin- others a A among encode stringent: discriminate must very kin element are Mendelian of requirements gle independent its altruism First, of could it selection. evolution is that genetic it unlikely the is mechanism it drive beard experiment, green (6) thought the intriguing Hamilton an While by altruism (42). formally) of Dawkins investigated evolution and the not for (but mechanism discussed a beard 43), “green altruis- (42, the is same effect” This recognizes individuals. the other and in where mutation copies through replicate is frequently scenario arises allele such tic One assortment, descent. identity generating without by occur mechanism also can main assortment the identical-by-state is identity sharing descent While related. by recipient positively are that and text, so individuals descent, interacting actor main by identical are the from that alleles in identical-by-state results disper- explained limited assortment under As by sal, and 17). favored populations family-structured 12, be in to (4, a altruism is selection genetic alleles, kin altruistic for bearing condition the individuals necessary from other benefit of preferentially altruism alleles altruistic individu- than bearing whereby state assortment, als by And identical average. are population that the and alleles actor more between that share means alleles recipient assortment of where assortment recipient, of and actor measure a Models. is Beard Relatedness Green and Relatedness 1: Box endoeainlya h ieiefins fet fa co on actor an of effects fitness are lifetime benefits the and as costs operationally (i.e., defined the This because cycle. recipient arises life the dependence determining the and parameter values parameter increasing actor the on behavior particu- both depends a a (i.e., of as altruism of fitness in cooperation—defined expression “selfish”). results merely the ) one whether or (or models, and only allele the “altruistic” considering lar of most (one many with variants In () competing variants (alle- These two cultural variants models. genetic or either evolutionary of les) 119 dynamics formal remaining the evolution- the present investigate of models formal do cycles present life which the both). not papers, scrutinized under do appeared We 5 models. papers papers; ary these 195 Appendix, “evolu- = of (SI of total Seventy-six altruism” S2; each of and for S1 “evolution selecting results Tables and by search cooperation” Scholar examples of Google tion prominent 100 most There- top the comprehensively. the review identified of to we evolution numerous the fore, for too account are to mechanisms altruism novel of claims The Discussion and Results kin without evolve can altruism selection). whether (i.e., inter- the between individuals relatedness allow acting positive they without whether altruism investigate of to evolution population) evolving organisms an by faced in events behavioral, all demographic, underlying assumptions the cycle genetic (i.e., and life models the these analyze of then assumptions and papers identify mechanisms to alternative literature differ- the claiming a survey take broadly therefore We we approach. Here ent unsolved. remains issue the that okwt neatosocrigbtennihoignds.Reprinted nodes). 17. a ref. neighboring of from between permission node with net- occurring a the interactions becomes as population with the represented work nodes, links individual, (using migration since single model structure; size a lattice stepping-stone of of the groups composed or (using “groups” groups) model most within kin the island occurring rediscovering probably papers the interactions is the either it of use Most yet populations. selection explored, challeng- plant least most for the the model remains is realistic and space analyze continuous to with population model ing of viscous local field The the the 18–21). in and (13, explored dispersal, been limited has between under structure interact- related relatedness locally dispersal positively models, are stepping-stone indicate individuals and because ing island, Arrows viscous, shown the groups. not For groups. within are individuals occurs younger island reproduction the models, dots In smaller stepping-stone parenthood. models, indicate and viscous arrows evo- and and the panmictic individuals, younger affects the population indicate In thereby various behavior. and social by relatedness of induced lution of dispersal patterns limited influences how structures discussed who (17), 1. 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EVOLUTION recipients and are therefore complex functions of all life cycle and has been applied concretely to the calculation of cultural features. In particular, since costs and benefits are affected by relatedness in the “island model” of Fig. 1 (31) and reviewed kin competition, they depend on parameters defining the spa- (33)]. The inconsistency between the novelty claims of these tial structure of the evolving population (equation 7.13 in ref. 13, publications and their content is difficult to explain. One likely equations 5–7 in ref. 24, and figures 1 and 2 in ref. 28), and since contributing factor is the nonbiological framing of the mod- they are affected by the type of interaction and the likelihood els; terms such as “site update” and “strategy invasion” replace of repeated interaction, they depend on parameters defining the birth and death, and “players” and “neighbors” replace organ- behavioral interactions between individuals (equation 5 in ref. isms, siblings, and offspring. This semantic divergence obfus- 29 and equations 8 and 9 in ref. 26). These (lifetime) fitness cates the relation between these models and the established costs c and benefits b are therefore nontrivial to calculate and theory. essentially never correspond directly to the proximate costs and The 26 papers which make little or no mention of related- benefits of the prisoner’s dilemma stage game matrix to which ness attribute the evolution of altruism to diverse alternative they may be naively equated (the exception being a panmictic mechanisms including “social diversity,” “social viscosity,” “topo- population with one-shot interactions). Further, for a given sit- logical heterogeneity,” “network heterogeneity,” “network reci- uation, the cost c may change sign, from altruism (positive) to procity,” “spatial ,” “spatial structure,” and “multiplex cooperation (negative), as a function of the model’s parameter structure” (SI Appendix, Table S4). Analysis of these models values, such as dispersal rate and group size (see figures 1 and revealed that in every case interacting individuals are related, 2 in ref. 28 for illustrative examples). Since quantitatively calcu- relatives benefit from each other’s altruism, and kin selection lating c and b can be very demanding for a given model, we here therefore operates. This occurs through limited dispersal (or lim- qualitatively infer whether c is expected to be positive or negative ited cultural mixing) and local interaction as in the island and as this can often be done on examination of the life cycle assump- stepping-stone models of Fig. 1. Again, the framing of these mod- tions. Overall, altruism evolved under some parameter values in els obscures the underlying role of relatedness. For example, models presented in 89 of these papers. Among the remaining Szolnoki et al. (ref. 34, p. 2) write, “First, a randomly selected 30 papers, cooperation evolved in 28 cases, and we were unable player x acquires its payoff px by playing the game with its to assess whether altruism or cooperation evolved in the remain- nearest neighbors. Next, one randomly chosen neighbor denoted ing 2 cases (marked as “insufficient information” in SI Appendix, by y also acquires its payoff py by playing the game with its Tables S1 and S2). four neighbors. Lastly, player x tries to enforce its strategy sx Among the 89 altruism models, 46 adopted Hamilton’s con- on player y in accordance with the probability, W (sx → sy ) = ceptual framework, attributing the evolution of altruism to wx / (1 + exp[(py − px )/K ]), where K denotes the amplitude of positive relatedness. The remaining 43 all claimed alternative noise.” For a biologist, this translates as follows: Individuals are mechanisms. To evaluate the veracity of their claims, we first sub- randomly killed and tend to be replaced by the clonal offspring divided these 43 papers into those where the role of relatedness of their most fecund neighbors. In this situation, individuals will was denied (17 cases; SI Appendix, Table S3), and those which interact preferentially with clonal relatives, and interactions are made little or no mention of relatedness (26 cases; SI Appendix, likely to occur between parents and offspring and siblings owing Table S4). to the stepping-stone structure (Fig. 1) of the model. Altruistic Among the 17 papers where the presence/role of relatedness alleles (or memes) therefore spread through genetic (or cultural) was denied (SI Appendix, Table S3), our analysis of the life kin selection. cycles of the models showed that the proposed scenario led to The most commonly cited alternative mechanism to kin selec- positive relatedness between interacting agents in every case. tion is “spatial selection.” This mechanism was pioneered by Moreover, in most of these models, agents reproduced clonally Martin Nowak, who has been uniquely vocal in attempting to (e.g., “parents pass on their type to their offspring”) with inter- differentiate it from kin selection [e.g., “it is clear that kin selec- actions occurring among nearest neighbors, as in the stepping- tion is different from and different from spatial stone model of Fig. 1, with only one individual per node/group. selection” (ref. 35, p. 26)] despite his claims being repeatedly This represents the tritest instance of kin selection. Relatedness and formally dismissed (22–27). Using Google Scholar we there- coefficients equal 1 between parent and offspring and between fore identified his 10 most impactful spatial selection papers (SI siblings, and dispersal is limited to neighboring nodes so par- Appendix, Table S5). All of these papers use models where indi- ents place offspring therein and subsequently interact with them. viduals interact with relatives and where kin selection affects the While many of these models are framed in terms of the trans- evolution of altruism. Three of these Nowak papers already fea- mission of cultural variants (or memes) and are often called ture in SI Appendix, Table S3 [Traulsen and Nowak (36) and “strategies” (with strategies with higher payoffs being more Nowak et al. (37)] and SI Appendix, Table S4 [Ohtsuki et al. frequently “imitated”), from a conceptual evolutionary dynam- (38)]. The remaining seven constitute SI Appendix, Table S6. The ics perspective these models are indistinguishable from genetic models are of various types but all use lattice or graph popula- models, since they both investigate the differential proliferation tion structures, which are akin to the stepping-stone model of of different variants in a population. Different modes of cultural Fig. 1. The occurrence of such clear-cut rediscovery is easier to transmission (e.g., payoff-biased learning, vertical transmission, understand when considering the chronological development of one to many transmission such as following a leader) (30) will the separate literatures. While Nowak’s earlier models adopted affect the level of relatedness between interacting individuals rather different assumptions from those of the more biolog- as well as the amount of (cultural) kin competition between ically oriented concurrent/earlier kin selection literature, they them, and this can result in higher or lower selection pressure converged to them over time (Box 2). on altruism than under genetic transmission (31). However, no The claims that spatial structure affects the evolution of altru- other mechanism has been discovered, since selection still acts ism are not incorrect per se. As Hamilton himself emphasized on the social trait according to relatedness (and competition) (17), limited dispersal and local interaction lead to positive because traits are inherited and subject to differential prolif- relatedness among interacting individuals, which may promote eration. Thus, altruism spreads via cultural transmission when altruism under certain biological scenarios, as long as kin compe- altruistic actors preferentially help individuals to whom they tition is not too strong. Hence, the finding that spatial selection are positively culturally related. Hence, these models represent favors altruism is not novel, and the emphasis on space can an advance only insofar as Hamilton never applied his frame- be misleading; space is merely a proxy for relatedness patterns work to cultural evolution [this was pioneered in the 1990s (32) and in itself not sufficient to explain altruism. Space provides

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May temporal and chaotic Nowak [e.g., undergoes dynamics but then maintained be assortment, can interacting altruism that identical-by-state simula- so experience the altruists multiple when individuals with But, initiated up. are build tions never means can This relatedness payoffs. higher that receiving on nonaltruists surrounded by be mutant sides would altruistic all it single as eliminated a immediately since be altruism rare, will that when any spread meaning for never deterministic, allow can fully not mod- therefore The do are drift). genetic 47) els (i.e., (46, reproduction in May effects and sim- chance the Nowak models, selection of them kin to ulations typical converged Unlike and initially time. (13)] models over 2004 only selection in reviewed kin 1990s; “typical” dif- the broad [in of models those colleagues’ The from and occurred. fered Nowak such Martin have how of could understand assumptions better rediscovery the can under- of one large-scale through history, as history useful this “rediscovery” is standing This the literature. explore selection spatial briefly here Models. Evolution We Theoretical of Evolution 2: Box c n benefit and b , )Frppr hc rsne omleouinr oe,w qualita- we model, evolutionary formal a presented which papers For 2) The presented. was model evolutionary formal a whether assessed We rele- search 1) each most For the follows: papers. as older the feature proceeded toward as will bias we well a result, results with as papers, our terms impactful that search and vant meaning the to citations, relevance of papers their Scholar, number and to Google S1) In according Table Scholar S2). ranked , Appendix Table Google (SI are Appendix, 100 altruism (SI first of cooperation evolution of the mech- of evolution selected by each we for evolve selection, results could search kin altruism than that other claims anisms the evaluate systematically To Methods and Hamilton’s Materials of stricture the to testament ideas. is reached conclusions systematically have fields similar sciences diverse natural from and social researchers the that across fact The by 17). outlined positive (4–6, originally than Hamilton as other recipient, mechanism and actor a between by relatedness altruism explanation of of relevant evolution aware we biologically the not a for While are provides that we operates. paper papers, con- other prominent selection any unconsciously most kin the have only which authors examined in these why situations and structed claims how these reveal of analysis knowledge. to broader-scale a established conducted with have we redundancy their Here, their models show Previous thus selection kin to and altruism. preceding (22–27) models from of results “novel” to evolution equivalence specific exact the reanalyzed have for claims papers mechanisms with replete novel become has of evolutionary of field The Conclusion of novelty the overselling dramatically findings. success- their studies highly publishing evolutionists been in some have ful for who good true backgrounds “in particularly nonbiological make from to proved able has felt they This that bold- faith.” claims the originality limit the could with of and so all effort ness doing and at long that time aware considerable such engage cost literature, as not would theory treated selection do kin was simply extensive it authors the while the some (41), at Finally, century only before. 20th obtained the was theory of transparent theory game turn conceptually selection a evolutionary kin of Hamil- wide-ranging of basis and integrate context The formally dynamics. wider by to adaptive the exemplified and decades is into four This rule took traits. ton’s it and social that theory of substantiate fact to genetic evolution the proofs the population hard of providing formal in models a rigorous do always as often not it they are that with biologists engage seems evolutionary not rule to Hamilton’s clear intuitively Second, so results. genetic impor- population and iconic dynami- tant well-established the textbook eschewing on while a focusing equation narrowly from replicator thereby altruism the perspective, of systems approach evolution cal to to the known tend of well nonbiologists problem are pro- scientists, theories stochastic latter trained and these formally system while genetics dynamical Yet, population of theories. and cess application result, an theory is genetics itself population a is nseicprmtrstig 1,2,2,2,2) swl so the on as well as 29), 28, of 26, sign 24, the (13, case settings which derive parameter in may specific action, actors on their sizes), game, from of group benefits types interactive direct other small (e.g., scenarios interaction, complicated and repeated “cooperate,” more action various the for than payoff But, “defect” higher action a a the in as panmixia, results modeled always under are game interactions dilemma when prisoner’s instance, one-shot (i.e., For others state. of population and reproduction or Whether survival behavior). whether helping the is, increase that individuals paper; the where in presented models b frequency the in in increases selection cooperation under or altruism whether evaluated tively empirical to treatises. research philosophical theoretical and books, from reviews, and substance to physics, research, in economics, law, range as and diverse as biology fields from come results search > and 0 c > PNAS .Almdl have models All 0. | oebr1,2020 17, November c > eed ntemdl’assumptions models’ the on depends 0 b > eas l osdrasituation a consider all because 0 | o.117 vol. | o 46 no. c depends | 28897 c > 0.

EVOLUTION frequency of traits, alleles, or memes in the population. We therefore on the basis of this qualitative analysis, we then stated that kin selection classified these papers according to whether the evolved trait is “altru- operates. ism,” “cooperation,” or “parameter dependent” (SI Appendix, Tables S1, In addition to these analyses, we focused on the most frequently cited S2, and S5). alternative mechanism to kin selection: spatial selection, pioneered by 3) If altruism could evolve in at least one model presented in a given paper, Martin Nowak. We used the search term “Nowak cooperation” to identify we next identified the mechanism to which the authors attributed the his 10 most impactful spatial selection papers (SI Appendix, Table S5). We evolution of altruism and subdivided the papers which attribute the evo- categorized all search results according to the scheme described above and lution of altruism to an evolutionary process other than kin selection then, again, analyzed the life cycle assumptions of these models to identify into two categories: those which deny the role of relatedness in their the modes of interaction and reproduction. Based on these, we indicated models (SI Appendix, Table S3, where quotes denying relatedness are whether or not kin selection will operate (SI Appendix, Table S6). provided) and those which make no mention of relatedness (SI Appendix, Table S4, where the proposed alternative mechanism is identified). For Data Availability. All study data are included in this article and SI Appendix. both of these categories we examined the life cycle assumptions model, ACKNOWLEDGMENTS. L.K. acknowledges funding by the European in particular the modes of reproduction (e.g., the dispersal kernel) and Research Council (ERC) (ERC Advanced Grant, “resiliANT,” 741491). We interactions (e.g., the group size within which individuals interact), to thank Charles Mullon, Michel Chapuisat, Thomas Richardson, Claus evaluate whether the model is expected to lead to positive relatedness Wedekind, Koos Boomsma, John Antonakis, and three anonymous review- between interacting individuals. If relatedness is expected to be nonzero ers for comments on earlier versions of this manuscript.

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