sign in sign up
<<
Home , Ancestor, Anthropology, Bilateral descent, Clan, Ethnocentrism, Incest taboo

Downloaded by guest on September 28, 2021 h h nettboadcranknhpsrcue emerge. and structures how certain unknown and still is cultural the it of why However, core the (1). at studies rules lies such structures of form kinship elucidation they corresponding the , and Indeed, among structure. rules kinship these certain their With a choosing which (2). in to to prefers as descent belong it the children clans on as rules well the as some of candidates, has mating which clan cultural, to be as each to Furthermore, thought on (2). is genetic origin than whose taboo, rather category” incest a as the “ called clan of a is marriage within the marry of cooperation, par- rarely prohibition This the particular, (4–8). as clans In the (1). such by to determined belong ties others, mostly are shared with marriage, is or rivalry, relationships common which socially Social in a clan, (1–3). form a Lineages called . group, a related called are common I social kinship of . distribution indigenous geographical conflict in the structures mating explain may the This when strict. Gen- is emerges taboo. exchange incest needed, restricted strongly the is whereas with cooperation when clans preferences, emerges of and exchange eralized traits emergence of the space in the demonstrate resulting in numerically clustered are We so- lineages process. the that follow Moran by and hierarchical selection fitness called -level smaller with introduce we eliminating for addition, compete In preferences own similar their brides. with to lineages traits - whereas similar mates’, lineages. having or among those marriage with conflict and cooperate and of can trait cooperation eages possibility of the degree the the characterizing determines and mat- parameters which over preference, has conflict mate and lineage mates Each and introduce ing. and kin com- conditions groups among of what cooperation model and or social a lineages emerge build of consisting we they munities Here, how structures. unknown different How- still determine consequences. is in cultural it distributed different flow are ever, show the structures and and with These clans, areas clans. brides different two different of to than exchange children direct more of a among an exchange, brides exchange, restricted of form generalized rules exchange including Such indirect structures, rules. certain kinship prefer- by by mating various relationships the prohibited descent governs is and attribution marriage clan ence The which social taboo. within of incest clan, the basis so-called the cultural a form a 2019) group, constitute structures 11, October societies. kinship review indigenous for in and (received relationships 2019 unit 19, December family approved and The CA, Stanford, University, Stanford Feldman, W. Marcus by Japan Edited 113-0033, Tokyo Tokyo, of University Institute, Biology Universal Biology, Systems a Itao Kenji tie marriage by and driven structures kinship of www.pnas.org/cgi/doi/10.1073/pnas.1917716117 and both by village, determined ’s is a which in when live affiliation, example, and children’s nei- For surname ’s children, (9). a authority of inherit parental attributions children nor of location flow the the flow arrows ther that the different Here, means respectively. children two children, structures and of where women of of 1, flow Examples the Fig. sent 2). in (1, shown relationships are descent and riage eateto ai cec,Gaut colo rsadSine,Uiest fTko euok,Tko1380,Jpn and Japan; 153-8902, Tokyo Meguro-ku, Tokyo, of University , and Arts of School Graduate , Basic of Department ua oit,afml n isi r omdb mar- by a sharing formed families are societies, kinship indigenous and In descent. family and a riage , n L ´ v-tas lsie isi tutrsacrigt mar- to according structures kinship classified evi-Strauss a | isi structure kinship n uiioKaneko Kunihiko and , | nettaboo incest a,b,1 | utlvlselection multilevel ⇒, → repre- aadpsto:Suc oe o hs oescnb on at found be can models these for codes KenjiItao/clan.git Source deposition: Data doi:10.1073/pnas.1917716117/-/DCSupplemental. at online supporting contains article This 1 BY-NC-ND) (CC 4.0 NoDerivatives License distributed under is article access open This Submission.y Direct PNAS a is article This interest.y paper. y competing the no wrote declare K.K. simulations; authors and the The K.I. conducted and K.I. data; model; analyzed the K.K. and designed K.I. K.K. and K.I. contributions: Author whole a as women of flow the A Thus, exchange, A. is restricted men clan in exchange, in whereas generalized in women C, marry clan a men they in In women Suppose B. marry B 1D). clan of clan in (Fig. in exchange women clans marry indirect clans two A different an than clan to more exchange, children among generalized of brides and flow 1C); the with (Fig. of brides exchange of direct 1 exchange a (Fig. clans organization, two dual between shows brides 1A); the 1 without (Fig. structure, Fig. taboo incest the mother’s. incest structures: and kinship of father’s classes both the from differs location, ,wihh sue ob h original the be to assumed which 1B), (Fig. respec- organization dual children, if exchange and restricted women of as system of the flow defined the of tively. (C cycles of cycle length marriage the ing observed. still are is structures it different Nonetheless, why (2). unknown structure to social leads egalitarian and and stable in a observed mainly classes. social is leads between exchange and differentiation Restricted status China of and emergence children. the and in to observed of is attribution exchange clan Generalized the tracing by observed A is it owo orsodnemyb drse.Eal [email protected] Email: addressed. be may correspondence whom To etdhr,wl neluieslfaue n omlt a formulate and features anthropology. universal in unveil pre- general as will models, here, constitutive simple sented societies. by indigenous studies in explain theoretical structures can The kinship which of conflict, distribution and the cooperation of on strengths depending the appear, structures spon- Different and studies, emerge. field taboo taneously with incest consistent agent- The structures, an kinship evolution. several applying multilevel by and coopera- family considered, model resultant of based are and model competition brides and simple of tion exchange a which build in we groups, remains Here, dif- determines social it structures. what of or ferent However, emerged basis have societies. the they how as unanswered indigenous descent in and with marriage relationships structures of kinship rules revealed certain has anthropology Cultural Significance ahmtcly isi tutrsaecaatrzdb defin- by characterized are structures kinship Mathematically, C d ⇒ oee,h aldtesse with system the called he However, . C ⇔ m B = nrsrce xhne ecn eainhp are relationships Descent exchange. restricted in B ⇒ · · · ⇒ . C y d 1 = .L 1A). (Fig. structure incest the in ⇒ ngnrlzdecag,whereas exchange, generalized in A m . y n ecn yl (C cycle descent and ) raieCmosAttribution-NonCommercial- Commons Creative ;rsrce xhne direct a exchange, restricted B); y https://www.pnas.org/lookup/suppl/ NSLts Articles Latest PNAS b C etrfrComplex for Center m C 2 = m 2 = https://github.com/ and regardless , ´ evi-Strauss d sthe as ) C d | 1 = f7 of 1 a

ANTHROPOLOGY A C ensemble of lineages within which the interaction of lineages can take place. Unmarried women are exchanged by marriage over lineages. We assign each lineage a trait t and a mate prefer- ence p as an optimal trait of the bridegroom. Marriage takes place according to the mating preference given by t, p. Lin- eages with similar traits cooperate with each other as well as with mates, whereas those with similar preferences compete for B D mates. Depending on the cooperation and conflict, the popula- tion of a lineage grows. By introducing mutations in t, p values, lineages with higher growth are selected. With numerical simulations, lineages were found to form clus- ters in (t, p) space under a certain condition. For each cluster, marriage occurs only with a certain different cluster, resulting in the . Lineages in the same cluster cooperate with each other, as well as with those in the bride’s cluster, whereas Fig. 1. Examples of kinship structures. Each symbol A, A1,A2, B, ··· is a clan. When clans are identified by a single trait, we denote them by conflict for brides occurs only within a cluster. Such clusters are characters as A, B, ··· , whereas when they are represented by two traits, regarded as clans. Thus, clan (= cluster of lineages) is an emer- they are denoted both by characters and indices as A1,B1, ··· . The dou- gent in this model. Next, by introducing multiple traits ble arrow from clan X to Y (X ⇒ Y) shows the marriage rule indicating (and preferences), such as habitats, , and occupations, that women in clan X marry men in clan Y. The arrow from clan X to Y we uncovered the transition from dual organization to gener- (X → Y) shows the descent rule indicating that children belong to clan Y alized and restricted exchanges, depending on the strengths of when their fathers belong to clan X. Hereafter, we refer to the length of cooperation and conflict. cycles of ⇒ and → needed to return to the original point, as marriage cycle The present paper is organized as follows. In the next section, Cm and descent cycle Cd. Structures are classified according to those cycles. we describe the model with one trait. Then, with evolution sim- ( ) = = 1 for incest structure. ( ) = 2, = 1 for dual organization. A Cm Cd B Cm Cd ulations, we show the emergence of clans and incest taboo and (C) Cm = 2, Cd ≥ 2 for restricted exchange. (D) Cm > 2, Cd = 1 for . present the condition for it. Next, we introduce the model with two traits and demonstrate the emergence of kinship structures. In the last section, we discuss the correspondence of our results pattern of both generalized and other restricted exchanges. with ethnographic records. Here, we limit the use of restricted exchange to the case with Cm = 2 and Cd ≥ 2 (Fig. 1C), to distinguish it from the dual Model 1: One-Trait Model organization. He defined generalized exchange by Cm ≥ 3 and Fig. 2 shows a schematic of our model. Lineages grow by inter- Cd = 1 (Fig. 1D). Structures with Cm > 2 and Cd > 1 are rarely acting with other lineages in the same community (Fig. 2A). ∗ observed (Table 1). When Cd = 1, children inherit from and Each lineage splits into two when its population reaches twice belong to the same clan as their father/mother, the rule of which the initial and is eliminated when the population goes to zero. is called “unilineal descent.” By contrast, when Cd ≥ 2, a Communities split and are eliminated in the same way in which inherits the character (A, B, ··· ) (e.g., land) from his or her their change by doubling and elimination of lin- father and the index (1, 2, ··· ) (e.g., ) from his or her eages within. When a community splits into two, one community, mother, as in Fig. 1C (2); this is called “.” selected at random from the system, is removed to fix the total The advantage of the incest taboo has been discussed bio- population of communities, to introduce community-level selec- logically and economically (12, 13). As for kinship structures, tion by removing communities with lower fitness. This multilevel how marriage and descent rules are chosen were numerically selection on lineages and communities follows the so-called hier- investigated, under given clan separation (14). Group-theory archical Moran process, as adopted in the studies of biological , known as “kinship algebra,” reveals structures that sat- and social evolution (25–31). isfy transformation symmetry under marriage and descent rules We assign a pair of a trait and a preference (ti , pi ) to each (15–17). These studies, however, can explain neither the social lineage i, which is culturally transmitted to the next . origin of the incest taboo (including the distinction between When a lineage splits into two, lineages inherit (t, p) of fathers’ ’ and fathers’ ’ daughters) nor the mother with slight variation, because cultural traits are mod- the emergence and transition of kinship structures. ified when transmitted (32). Specifically, (t, p) are “mutated” Note that an important point was not considered in the ear- each step by adding a small noise component η, following a lier theoretical studies: Marriage brings social unity. Indeed, uniform distribution in [−µ, µ]. This variation corresponds to a field studies revealed that lineages cooperated and conflicted genetic mutation in biology, but the and variation of with each other according to their social relatedness and mate traits here are of a cultural basis. Human beings categorize social preferences. Socially related lineages mutually cooperate and groups even without genetic relatedness (33). constitute a clan (2). Each lineage proposes marriage to cer- We introduce cooperation among social kin and that by mar- tain lineage(s) depending on its mating preference (2). After riage (blue and orange solid lines in Fig. 2B). Here, relationships marriage, the lineage of the bridegroom and that of the bride of lineages are recognized by comparing the trait and preference cooperate (2, 18), as well as social kin that share common traits values with a tolerance parameter σ. Thus, lineages i and j coop- (19, 20). There also exist strong conflicts among rival lineages erate when |ti − tj |/σ, |ti − pj |/σ, or |pi − tj |/σ is sufficiently competing for mates (21–24). small. The density of cooperators for each lineage i, denoted Here, we introduce an agent-based model of indigenous soci- eties adopting the multilevel evolution of lineages and commu- nities. Lineage is a unit of the dynamics, and community is an Table 1. Classification of kinship structures

Cd\Cm 2 3 ∼ *Levi-Strauss´ assumed that the so-called Murungin structure fulfills these conditions; 1 Dual Generalized however, this was later proved to be a mere generalized exchange with alternative 2 ∼ Restricted (Murungin?) pathways (3, 10, 11).

2 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.1917716117 Itao and Kaneko Downloaded by guest on September 28, 2021 Downloaded by guest on September 28, 2021 ne eti ag fprmtrvle.Hr,w sdthe used we Here, values. parameter of range certain a under 3 2. Fig. Table 3 in Fig. in in plotted shown are ulation parameters the changing Taboo. (t by Incest simulated the with was Clans of parameter 2. Emergence and Table in Source notations summarized are The details. simulations the (34) for in adopted online Methods values available and are Materials codes See conditions, distribution. of initial distribution uniform other the as under such no observed However, are lineage. a changes within qualitative even married, get can couple every and to belong Children marriage. inherit after lineage ’ their lineage lineage in in men unmarried Then, small. lineage conflict. by uae ysmigtedge fcnitars l iegs A lineages. all where across conflict by of denoted degree larger rivals, the bridegrooms of summing sufficient density by culated are The (22). there brides when and even because occurs lineages, pref- of preferred conflict close of strength the that with of The lineages independent of is 2B). number and Fig. erences the on in only line depends dashed conflict (red small sufficiently noncooperation). of disadvantage a (or cooperation popula- by its of growth where larger tion, in resulting cooperation, more larger gains A lineages. all across by shown. are lineage toadKaneko and Itao or when i fixed— traits their communities (solid on cooperate of depending ences Lineages line), number (B) (dashed process. conflict the and Moran removed keep line) hierarchical is the to adopt community random we (com- another at i.e., lineage splits, system the community the threshold, a from given of When population a the splits. beyond When munity) goes As die. and con- (community) gray). children, mating lineage or (light to cooperation a birth adults of give lack and mate, a Adults of gray) because flicts. die (dark some children up, Gen- grow grow. into children can separated (black) population is whose eration (blue), lineages of consist () 2. Fig. † AB h ersnaino oprto oeyb h rsn (t present the by solely cooperation of representation of the the of is the lineage bridegroom’s nraiy oprto sahee fe h arae Thus, marriage. the after achieved is cooperation , In and , h nta ausof values initial The hr samtn hnefrec ieg nec tp Each step. each in lineage each for chance mating a is There aigcnito lineages of conflict Mating |p p friend i ) j − i n ae oprt,weesmtn iascnit Lineages conflict. rivals mating whereas cooperate, mates and Kin p. |p r i bu)when (blue) kin are auso iegsi omnt fe 0 tp fsim- of steps 500 after community a in lineages of values rival d t ieccei h oe.Communities model. the in cycle Life (A) model. the of Schematic i (t j m i − |/σ i , ieycosslineage chooses likely scluae ysmigtedge fcooperation of degree the summing by calculated is , D–F p saprmtridctn h eln ftepopulation the of decline the indicating parameter a is p j j au mle agrsprsino h rwhrate, growth the of suppression larger a implies |/σ ssfcetysal nyterltosiswt h pe left upper the with relationships the Only small. sufficiently is ) d omculsi lineage in couples form c fterfte’ lineage. father’s their of si i.3 Fig. in As . saprmtrta ie h eln fdahrate death of decline the gives that parameter a is ssfcetysal n ae oag)when (orange) mates and small, sufficiently is j a lgtydfe.Hr,w elc hssih eito,because deviation, slight this neglect we Here, differ. slightly may |t t , i µ − p ( t r eoi hsmdl hs tfirst, at Thus, model. this in zero are n hi iesre r shown are series time their and A–C, j friend |/σ σ B ,acrigt h euto h iuain and simulation, the of result the to according ), i and and ssfcetysal aigrvl (red) rivals mating small, sufficiently is j when (t au mle httelineage the that implies value hyfr e clusters few a form they C, j , i p cuswhen occurs hs oe oeinto move women Thus, . ) i |t

∈ preference (p) n nare women unmarried and i 0 1] [0, − hsoetatmodel one-trait This , sese oformulate. to easier is p) p p j i 2 |/σ n h actual the and t rteGaussian the or trait (t) n aeprefer- mate and |p ssufficiently is rival i − † |t i p i scal- is , − j |/σ t p j j fa of |/σ X is - σ d ee oit sdfie oaheeteics ao hnmore when taboo satisfy incest to communities the equivalent of achieve 90% is to than defined taboo is incest obtain society the Here, to condition of every existence C for the that 50 Recall and steps 500 over with structure and the whole, a eliminated, as be will and, trait communities collapsed in other, each drifts with peting random of marriage 4A because preference of and structure collapse Fig. the soon in community, will one one just exchange is is there system If num- the 4B. the Fig. in Thus, communities selection. of lineage-level ber to series addition Time in cycle. the selection, in engaged (C clans cycle of of marriage sending number the of or the length having counting the without define lineages we Then, some brides. be cyclic would are there relationships The unless selection. multilevel by sustained this are In (36). study indigenous previous in emerges. exchange a spontaneously obser- marriage societies of with this kinship that compositions; social the with fluid manner, consistent are here is clans observed ethnographic vation in The is reported (2). as relationships, records parallel social and different Such the cross promoted. in the is daughter between ’s distinction mother’s thus, husbands’ and, a to clan, brides with mate’s the of marriage to move belongs the brother opposite by mother’s a the clan lineages, different of a siblings to incest because belong the contrast, sex when In marriage prohibited, organized. thus, is is and, daughter taboo clan, clan, brother’s same same father’s the the a to to with belong belongs of sex brother same father’s because the a mar- cooperate of by united siblings clans are Because clans same riage. different in indirect the those and (blue)—conduct in relatedness, social lineages C Here, and clans. (green), A as B exchange (red), (blue)—conduct A B and namely, A (red) as A exchange In clusters—namely, direct emerges. two clusters 3B, among but of Fig. exchange cluster a values Marriage within preference clusters. not married and across get trait people which Thus, mates, the centers. their comparing cluster as clusters by other determined the of is one in those prefer ter adopting by clusters of (35). criterion number information the Bayesian the optimize to method means o.Iiilpplto nalineage a in population Initial N N Pop. Explanation Symbol Parameters 2. Table also 5 Fig. exchange. marriage with leading as clans diverged, that of shows and formation clustered the are to both lineages if rivals, large, Hence, mating diverged. sufficiently many become with lineages without lineages that large so eliminate lineages contrast, to In isolated pressure clusters. eliminate form creates lineages to that so pressure cooperators more is there S1 d µ r m c c l m yipsn hsmliee eeto,w iuae h model the simulated we selection, multilevel this imposing By taboo, incest the in resulting relationships, preferential The clus- a in lineages 3, Fig. in shown as formed are clusters When C o h eedneof dependence the for ≥ d m m i.5sostepaedarmo h nettaboo. incest the of diagram phase the shows 5 Fig. 2. r hw nFg ihadwtottecommunity-level the without and with 4 Fig. in shown are r ufiinl ag oag iei i.4B). Fig. in line (orange large sufficiently are oeac o similarity for Tolerance nrmn fdahrt ymtn oflc Variable conflict mating by rate death of Increment ubro omnte nasystem a in communities village of a Number in lineages of number Initial eln fdahrt ycooperation by rate death of Decline uainrt for rate Mutation rate growth Intrinsic µ p ⇒ nrae,i eoe oedfcl oestablish to difficult more becomes it increases, hra fteeeitmn omnte com- communities many exist there if Whereas . B ⇔ ⇒ he clusters— three 3C, Fig. in whereas B, C C ⇒ m t i and on .W en hs lsesas clusters these define We A. C p d C m i c m ≥ and ≥ 2 NSLts Articles Latest PNAS 2 (see d sssand when sustained, is m .As ). Fig. Appendix, SI d c d c and n 0 in 100 and increases, Variable Variable d | Value m m 100 1.0 50 f7 of 3 4 5 C by ) are d m d m c t .

ANTHROPOLOGY Fig. 3. Example of clan separation. (A–C)(t, p) values for lineages in a community after 500 calculation steps. Clusters of lineages are generated, which are clans. The arrow shows the preferential relationship that corresponds to ⇒ in Fig. 1. (D–F) Time series of separation of lineages. Temporal evolution of the values of traits and preferences of lineages in a community are represented in blue and red, respectively. Parameters are dc = dm = 0.1 in A and D; dc = dm = 0.5 in B and E; and dc = 0.5, dm = 2.0 in C and F; µ = 0.1 for all cases.

the incest taboo. For larger µ, the changes in traits and prefer- first trait is clustered into three groups (Fig. 6 A, 1), whereas ences are larger, so that the structure of marriage exchange is the second is not (Fig. 6 A, 2). The green clan prefers red, the more fragile. red prefers blue, and the blue prefers green. The relationship of Here, lineages spontaneously form clans and the incest taboo marriage exchange forms a three-period cycle. Thus, generalized emerges. The structures with various Cm values emerge as in exchange in Fig. 1D emerges. In Fig. 6B, there are four clans, Fig. 3. In this model, however, children always belong to their where each trait is clustered into two, and thus two-by-two clans fathers’ clans and, thus, Cd = 1. Thus, this model is insufficient are formed (Fig. 6 B, 1 and 2). Considering the two-dimensional for modeling some kinship structures, such as the restricted distance of preference relationships, red and purple clans pre- exchange shown in Fig. 1C. fer each other, as do blue and green clans. Here, most lineages adopt bilateral descent rules. A child of a father in a red clan and Model 2: Two-Trait Model a mother in a purple clan inherits t1 from red and t2 from purple Recalling that children can belong to different clans from par- and, thus, belongs to a green clan. Hence, restricted exchange in ents by inheriting traits from both , as in Fig. 1C, we Fig. 1C emerges. Such structures are classified as shown in Fig. 1, extended the model to have two culturally independent traits and by computing the marriage cycle (Cm ) and descent cycle (Cd ). preferences, t = (t1, t2) and p = (p1, p2). These traits are inher- Fig. 7 shows the phase diagram of kinship structures. We ited maternally or paternally. Because there are only two sexes, use the classification in Fig. 1. Incest taboo is not generated there exist only two pathways of inheritance. If several traits are (orange in Fig. 7) when dm is small, as in the previous model. inherited via father/mother, they can be effectively regarded as As dm increases, dual organization (green) appears, and, thus, one trait. Thus, the two-trait model is sufficient for considering the incest taboo emerges. Then, more sophisticated structures kinship structures with multiple traits. as generalized exchange (red) and restricted exchange (purple) In the previous model, children belong to and inherit t, p from emerge. When both dm and dc are large, population suppres- their father’s lineage. In reality, however, a child can inherit some sion is so strong that it is hard to achieve high cooperation and traits from father and other traits from mother, as observed in low competition to overcome the suppression. Hence, all com- many indigenous societies (2, 37, 38) (e.g., Fig. 1C). For exam- munities are extinct in the upper right region in Fig. 7 (blue). In ple, he or she inherits land from the father and the name of the this model, other structures with Cm > 2 and Cd > 1, such as the mother. We assume that children inherit t1, p1 from their fathers. Next, each lineage can choose whether they inherit t2, p2 from the father or mother. The former (latter) corresponds to a uni- lineal (bilateral) descent rule. Suppose men in lineage i marry AB women in lineage j . If lineage i adopts a unilineal descent rule, children possess traits and preferences ti, pi. By contrast, if a bilateral descent rule is adopted, lineage i adopts the trait and i j i j preference to t = (t1, t2), p = (p1, p2). For both cases, children’s lineages and fathers’ lineages’ kin cooperate. In the initial gen- eration, either of the rules is assigned at random, and the rule would switch with a probability µd = 0.01. Time Time Emergence of Kinship Structures. Lineages are clustered into clans Fig. 4. Time series of Cm.(A) Time series of Cm in a single community, i.e., in (t, p) space as with one-trait model. For the two-trait model, under lineage-level selection without community-level selection. (B) Time descent relationships of clans emerge, as well as those of mar- series of the average Cm over 100 communities both under lineage- and riage. Fig. 6 shows examples of the final after 500 steps community-level selection. µ = 0.01. Blue and orange lines show the results of simulation. In Fig. 6A, there are three clans where only the under parameter values of dc = dm = 0.1 and dc = dm = 0.5, respectively.

4 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.1917716117 Itao and Kaneko Downloaded by guest on September 28, 2021 Downloaded by guest on September 28, 2021 hscs,hwvr ahca a oeta n noncoopera- one than more has clan each In however, emerges. exchange case, restricted this within Then, clans conflicts. separate avoid to a to better with villages be con- would mating community it As stronger, fitted. the is becomes marriage little, flict by is united clans conflict of number mating small the If L to sification. contrast This in exchange, important. exchange restricted generalized more than to rather similar is is conflict organization dual mating that suggests of emerges avoidance exchange the restricted when whereas important, is cooperation our in shown model. as disappear, structures decreased, kinship is sophisticated par- influence Then, societies of parental the and As preferences centralized connections. mate are lineage the strong requires to which according ents, marry edu- likely with small those a people Furthermore, in (32). than families teachers within (i.e., by cation faster teaching be mass of to with known speed societies is The traits structures. cultural in kinship change sophisticated and taboo incest incest clus- the and and siblings dynamics of emerge. the simultaneously categories of taboo social result the mathematical lineages, a of or as tering Here, biological (2). previous ignored ethnographic studies but some daugh- which emphasized, brother’s daughters, records mother’s brother’s as father’s cross such and the made, ters same between is cousins distinction the women parallel a Because in and category.” marriage, people a after as Thus, lineages “siblings change prohibited. as is recognized marriage are clan preferences, clusters clan and as same traits with formed the of model are values within close clans the with When in lineages preferences. of emerge structures and society kinship traits the indigenous two of the all in mat- Furthermore, the observed rivals. as well of as by conflict mates, spontaneously and ing kin emerges of taboo cooperation incest the the considering that shown have We Discussion exchange restricted smaller thus and and larger with 5, (see diagrams larger exchange Fig. generalized With by in replaced 6. shown is Fig. sin- as in a fragile, only shown more of as that trait, needs gle exchange generalized whereas cluster, when collapse soon will it initially, generalized if d even is example, exchange For restricted values. against or initial robust the is of choice diagram the phase this Furthermore, because cooperators. exchange, restricted to larger to organization a then dual and the exchange from generalized changes generally structure gent toadKaneko and Itao of weight relative the on time, d depending This emerge, observed. structures scarcely various are structure, Murungin so-called parameters 5. Fig. unyo nettboi oeta .,weeswt lepit,i sless is it points, blue with whereas 0.9, (A) than 0.9. more than is taboo incest of quency AB c c eeaie xhneadda raiaineeg when emerge organization dual and exchange Generalized rate” “mutation small A each by traits two of separation the needs exchange Restricted and and hs igaso h mrec fteics ao gis the against taboo incest the of emergence the on diagrams Phase d d m d m m d r small. are sterltv egtof weight relative the As . µ c /d = and c 3 (B 0.03. aosrdcn aigrvl tteepneof expense the at rivals mating reducing favors d m tteprmtrvle ihrdpit,tefre- the points, red with values parameter the At . ) µ = 0.1. µ aiiae h mrec fthe of emergence the facilitates µ values). d m i.S2 Fig. Appendix, SI lnsprto is separation clan µ, nrae,teemer- the increases, ´ v-tas’ clas- evi-Strauss’s µ µ niae that indicates µ slre)in larger) is increases. for mre nywe h viac fcniti oeimportant more is conflict i.e., of cooperation, avoidance than the when only emerges as such clan, tive ciiisado oilfcosbsdsknhpfrexample, kinship—for besides factors economic consider social to and/or needs one activities issues, Todd such as For systems (46). social discussed and structures kinship for L between as tionships Hence, strata finite. social of of remain emergence evolution would set the it we introduce marriage, simplicity, we of if possibility even the lack conflict, Thus, from mating suffer mates. would stricter of lineages fewer by to proposed eliminated those be whereas than would lineages lineages large fewer sufficiently more or with more reality, However, to In others. marriage marriage. propose of possibility can the lineages increase and the relatedness as social included ing implicitly be can of it among thus, massive tie and, strong However, a lineages, need communities. example, for of communities, between interaction wars direct the sider between relationship the clarify parameters—d and to therein. lifestyles necessary deaths and is conflicts it of of Furthermore, cause degree society—for the indigenous examining the by each on example, in conflict needed mating are and analyses cooperation detailed structures, ship is as exchange, generalized observation. the requir- conduct with consistent those cooperation whereas stronger exchange, mat- ing restricted stricter require mas- under conduct rights societies, conflict the fishing fishery ing conclude, to In To access 45). (21). for (44, food cooperation competition or and including land fishing cooperation, over sive wars massive for (21–23). needs that societies agriculture hunter-gatherer contrast, the By in cause lineages often females among Aboriginal over the fights societies conflicts on that Studies fishery reported 39–43). and (2, Yanomamo Russia and Myanmar, in in Nivkh the Kachin as agricultural such the , gen- as Chinese whereas such in Amazon, societies observed the is in exchange Yanomamo eralized and is Australia Aborig- the in exchange as inal such Restricted societies, societies. hunter-gatherer in different observed mainly in adopted are tures etitdecag.Rd green, Red, exchange. Restricted (B) 1. A 1. clans Fig. Fig. to in correspond in clusters respectively, purple and C, clans blue, to and correspond clusters B, blue and A, clusters. red, of Green, relationships exchange. descent Generalized and (A) marriage the as emerge structures ship the show Images simulation. map, of steps 500 after munity i.6. Fig. h rsn oe a oelmttos is,w i o con- not did we First, limitations. some has model present The kin- of emergence the of understanding better a for course, Of struc- kinship different why on light sheds study present The d c t eod euetesm xdvleof value fixed same the use we Second, . 1 a1 − xmlso mretstructures. emergent of Examples 1b 3b4 b3 b2 b1 t 2 a,adtecrepnigsrcuefo ett ih.Kin- right. to left from structure corresponding the and map, B σ 1 m 2a a4 a3 a2 for = d m σ A hr,ormdlcno xli the explain cannot model our Third, . /d 1 c c nFg .Tu,rsrce exchange restricted Thus, 6. Fig. in , ssfcetylarge. sufficiently is d ´ v-tas icse 2 rrela- or (2) discussed evi-Strauss m and , t , p µ. ausfrlnae nacom- a in lineages for values 1 NSLts Articles Latest PNAS A , d m 2 B , hs rpsdto proposed those , 1 t n B and 1 − σ p 1 o measur- for 2 map, respectively, σ | t m 2 f7 of 5 − for p 2

ANTHROPOLOGY ABIn these forms, the suppression of population is relaxed from 1/(1 + dc) to 1 by cooperation as friend increases from 0 to 1, whereas it is amplified from 1 to 1/(1 + dm) with the increase of rival. Note that the results to be pre- sented are qualitatively independent of these specific forms as long as cooperation enhances and conflict suppresses the population. We adopted the following algorithm for the population change in lin- eages. For lineage i of time step n, the number of boys, , unmarried n n n n men, unmarried women, and couples are denoted by Bi , Gi , Mi , Fi , and n Ci , respectively. The intrinsic growth rate is denoted by r. Next, we repre- sent the set of lineages in a community by Λ and the set of lineages that accept lineage i as a by Λi. Then, the population change in lineage i is given by

n n−1 n n n n λi = r × Ci , Bi = Poisson(λi ), Gi = Poisson(λi ), [1] Fig. 7. Phase diagrams of kinship structures against the parameters dc and tn = tn−1 + η, pn = pn−1 + η, [2] d . Images show the classes of structures that appear most frequently under i i i i m     several conditions, according to the classification in Fig. 1. Incest structure exp − min |tn − tn|, |pn − tn|, |pn − tn| 2/σ2 n X i j i j j i is plotted in orange, dual organization in green, generalized exchange in friend = , [3] i #Λ red, and restricted exchange in purple, whereas the conditions with which j∈Λ µ = . µ = .     all communities are extinct are plotted in blue. (A) 0 01. (B) 0 1. exp − n − n 2/σ2 X pi pj rivaln = , [4] i #Λ -purchasing that appear under the unbalanced j∈Λ 1 1 population among clans. Mn = × Bn, [5] i 1 + d × rivaln 1 + d × (1 − friendn) i To conclude, we have shown that the incest taboo and kin- m i c i 1 1 ship structures spontaneously emerge by considering social tie n = × n, Fi n n Gi [6] and competition by marriage. The incest taboo emerges when 1 + dm × rivali 1 + dc × (1 − friendi ) the necessity of cooperation, the conflict for mating, and cultural   n n X n similarity across are sufficiently large. The distribu- Ci = min Mi , Fj . [7] tion of kinship structures is explained in terms of the strengths of j∈Λi cooperation and conflict. Generalized exchange emerges when the former is higher, whereas restricted exchange emerges when Couples in each lineage give birth to children following the Poisson distri- the latter is stronger. bution, as given by Eq. 1. Noise component is added to (t, p), following the uniform distribution in [−µ, µ] as Eq. 2. As they grow up, the population Leach (47) emphasized the general logic underlying the struc- is suppressed with regards to friend and rival, as given by Eqs. 3–6. People tural pattern of indigenous societies. In addition to field studies, get married according to the traits and preferences of their lineages. After theoretical studies by simple constitutive models, as we present marriage, the women move into husbands’ lineage, as in Eq. 7. Here, we here, will open a door for to construct a assumed , but the result is qualitatively independent of such a general theory therein. marriage system.

Materials and Methods Data Availability. Source codes for these models can be found at https:// To simulate the population dynamics considering cooperation and conflict github.com/KenjiItao/clan.git. among lineages, the possibility of marriage and the degrees of cooperation ACKNOWLEDGMENTS. We thank Tetsuhiro S. Hatakeyama, Yuma Fujimoto, and conflict were measured by a Gaussian function of traits and prefer- and Kenji Okubo for stimulating discussion; and Takumi Moriyama, Yasuo ences. For example, the degree of cooperation between social kin is given Ihara, Atsushi Kamimura, and Nobuto Takeuchi for illuminating comments. 2 2 by exp(−(ti − tj) /σ ). Furthermore, we introduce the suppression term of This research was partially supported by Ministry of , Culture, the population with friend and rival. In the present model, the suppres- Sports, Science, and Grant-in-Aid for Scientific Research on sion term is represented by 1/(1 + dc × (1 − friend)) and 1/(1 + dm × rival). Innovative Areas 17H06386.

1. R. Fox, Kinship and Marriage: An Anthropological Perspective (Cambridge University 15. A. Weil, “Sur l’etude algebrique´ de certains types de lois de mariage” in Struc- Press, Cambridge, UK, 1983), vol. 50. ture El´ ementaires´ de la Parente´ , C. Levi-Stauss,´ Ed. (P.U.F, Paris, , 1949), 2. C. Levi-Strauss,´ Les Structures El´ ementaires´ de la Parente´ (Presses Universitaires de pp. 279–285. France, Paris, France, 1949). 16. R. R. Bush, “An algebraic treatment of rules of marriage and descent” in An 3. K. Maddock, Alliance and entailment in Australian marriage. Aust. J. Anthropol. 7, of Kinship, H. C. White, Ed. (Prentice-, Englewood Cliffs, NJ, 1963), pp. 159–172. 19–26 (1969). 17. R. R. Bush, An Algebraic Treatment of Rules of Marriage and Descent (1963). 4. B. Malinowski, Sex, Culture, and (R. Hart-Davis, London, UK, 1963). 18. M. Alvard, Kinship and cooperation: The axe fight revisited. Hum. Nat. 20, 394–416 5. G. P. Murdock, (Macmillan, New York, NY, 1949). (2009). 6. K. , Brother- marriage in Roman Egypt. Comp. Stud. Soc. Hist. 22, 303– 19. R. McElreath, R. Boyd, P. J. Richerson, Shared norms and the evolution of ethnic 354 (1980). markers. Curr. Anthropol. 44, 122–130 (2003). 7. W. H. Durham, Coevolution: , Culture, and Human (Stanford Univer- 20. R. A. Hammond, R. Axelrod, The evolution of . J. Confl. Resolut. 50, sity Press, Stanford, CA, 1991). 926–936 (2006). 8. K. R. Hill et al., Co-residence patterns in hunter-gatherer societies show unique 21. J. Helbling, The dynamics of war and alliance among the Yanomami. Sociologus 1 human social structure. Science 331, 1286–1289 (2011). (suppl.), 103–116 (1999). 9. A. K. Romney, P. J. Epling, A simplified model of Kariera kinship. Am. Anthropol. 60, 22. N. A. Chagnon, Life , in blood a tribal revenge, and population warfare. 59–74 (1958). Science 239, 985–992 (1988). 10. L. R. Hiatt, Authority and reciprocity in Australian aboriginal marriage arrangements. 23. G. Blainey, Triumph of the Nomads: A of Aboriginal Australia (Overlook Press, Aust. J. Anthropol. 6, 468–475 (1967). New York, NY, 1976). 11. L. R. Hiatt, Arguments About Aborigines: Australia and the Evolution of Social 24. K. F. Otterbein, The origins of war. Crit. Rev. 11, 251–277 (1997). Anthropology (Cambridge University Press, Cambridge, UK, 1996). 25. A. Traulsen, M. A. Nowak, Evolution of cooperation by multilevel selection. Proc. Natl. 12. K. Aoki, Y. Ihara, M. W. Feldman, “Conditions for the spread of culturally transmitted Acad. Sci. U.S.A. 103, 10952–10955 (2006). costly punishment of sib mating” in Explaining Culture Scientifically, M. J. , Ed. 26. C. S. Spencer, E. M. Redmond, Multilevel selection and political evolution (University of Washington Press, Seattle, WA, 2008), pp. 100–116. in the valley of Oaxaca, 500–100 BC. J. Anthropol. Archaeol. 20, 195–229 13. N. W. Thornhill, The evolutionary significance of incest rules. Ethol. Sociobiol. 11, 113– (2001). 129 (1990). 27. N. Takeuchi, P. Hogeweg, K. Kaneko, The origin of a primordial genome through 14. J. P. Treuil, “Emergence of kinship structures: A multi-agent approach” in Artifi- spontaneous symmetry breaking. Nat. Commun. 8, 250 (2017). cial Societies: The Computer Simulation of Social Life. N. Gilbert, R. Conte, eds. 28. D. S. Wilson, and organism: Disentangling the themes of multilevel selection (Routledge, Abindgon, UK, 1987), pp. 48–71. theory. Am. Nat.150, S122–S134 (1997).

6 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.1917716117 Itao and Kaneko Downloaded by guest on September 28, 2021 Downloaded by guest on September 28, 2021 3 .Sebr .A ished h ontv onain fclua tblt and stability cultural of foundations cognitive The Hirschfeld, A. L. Sperber, D. 33. Feldman, W. M. Cavalli-Sforza, L. L. 32. 8 .Goy h lsicto fdul ecn systems. descent double of classification The Goody, J. descent. 38. selection Double Group Murdock, P. gatherings: G. and Categories 37. Tilley, F. C. Fredrickson, E. B. Palmer, T. C. 36. the of estimation efficient with k-means Extending “X-means: Moore, https://github.com/KenjiItao/clan. W. A. GitHub. Pelleg, D. Structures. 35. Kinship of Evolution Itao, K. 34. multilevel-selection societies. A hierarchical complex complexity: of social Evolution Gavrilets, of S. Turchin, evolution P. the 31. and biology. of Warfare review quarterly Peter, The Wilson, T. O. E. 30. Wilson, S. D. 29. toadKaneko and Itao diversity. 16. vol. 1981), NJ, Princeton, Approach titative (2009). 167–198 (1961). anthropology. cultural of mythology the and Francisco, San Inc., 727–734. Publishers pp. Kaufmann 2000), (Morgan CA, ed. Langley, P. Learning, Machine in clusters” of number 2019. December 3 Deposited approach. rnsCgi.Sci. Cognit. Trends tut y.J nhoo.Rlt Sci. Relat. Anthropol. J. Dyn. Struct. Mngah nPplto ilg,PictnUiest Press, University Princeton Biology, Population in (Monographs rceig fteSvnenhItrainlCneec on Conference International Seventeenth the of Proceedings 04 (2004). 40–46 8, m Anthropol. Am. utrlTasiso n vlto:AQuan- A Evolution: and Transmission Cultural vl u.Behav. Hum. Evol. –7(2010). 1–37 4, 5–6 (1940). 555–561 42, ur Anthropol. Curr. Lancet 9–0 (1997). 291–308 18, 1 (2003). 918 207, o.Hs.Evol. Hist. Soc. 3–25 2, 8, 7 .R Leach, R. E. 47. Todd, fishing. E. of Anthropology 46. Acheson, M. J. 45. Amur. Lower Bennett the E. and Sakhalin 44. of (Gilyak) Nivkh The Kachin Black, The L. Burma: 43. in minorities the understanding for basis a “Toward Raw, La M. 42. Leach, R. E. 41. in kinship Dravidian and networks Marriage sides: “Taking White, D. Houseman, M. Amazon. the in 40. aggression and conflict of arena An Yanomami: Sponsel, E. L. 39. 1999). . the (2001). and 376 Bangladesh Ghana, from Evidence fisheries: (1973). 1–110 125–146. pp. 1, vol. 1967), NJ, Princeton, Press, University (Princeton in example” 1964). UK, London, Ltd., , and Bell (G. 214– pp. 1998), D.C., Washington, Press, (Smithsonian 243. eds. Fat, Sie Tjon F. in America” South Lowlands Behav. ulses xod K 91,vl 22. vol. 1961), UK, Oxford, Publishers, 712(1998). 97–122 24, aDiversit La oad etrudrtnigo oflc aaeeti tropical in conflict of understanding better a Towards al., et ehnigAnthropology Rethinking oiia ytm fHgln um:ASuyo ahnSca Structure Social Kachin of Study A Burma: Highland of Systems Political .Kntde,Ed. Kunstadter, P. , and Minorities, Tribes, Asian Southeast uMne tutrsFmllse Modernit et Familales Structures Monde: du e ´ .Gdle,T Trautmann, T. Godelier, M. Kinship, of Transformations LEMngah nSca nhoooy Berg Anthropology, Social on Monographs (LSE nu e.Anthropol. Rev. Annu. NSLts Articles Latest PNAS 7–1 (2003). 275–316 10, rtcAnthropol. Arctic e ´ a.Policy Mar. Sul ai,France, Paris, (Seuil, | Aggress. 365– 25, f7 of 7 10,

ANTHROPOLOGY