Downloaded by guest on October 6, 2021 aenlcare paternal hominin the in provisioning paternal asso- of lineage. conditions and emergence of with timing ciated the establish to evidence and archaeological, genomic paleo-climatic, affecting using suggests for effort factor possibilities primary different and the- mating a Our male uncertainty. as between trade-off change paternity the ecological high on of focus face oretical the in can sim- dads even complementarities, Our emerge sufficient cads. with eliminate that necessarily suggest not ulations possible, need are dad dads states the that polymorphic meaning and Stable uncertainty provi- viable. from becomes paternity gains strategy from where costs point dads overcome tipping of a sioning identify fitness We the cads. and altering versus female–male energet- thus enhances male of complementarities, foods to male–male availability difficult-to-acquire obstacles Greater rich, social overcome. ically how be theoretically can incen- show provisioning provisioning we male and in tives, change improvements ecological that widespread over- posit favored to instead We choice dilemma. female social this and exacting come provisioning require nonpro- male models of between paternity hands Recent interplay the to “cads.” at mate-seeking fitness subject loses visioning, been “dad” provisioning have is A because theft. and would it nonhuman provisioning because in 2019) puzzling emergent absent 3, October and is review for among (received rare 2020 among 30, March provisioning approved and Paternal CA, Berkeley, California, of University Wachter, W. Kenneth by Edited 87131; c a pigo eaewt hmh ae,rte hncnuethe off- consume than the rather mated, he provision whom ancestral with to female an a him in of spring arose predisposing variant male, what genetic on a depends nonprovisioning Suppose instead but do. vacuum males a in other occur Pater- not provisioning. does care male nal incipient would of that is benefits dilemma” fitness “social provisioning the undermine paternal of light extensive in to challenging especially no from transition tionary in evolve rela- provisioning closest male our extensive of ? did our how that of then polygynous resembled system (5–8), ancestor mating–parenting or tives common the promiscuous If last either provisioning. our are male great lack who three and , bono- the , and related, of closely 18, most bos, are that = we mating–parenting which from SD to This species dramatically (4). 66%, ages differs = calo- different system men of of young by majority dependent provided the calories providing n % men (mean provi- with ries childhood are throughout which adolescence, parents, 3) often in and women, (2); and sex, fishing men processing, and/or by by food sioned hunting differs and in 12, gathering males labor pair = childcare, and 2) recognized in SD (1); specialize 92%, socially females = ) in monogamous foraging mated unions 339 are % adults (mean which bonds in of among groups multifemale majority distinctive follow- multimale, the are in The live characteristics niche. They 1) ecological ecological humans: and unique social a ing occupy also gatherers T cooperation change Alger ecological Ingela from results provisioning Paternal www.pnas.org/cgi/doi/10.1073/pnas.1917166117 nttt o dacdSuyi olue 18 olueCdx6 France; 6, Cedex Toulouse 31080 Toulouse, in Study Advanced for Institute olueSho fEoois S- NS(M51) 18 olueCdx6 France; 6, Cedex Toulouse 31080 (UMR5314), CNRS TSE-R Economics, of School Toulouse oaigsceis 3;ad4 aiisicuemultiple include families 4) and (3); societies) foraging 9 = nesadn h eeto rsue neligteevolu- the underlying pressures selection the Understanding ahrr suiu mn aml.Hmnhunter- . among unique hunter- is human modern gatherers among system mating–parenting he e cnmcSineIsiue hpa nvriy rne A986 and 92866; CA Orange, University, Chapman Institute, Science Economic | fatherhood a,b,c,1 alL Hooper L. Paul , | ua evolution human d,e oadCox Donald , | aetlinvestment parental f oahnStieglitz Jonathan , | n = d eateto nhoooy nvriyo e eio luuru,NM Albuquerque, Mexico, New of University Anthropology, of Department uinr hne nbt sexes. both incipient evo- an simultaneous in dilemma requires constitute social also changes to the scenario lutionary This be were with. still sex contend would to deter- for Even there key (12). meat strategy, as success reproductive of reproductive aggression exchange pre- on male and doubt if Rather, rank casts access. of to (11) sexual minants review points buys detailed evidence provisioning a vailing that 10), (9, notion sex the exchanges for of path meat reports this of Notwithstanding for devoted provisioning. odds attract paternal slim to to suggests their behavior have but Chimpanzee somehow mates, females. would for preferential competing investments their than offer paternal or rather to provisioning them advan- in comparative provision were a tage have who might females males males Lesser-ranked to if offspring. faithfulness is and overcome mating be could its preventing thus variant, genetic novel the spread. carry others offspring, of not the fitness did the of increase who would biological investments the his is that meaning he that implies probability polygyny low dominance-based a or Promiscuity himself. food doi:10.1073/pnas.1917166117/-/DCSupplemental at online information supporting contains article This at GitHub on readers to available is com/systemsscience/paternal code simulation The deposition: Data 1 BY-NC-ND) (CC 4.0 NoDerivatives License distributed under is article access open This Submission.y Direct PNAS a is article This performed interest.y competing research, no designed declare authors H.S.K. The and paper.y J.S., the wrote D.C., and P.L.H., research, I.A., contributions: Author † * f owo orsodnemyb drse.Eal neaagrtef.uo hkaplan@ or [email protected] Email: chapman.edu. addressed. be may correspondence whom To aenlpoiinn at ob ntento hthmnrpoutv eairhas behavior (13). reproductive ancestors human chimpanzee-like that in notion origins the its on doubt casts provisioning paternal steal.” to paternity more is production offspring ned oeageta h ope lcwr faattosnee ogenerate to needed Increased adaptations of dilemma: clockwork male’s complex the “The that predicament: argue some this Indeed, summarizes 5 ref. of title The eateto cnmc,Bso olg,Cetu il A02467 MA Hill, Chestnut College, Boston Economics, of Department aiisaesrn,ee ne ihptriyuncertainty. paternity fatherhood. the of understanding high for evolution paths under additional complemen- illuminates even model when This strong, strategy are reproductive tarities viable provisioning a Paternal becomes complementarities. male–male female–male to and/or due provisioning paternal to payoffs resources increases favor- difficult-to-acquire rich, change energetically Ecological on reliance investment. ing evolu- paternal the human of of provi- theory ecological the tion an increase present to by We unlikely fitness. this expropriated is sioner’s investment be Since this can dilemma: males, offspring other social prospective provi- a in anomalous encounter investment An would apes? mating male other polygynous sioning characterize or promiscuous that provision- from systems paternal emerged could have How apes. ing among unique soci- and subsistence human eties in ubiquitous is provisioning Paternal Significance arlt 7 rudta ehp h nywyti dilemma this way only the perhaps that argued (7) Gavrilets ∗ b b,c,d nvriyo olueCptl,302Tuos ee ,France; 9, Cedex Toulouse 31042 Capitole, Toulouse of University y n ilr .Kaplan S. 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ANTHROPOLOGY ANTHROPOLOGY social dilemma by considering ecological factors that affect and among men can select for male provisioning, even when the fitness benefits and costs of alternative male reproductive paternity is not fully certain. The model connects ecology to strategies. male reproductive strategies to predict the effect of ecological This paper presents an ecological theory of the evolution of change on the evolution of paternal provisioning. Reproduc- paternal provisioning in our species that depends only on selec- tive strategies are modeled by imagining the behavior of pairs tion on males (Fig. 1). We propose that the drying of the African of male neighbors. Males are of two types, “cads,” who do savanna in the Late Pliocene and Early Pleistocene—with asso- not provision offspring and who mate with multiple females, ciated increases in mammalian biomass, tubers, and nuts and and “dads,” who do provision offspring and who mate with decreases in ripe fruit availability—gradually resulted in obli- only one female. In an initial population predominated by cads, gate bipedality, increased mobility, prey encounter rates, and a variant dad paired with a cad would have lower reproduc- returns to hunting and extractive foraging. Those changes in tive success than his neighbor. Following ecological change that the profitability of different ecological strategies selected for increases the synergistic benefits of cooperation (complementar- increased size, greater time devoted to learning and cul- ities) between sexes and between males, changes in the fitness tural innovation, and lengthening of the juvenile period (3). of dads and cads select for male provisioning. We show that Those changes in ecology and history generated new sources these forces can be strong enough to coexist with an appre- of female–male complementarity in producing surviving off- ciable degree of extrapair mating, so that complete spring and male–male complementarity in acquiring and sharing is not necessary for the initiation and maintenance of paternal food (4, 14). provisioning. Complementarities between males and females, i.e., synergis- tic effects that increase per capita benefits, arose from the gains Model to male specialization in hunting and female specialization in We model a population in which males and females in each activities compatible with offspring care. Because hunting is not generation interact in groups; each female has a mate, but she easily compatible with existing adaptations to lactation can also copulate with other males. For analytical simplicity, and carrying , and because hunting skill is acquired over a we consider groups with two males and two females each. The long period of practice, there were significant gains from a sexual males forage together and share the outcome equally. We envi- division of labor (14, 15). Altriciality, prolonged development, sion two types of males, dads (nonphilandering provisioners) and and the simultaneous dependence of multiple offspring ampli- cads (philandering nonprovisioners). A dad favors his mate’s off- fied these gains. Since hunted foods tend to be dispersed and rich spring’s survival by sharing some of his food with them and his in protein, fat, and certain micronutrients (e.g., zinc, B vitamins), mate. In contrast, a cad uses extrapair matings rather than provi- while the foods gathered by females tend to be rich in carbohy- sioning to increase his . This is the primary drates and spatially segregated from hunted foods, female–male tension in the model. Complex foraging enhances dads’ repro- synergies also arose directly from the dietary complementarity ductive success (i.e., offspring survivorship) because dads are of different macro- and micronutrient inputs to an omnivorous more adept at exploiting its inherent complementarities. The diet (16). model examines whether enhanced offspring survival prospects Greater dietary reliance on animal products also generated can allow the dad trait to spread in an ancestral environment of complementarities between males in producing and sharing promiscuity, i.e., in a population where almost all dads have a food. Returns to scale in cooperative prey capture allowed cad as a neighbor. hunters to achieve higher per capita return rates (14). Highly Importantly, we suppress the evolution of female faithful- variable success rates in hunting also generated returns to food ness to focus on the interplay between ecological change and sharing that buffered risk and smoothed variability in con- male reproductive behavior in overcoming the social dilemma. sumption over time (4). Reducing risk through food sharing Specifically, we take all females to be identical within and across was essential to the long-term sustainability of omnivorous for- generations in terms of fertility, ability to care for offspring, ager diets that include high-risk, high-reward foods such as and openness to extrapair matings. (It is reasonable to imag- large game. ine scenarios, not considered here, whereby male provisioning We present a simple evolutionary game theoretic model that and female faithfulness coevolve, but only after the initial social shows how these complementarities between women and men dilemma has been overcome.).

Fig. 1. An ecological theory for the evolution of male provisioning in the hominin lineage.

2 of 9 | www.pnas.org/cgi/doi/10.1073/pnas.1917166117 Alger et al. Downloaded by guest on October 6, 2021 Downloaded by guest on October 6, 2021 ttime at dynamic cator time at males Cads. among and Dads of Shares McNamara and Houston Eq. sensu holds.] explains producing condition, (17), this to Fisher offspring; the his time for that his care [Note of of types all other devotes and food dad Each uncertainty. share nity uncertainty a paternity average, no faces on (Eqs. and himself steals, neighbor his dad (Eq. to a average born on offspring with him, matched from cad does neighbor A from paternity his much as as neighbor poaches his cad another with matched cad A aayat htafml ocdst h egbri ei a is he if neighbor expressions: the to successes concedes ductive 1 female dad while a the that cad, that odds unrealistic, acts let the (although latary reduces Thus, all it spread). since at genes engage conservative copulations dads is that do extrapair assumption assumption than extreme no philandering the time in make we less Here spend cads. dads matings, extrapair t fteofpigo eaewoemt a type type has has mate male whose dad female neighboring a a is whose of neighbor write offspring and philander- his the we a whether of Accordingly, on or ity cad. depend dad also a provisioning may or a it is cad, he ing offspring whether below). mate’s male’s on detail a male–male of depends probability in be survival the (described may while Hence, production sex- there Since in together, matings. to complementarities extrapair forage survival survive to males offspring who openness neighboring by female offspring determined and wholly biological probabilities then his success— maturity—is reproductive of ual male’s a number identical, the being females the of number same the is game the the (since of 2 success reproductive Fig. player). the row in only shows shown matrix is the symmetric, game evolutionary the of (D i dad aforementioned types—the (C with game or evolutionary strategies of an inter- two as groups the males formalize neighboring the we between formed, that action randomly are Assuming females strategies. and males reproductive male in Interactions. Male–Male le tal. et Alger = sue o ipiiy htec dl eaegvsbrhto gives female adult each that simplicity, for Assume, .Let ). D , C t i written —is π π hs egbri ftype of is neighbor whose CC ij i.2. Fig. eoeterpoutv ucs faml ftype of male a of success reproductive the denote − [(1 = 2 d ˙ d ˙ t and t φ = 1,1)tert fcag ntesaeo dads of share the in change of rate 19)—the (18, π 2N h aofmti fteddcdgame. dad–cad the of matrix payoff The stesaealtdt e ae h repro- The mate. her to alloted share the is π d ij − .Addmthdwt a ae opater- no faces dad a with matched dad A 3). π CD t , t DC · φ) i na nntl ag ouain h repli- the population, large infinitely an In . fofpig(N offspring of (1 , (s = j h oe oue nieyo variation on entirely focuses model The π · (1 = − Let = DD s CC φ d C CD t ∈ = d )· , + − t D 0 1] [0, s + [¯ ∈ DD φ φ)· π r hngvnb h following the by given then are , φ D · 0 1] [0, s s · (d · s ij CC j s eoetesaeo copu- of share the denote DC 2N DC t = ae and males o h uvvlprobabil- survival the for ) ]· eoetesaeo dads of share the denote − D . · )· 2N 2N , π ¯ j 2N C C = = (d h aofmatrix payoff The . C s t CC , )], N D · unn to Turning . eae) All females). 2N n cad and ) i φ = fthe of C [5] [4] [3] [1] [2] , 1). D 4. • by given average strategy, the each on of depends success cads ultimate reproductive versus the that dads indicates of brackets success square evolutionary the in term the where htsdel h inequality the s suddenly that examples. two with the this in illustrate increases We stimu- favor dads. can that of they classes share enough, game large between cads if transitions dads; versus late for dads prospects successes the of reproductive alter successes in can changes reproductive However, the unchanged. as remain to long closer as getting true time, If over time? decline over will increase initially to and dads stable, of by asymptotically share predominated the cause initially could population where a and In cads, follows: as formally and ,switches [8], of sign the on hinges repli- The sign dads]. whose and [cads The dynamic, to changing”: [cads] cator “game from literally transitions is class switch game This hold. to continues civ h aeaeaerpoutv ucs.Rwiigthe Rewriting success. reproductive average difference ( same constant the remains it achieve and it dads; where cads; than than success (i.e., average present on ( success types decreases reproductive higher male a both achieve with d population a In egbri a racd n h hr fdd ildecrease. will dads of share the and the if cad, whether contrast, a of or regardless By dad dad a a is of neighbor that exceeds success ductive if example, of For signs the that reveals oadteesae ftesaeo asi lgtyperturbed slightly is Eqs. π dads in of given share values back the dads from of if away share states the brings these dynamic toward replicator the states; ble increase. will dads of share the and cads outperform ofu itntgm lse,ec ihqaiaieydifferent qualitatively • with each 3): (Fig. classes, states stable game asymptotically distinct four to • • CC t DD aecas[aso as ban if obtains dads] s or [cads class Game yei lasbte hnbigmthdwt aeo a of male asymptotically a are with states matched monomorphic being stable: Both than type. better different always is type aecas[as ban if obtains [cads] s class Game aecas[as ban if obtains [dads] unique the class and dad, cads: Game only a has of state stable that asymptotically exceeds success reproductive erdciescesecesta facd n h unique the and cad, dads: a only has of state stable that asymptotically exceeds success reproductive (1 aecas[asaddd]otisif obtains dads] and [cads class Game mle htteei nqeaypoial tbesae which state, polymorphic: stable is asymptotically asymmetry unique This a cad. a is with there matched that when implies dad a and dad a with (1 eaeitrse nvle of values in interested are We is,spoeta ntal h aecasi cd]and [cads] is class game the initially that suppose First, expressed be can question our hand, in concepts these With (1 CC CC < − − = − > > (1 φ) φ) π d CD t (1 (1 − d )> · · π ¯ s s d 0 = d − − φ) ˙ d DC DC and/or D t t ,tesaeo astu nrae ( increases thus dads of share the 0), φ) φ) < (d · · rf 0 .23.Fo h erdciesuccess reproductive the From 243). p. 20, (ref. π ¯ (π π ¯ or s > > t π π fcd civ ihraeaereproductive average higher a achieve cads if 0) C DC D · · ) DD DD DD s s s s (d (d d d − d DC DC CC CC π 0 = t 1 = = t π DC ¯ − π > = ) π < hl h inequality the while = ) n goigkieeg ae where cases knife-edge ignoring and 1–4, en ace ihaml ftesame the of male a with matched Being . eadeso h egbrstp,acad’s a type, neighbor’s the of Regardless . eadeso h egbrstp,adad’s a type, neighbor’s the of Regardless . ti rfrbet eacdwe matched when cad a be to preferable is It . C π π . (d DC = CD π CD d sa smttclysal tt,what state, stable asymptotically an is CD d t t DD t π −π ) · · +(1 )+ CC π π as and π and DC CC − CD DD h elctrdnmcgvsrise gives dynamic replicator the , π −π +π s π CC (1 + CD − (1 + π DC CD CC d d DC d t > and htaeaypoial sta- asymptotically are that t −π ' π < ) − − s π > s (1 · CD DD DD hntesaeo dads of share the then 0, s s d (π d NSLts Articles Latest PNAS DD CD d − π CC t t CC ) DC DC ) + = > 0 = φ) d · d · > s hnacdsrepro- cad’s a then , + d π ˙ φ hndd always dads then , π s CD s 0 = t 1 = − − CD CC DC · DC s hswl remain will This . φ · 0 = s CD (1−φ) s π DC π · + −s DC . . . + s CC CC d fbt types both if ) DC ˙ + φ CC t φ > ) > · s wthsto switches φ r crucial. are +s DC · s > s s DC · fdads if 0) DD DC CD s −s s d DC DD | > −s CC 0 = f9 of 3 s DD and and and and [6] [7] [8] DD is .

ANTHROPOLOGY ANTHROPOLOGY eter κ ∈ [0, 1]measures the female–male complementarity. There is no complementarity if κ = 0: Only the sum of x and y matters. The complementarity is present and increasing in κ if κ > 0. This is revealed by the sign of the cross-partial derivative + Game class Game class [Cads] [Cads-or-Dads] ∂2s (x, y) κ = . [10] ∂x∂y A

CC - DC 0 The positive sign of this expression implies that when κ > 0, resources provided by one sex increase the value of resources provided by the other. Neighboring males forage together and equally share the col- Game class Game class lectively produced food. Using yDD and yDC to denote the [Cads-and-Dads] [Dads] amount of food that a dad brings to his mate and her offspring when his neighbor is a dad and a cad, respectively, let

(1 − µ)· 2Y + µ · Y 2 y = D D [11] DD 2 0+

(1 − µ)· (YD + YC )+ µ · YD YC DD - CD y = . [12] DC 2 Fig. 3. The evolutionary game class, which determines whether the share of dads in the population increases or decreases over time, depends on the YD ≥ 2 and YC ≥ 2 measure the productivity of the two types of males in procuring food: While all males may spend the difference πDD − πCD (the horizontal axis) and the difference πCC − πDC (the vertical axis). same amount of time producing food together, we allow for the possibility that time spent by cads and dads could differ in productivity. from negative to positive. The share of dads will keep increasing The parameter µ ∈ [0, 1]measures the male–male complemen- toward the asymptotically stable state d = (1−φ)sDC −sCC . tarity in food production. If µ = 0, there is no complementarity: sDC −sCC +sCD −sDD Second, again start with dt ' 0 but now suppose the initial Only the sum of YD and YC matters. If µ = 1, the complemen- game class is [cads or dads] and that suddenly the inequal- tarity is maximal: Only their product matters (since when YD ≥ 2 ity sCC > (1 − φ) · sDC switches to sCC < (1 − φ) · sDC while the and YC ≥ 2, the product YD Yj , j = D, C , is at least as large as inequality sDD > sCD + φ · sDC continues to hold. Then the game the sum). The 2 in the denominator of Eqs. 11 and 12 means that class transitions from [cads or dads] to [dads]: The replicator the food is shared equally between the two males. dynamic becomes positive, and the share of dads will increase How do ecological changes in µ and κ confer an evolutionary toward the asymptotically stable state d = 1. advantage to dads? And what are the effects of paternity uncer- Given that female openness to extrapair copulations φ is tainty (φ) and cad–dad differences in productivity (YC − YD ), constant, such transitions between game classes can only be if any? The next section (Results) answers these questions by driven by changes in offspring survival probabilities. The key reporting results based on analysis in SI Appendix, Lemmas 1 and point of our analysis below is that enhanced female–male and 2 and Propositions 1–10. We also conduct simulations of finite male–male complementarities in production can trigger pre- populations to illustrate the plausible emergence of dads as a cisely such changes. We now describe how we model these result of ecological change. complementarities. Results Complementarities and Survival. Let s(x, y) denote the survival Complementarities Favor the Spread of Dads. Keeping the param- probability of an offspring who receives resources x from its eters for male contributions (YD and YC ) and female extrapair and whose mother’s mate brings the amount of food y copulations (φ) fixed, increases in female–male complementarity back to the mother–offspring pair. Central to our model is that (κ) and/or male–male complementarity (µ) can cause the share dads provision more than cads. For simplicity, and without los- of dads to increase over time in a population initially predom- ing anything essential, we assume that cads do no provisioning inated by cads. This is easiest to see when dads and dads are at all.‡ equally productive (YC = YD ). In this case, a dad brings to his To highlight the role of complementarities, as distinct from mate–offspring pair the same amount of food whether matched forces such as increasing or decreasing returns to inputs, we with a dad or a cad (yDC = yDD = yD ), so that sDC = sDD = sD . adopt a survival function with constant returns to male and We show in SI Appendix, Lemma 1 that the game class is then female inputs, either [cads] or [dads] and that the game class switches from [cads] to [dads] if the following expression switches from being x + (1 − κ) · y + κ · x · y negative to being positive: s (x, y)= , [9] A s (1 − φ) − s . [13] where A > 0 is a constant large enough for s to be smaller than D C one, and where x > 1 (this ensures that the female’s contribution cannot reduce the value of the male’s contribution). The param- A shift from [cads] to [dads] thus requires either an increase in sD (1 − φ) or a decrease in sC . Can an increase in κ tip outcomes in favor of dads and achieve such a change? Yes. Because nonpaternity is held constant, and ‡Having cads provision a positive amount complicates the analysis without affecting the qualitative results. Furthermore, no paternal provisioning is arguably a reasonable cads do not invest in a mate or her offspring, neither φ nor sC ancestral benchmark given its absence in nonhuman apes. changes with κ. In contrast, for any given amount provisioning

4 of 9 | www.pnas.org/cgi/doi/10.1073/pnas.1917166117 Alger et al. Downloaded by guest on October 6, 2021 Downloaded by guest on October 6, 2021 iin h rteooia n eairlsitaon Mya 2 animal around of consumption shift and behavioral acquisition, and availability, ecological (increased popula- first the the (Y dition, of production group to entirety more of relatively near number 4, a the Fig. Within tion. compose scarcity. dads relative their generations, despite dads, favor ( 13 productivity equal have dads Once and cads which in tion and harvest remains). efficiently faunal more process to axes] hand bifacial fire, controlled kya 400 around of again (emergence and (correspond- scavenging) Mya and hunting 2 from by around products increase first an time: to roughly in ing points complementarities two that at increase posits simulation (Dis- the evidence prehistoric cussion), existing with correspondence rough In (10 small a and is this However, dads. [cads]). favor complementarities to that not rule (See the (but to exception dads] only and the [cads to increases. [dads] paternity stealing of and/or both by value when provisioned the an fact, since offspring that In trivial, of means means probability also no survival dads by the is game it in three intuitive, other increase the is the of this enough, one pronounced While to [cads] is classes. class effect from the switch if will reproductive that game dads’ sense to the contributes in generally success This dads. by sioned κ Appendix, (SI survival, offspring on impact positive a has this in increase increases. cads in increase y An intuitive: is This complementarity, when male equal, else all Appendix, (SI offspring, mate’s mother, the from le tal. et Alger a with of begins evolution finite simulation (d the cads of Each all of of simulations generations. population simulations numerical 100,000 two over in shows dads out 4 borne Fig. is offspring; populations. dads her of and lution mate his to back in brings in a dad increase includes an a that that model general food more slightly parameter a describe which (Y not or cads. to tive relative and dads mate for a fitness to higher in comple- dads resulting male–male by offspring, contributed greater her food words, the other increases In mentarity spread. to dads complementarity, for male–male in increase sufficient 7 sitions D and/or i.4, Fig. increasing Can h oeta o opeetrte oudrrt h evo- the underwrite to complementarities for potential The produc- equally are dads and cads whether generally, More κ wthsfo eaiet oiie n eeto eisto begins selection and positive, to negative from switches rmdd oevlal,adtefins fdd eaieto relative dads of fitness the and valuable, more dads from or IAppendix, SI κ µ. µ and and µ a ao asb nuigasic rmgm class game from switch a inducing by cads favor can Top δ nrae h uvvlpoaiiyo fsrn provi- offspring of probability survival the increases µ Bottom ∈ ems1 Lemmas µ .A eut l leeul when equal, else all result, a As 8). ems1 Lemmas nal nices ndd’provisioning, dads’ in increase an entails C oosapiens Homo 0 1] [0, hw h vltoaytaetr fapopula- a of trajectory evolutionary the shows δ −4 approach = s a fet ntesm ieto sincreases as direction same the in effects has x rbblt fmtto ewe aetypes. male between mutation of probability ) D µ Y n rmtedad, the from and , rpstos4 Propositions Y ssrcl nraigin increasing strictly is , htrpeet h hr ftecollected the of share the represents that D i h aac nfvro as e.An Yes. dads? of favor in balance the tip lutae aei hc ascontribute cads which in case a illustrates Y ds C d , C µ seog o ast ucmeecads. outcompete to dads for enough is κ, D > Y and 0 = and = C = Y 1/4 Y > D ∂ ,n opeetrte (κ complementarities no ), ∂ ∂ 2, ∂κ n aiulueo ehooy[e.g., technology of use habitual and Homo 2, D s y Y s and D ufiin nraei female– in increase sufficient a , and 1, Proposition D D .Thus, S2). Fig. and 1, Proposition rud2Ma h ino Eq. of sign the Mya, 2 around D κ > or , · edr h odcontribution food the renders and ∂ φ 0 ∂µ ndeayrlac nanimal on reliance dietary in y r ag,a nraein increase an large, are D Y y C 5 D > D > and h uvvlo dad’s a of survival the , > 0 Y κ: Y D C rpstos7–10, Propositions .Udrti con- this Under ). s ,a nraein increase an ), D Proof : senough is µ, Y Y C C of = = κ y = µ D Propo- Y and and , 0 = Y [15] [14] D D a , ). ), µ κ rud40ka (Top) kya. 400 around 1/2 to 1/4 from and Mya 2 around males 1/4 2,000 at of fixed populations (κ held mentarities simulated nonpaternity two with generations in 100,000 dads over of frequency the shows 4. Fig. rdhl,o h te ad hw h aaee combinations parameter the shows multicol- hand, class The other of suppressed. the game is on dads in hill, of 5 ored result Fig. evolution [dads], in the cube that or where each [cads], of combinations [cads] part top parameter either the in represents space is blank The class 1). Appendix, Lemma (SI game nonpaternity and ( the complementarities dads on depending and that cads point. means of this productivity generalizes which 5 equal Fig. assumes cads. 5 to diverted Fig. is cad a is hold neighbor example, for 4, at extrapair Fig. stant to in openness simulations female Uncertainty. The low copulations. require Paternity not High do above Despite reported Thrive Can Dads and reproduction stochastic finite of a presence in mutations). the simulations, reasonable in the within and in population as states (even, stabilizes dad-favorable timescales pop- then evolutionary more push complementarity and toward in [cads increases state ulations increases class sufficient stable dads the that asymptotically in of confirm new remains share the game The at the but dads]: dads, and enhances of further viability products) and animal of the increases of (emergence acquisition dads kya efficient 400 of more around state share shift stable to the second asymptotically [cads] The result, the from around a transition fluctuates As then to dads]. class and game [cads the induces products) 10 = probability (Bottom) ol tl lo h naino as ti la hta either as that clear is It dads. of invasion that the κ (φ) allow uncertainty paternity still of would degree maximum of values the given indicates any For evolve. to Dads Dads or κ, 0101 and µ, µ ma2y mapresent 1mya 2mya present 3mya 1mya 2mya 3mya nrae ncmlmnaiisalwteeouino as h plot The dads. of evolution the allow complementarities in Increases nrae,terneo loal aent uncertainty paternity allowable of range the increases, Y enn that meaning 1/2, C = φ and 5, −4 htrsl ngm ls dd] hr asaeable are dads where [dads], class game in result that Y . D ei t0adices ttopit ntm:fo to 0 from time: in points two at increase and 0 at begin µ) = .I both In 2.5. complementarities complementarities Increasing Increasing 50% Top ftefriiyo n a whose dad any of fertility the of Time Time and κ and Bottom, NSLts Articles Latest PNAS d h egto h hill the of height the µ, ' x hs results These 0.76 = 5, φ .sapiens H. A = = mentarities mentarities Increasing Increasing Y comple- comple- h results The .Comple- 1/2. C Y 0 mutation 20, = C d Y = ' | D φ = Y 0.55 f9 of 5 con- and 2.5. D ),

ANTHROPOLOGY ANTHROPOLOGY Fig. 5. The greater the female–male complementarity (κ) and/or the male–male complementarity (µ), the higher the nonpaternity (φ) that dads can confront yet still prevail. Points inside the multicolored hill favor the evolution of dads, while those in the blank space above it do not. As either female– male or male–male complementarities increase, dads can evolve at higher levels of nonpaternity. The same plot is displayed from three different angles to enhance clarity. YD = YC = 2.5; x = 5; A = 20.

grows; in other words, dads can evolve at a higher degree of ciently high female–male and/or male–male complementarities paternity uncertainty when there are greater complementarities can enable dads to evolve amid even high probabilities of non- (SI Appendix, Proposition 6). paternity. The next sections discuss available paleontological and archeological evidence relevant to the model and the pre- Dad–Cad Polymorphism. The model encompasses the possibility dictions generated by the theory. The final sections of the that a dad’s reproductive success is higher when matched with a paper discuss the relationship between this model and other cad than with a dad. Dads gain from cads if cads procure enough models of paternal care and additional directions for theory additional food (YC > YD ) to compensate for the paternity they development. steal from dads. Such payoffs can lead to a stable dad–cad poly- morphism, as illustrated in Fig. 4, Bottom. More generally, Fig. 6 Evidence for Complementarities from the Paleontological and Arche- shows that YC must strictly exceed YD for such a stable polymor- ological Record. The fossil and paleo-climatic record provides phism to arise: If YD ≥ YC , the game is never in class [cads and clues about specific ecological forces generating complemen- dads] (SI Appendix, Propositions 2 and 3). Fig. 6 further shows tarities in the hominin lineage. Since the last shared common that a stable dad–cad polymorphism is possible only if comple- ancestor with chimpanzees (8 to 5 Mya), hominins increas- mentarities are strong enough but not too strong (i.e., κ + µ is ingly inhabited ecologies characterized by high habitat instability; neither too small nor too large). Interestingly, when ecological heterogeneous patterns of vegetation; and long-term trends conditions favor such a mutualism between dads and cads, cads implicitly “trade” food for sex, but in contrast to the standard food-for-sex scenario between a male and a female, here the trade is between males: A cad’s food production increases the amount of food a dad can provide his mate and her offspring, and in return the dad is willing to lose paternity. 1 [Cads -or- In our view, YD = YC or YD > YC is the most plausible sce- Dads] nario based on empirical observations of modern human hunter- [Cads] [Dads] gatherers. Hence, our model would need to be enriched to help

understand the factors that can sustain stable dad–cad polymor- C Y

phisms over hominin evolutionary history. Nonetheless, the poly- 0

morphism described above may be relevant for understanding D the evolution of provisioning in other ecological contexts. Y [Cads] [Dads] Discussion [Cads Our theory is that ecological changes in the availability of -and- Dads] difficult-to-acquire, energy-dense foods interacted with existing -1 traits in ancestral hominins to promote foraging specialization by sex—with males largely acquiring protein- and fat-rich ani- mal products and females largely gathering carbohydrate-rich plant-based foods while providing offspring care. This spe- 0.0 0.2 0.4 0.6 0.8 1.0 cialization in turn generated complementarities—both between males and females and between males—which would have given   a reproductive advantage to provisioning males. The model reveals the following sufficient conditions for the evolution Fig. 6. Complementarities (here shown as the sum of the male–female complementarity κ and the male–male complementarity µ) and differential of paternal provisioning: 1) Male hunting reliably comple- production of dads versus cads (Y − Y ) determine the game class and thus ments female gathering and offspring care and/or 2) males D C the asymptotically stable states and evolutionary outcomes. When YD < YC cooperate with each other in the pursuit and/or sharing of at intermediate levels of complementarity, the game class is [cads and dads], hunted game, generating complementarities in their efforts. meaning that dads and cads coexist in a polymorphic stable state. When The model results, as displayed in Figs. 4–6, show that suffi- YD ≥ YC , any stable state is monomorphic. φ = 1/2; YD = 2.5; A = 20; x = 5.

6 of 9 | www.pnas.org/cgi/doi/10.1073/pnas.1917166117 Alger et al. Downloaded by guest on October 6, 2021 Downloaded by guest on October 6, 2021 le tal. et Alger ayfrgr hwrdcddmrhs nbd ierltv to relative size body in Contempo- dimorphism diet. is reduced and show evidence behavior foragers in More rary dimorphism research. sexual on additional record, that needed paleontological for evidence and guidance of archeological pieces providing the critical from Model. to missing the attention are by directs Generated theory Predictions Our and Directions Research New time. this have by also lineage would our in provisioning evolved paternal archaic that of imply time developments dependence the by juvenile place extended in sapiens H. were that size certain brain 450 more near-modern to and is first typ- 500 it late by and (39), camps 38) very base kya ref. of hunter-gatherer see evidence human (but Given modern fossils ically Mya. Neanderthal 1.5 in by eruption histories adolescent molar evolve life of an human to modern lack or yet fully a that 38) had possible Given ref. is (37). it (e.g., spurt, weaning growth growth at protracted age for earlier maturation evidence an particularly Slower with provisioning, 36). coupled offspring 35, if postlactational (22, imply humans modern might in than faster of of slowing modest a and (34) (22). development dimorphism after sizes sexual found Brain in suggests reductions tissues. are (33) pro- animal cc km) for accessing (>10 >700 stones in hominins distances investment transporting omnivorous long substantial of over that tools costs carcasses fact requiring cessing energetic The of foods the prepare. proportion plant-based absorbed and and greater and diverse acquire a a (32) to included gut, implies products diet (29–31) and animal size This of jaw brain diet. range smaller and high-quality wide body complexity, a larger molars, textural and and microwear incisors dental smaller of fatherhood combination in hominin be to conducive may complementarities stature with taller ated and legs elongated of appearance beginning be the sug- entail to is by and mobility tended gested hominin distances, foods Greater foraging expenditures. animal energy greater increased foods, require before plant predictable, intermittent to less is Compared foraging Mya. tool-assisted 2 stone of before bones evidence animal large have on marks cut found Tool been (27). tubers) mammals nuts, with grassland-adapted (e.g., large nutrients, foods and plant of protected distribution of new abundance increased a open, offered More environments animals. frugivorous arid and arboreal in decline relative by evident is Africa have would 1). (Fig. turn complementarities in intrasexual which and learning, inter- favoring and increased conditions hunting to likely ecological gains and experienced greater species size, have hominin Some with would brain behavior. social evident, species morphology, and histories is tooth life of features size, species other body Late hominin to in of Mid tran- varying radiation Plio-Pleistocene the the a during During foods 24). sition (23, plant Mya) of (∼3.5 range Pliocene broad a environmental porating to solutions novel migration finding in (22). and flexibility, problems survival habitats, dietary facilitating new including to activity. traits environments, favored endurance shifting also and ther- conditions for efficiency, Varying adaptations promoted locomotor and including (pri- ecologies incipient moregulation, bipedality, allowing biomass These morphologies obligate C4 (21). hominin ultimately of greater sedges) evolution and and the habitat, grasses open marily aridity, toward .erectus H. associ- characteristics of cluster the of evidence first The southern and eastern in mammals grazing of burgeoning The incor- diets hominin of array diverse a identify studies Isotopic Australopithecus 0 y.Vee hog h eso h oe,these model, the of lens the through Viewed kya. ∼400 Mya. ∼2 nearly In erectus. Homo noeywslkl oehtsoe hnthat than slower somewhat likely was ontogeny n oencipnes u considerably but chimpanzees, modern and . o2Ma(5 6 n onie iha with coincides and 26) (25, Mya 2 to ∼2.5 . y,aogwt vdneof evidence with along Mya, ∼1.8 .erectus H. y 2) although (28), Mya ∼3 . y) the Mya), (∼1.8 ihvraini opeetrt n ehp potnte for opportunities associated mating. perhaps be extrapair and will complementarity off- classes in avian variation and and with invest- feeding mammalian paternal in the in variation within specialization that ment or predicts theory taking Our turn care. complementary spring of from form gains generates size the situation body in adult This reach fly. they can for until and vulnerable hatching often after are periods young extended The hatchlings. vul- other and protecting the and food on nerable acquiring , between flying trade-off a of face species hand, Most “crowd investment. effectively male and out” feeding complementarity female–male combine the lower for to however, scope adaptations, females environ- Those care. allow protective offspring direct and a with development, adapta- provide for mammalian lactation ment the and survival: that offspring gestation in note investment Internal to increased with interesting associated is common is tion so It and mammals birds. why in example, in uncommon for so explain, is help provisioning can male It (41). far understood still well are from of which investment, paternal level with associated conditions exceptional primates an other to constella- to relative special rise species mammals. a our and gave in is that provisioning This paternal conditions process. of learning development tion slowing the favored facilitate These have provisioning. to also male would of conditions for benefits same unprofitable the hunting increased and rendered females have for- would flexible with and strategies, commit- coupled complex aging young, a learning vulnerable for time, requirements carrying time same and lengthy for the and caring At intelligence to scav- behavior. increased ment to for animal strategies selecting about creative game, learning utilize kill to and/or ability enge the by have would limited carnivory been hominin early canines, weapons, sharp projectile Without or obtain. packages claws, to food dangerous and valuable expanded difficult concentrated, are of and that resulted abundance use shifts greater Ecological a tool foraging. and in greater hunting for for years. range day several hands the over the offspring to freed in committed Bipedality investing females and with common offspring using, last carrying the tool of and features intelligent the con- ancestor: with environmental same begins the answer to The exposed ditions. species other humans in in evolved not provisioning but paternal why of question the Species. into Nonhuman to traits Applications those of look emergence can the we well. investigate changes, as those to bet- of paleogenomics we bases As to genetic (40). brain the processing in understand emotion ter activation face increased for pro- and important regions bonding, higher facilitate drive, to sexual lower duction underly- including and responses humans, in production modern evidence behavioral in changes of fatherhood and these body to hormonal, transition growing of ing a neural, timing now joint the is on of aging There lineage. and light hominin development crucial differences the of shed age rates and also on sex will data for existing Paleogenomic test to diet. to applied in fossils be discovered can newly analysis) and radioisotope to (e.g., critical position is diets juvenile emerges. of provisioning paternal part when not important determining an but when becomes weaning regarding molar Evidence meat composition. about about dietary or evidence known food of provide sources is may what which beyond eruption, development sharing juvenile regard- food evidence ing additional intersexual need we extensive Similarly, prevalent. when dimor- became and those especially hunting in and changes to regarding phisms respect evidence need with shar- We food dimorphism gathering. to pronounced due diet and in ing, dimorphism little very apes, nonhuman hsmdlcnas eapidt nesadmr general more understand to applied be also can model This com- dietary assessing for methods sophisticated Increasingly h oe rvdsinsights provides model The NSLts Articles Latest PNAS | f9 of 7

ANTHROPOLOGY ANTHROPOLOGY Our theory also provides insight into why we still find male investment. This model sheds light on how ecological changes in birds, despite evidence of extrapair mat- in the distant past may have altered the trade-off between mat- ing and paternity. Penguins provide an exception that proves ing effort and paternal investment and promoted the evolution of the rule. Penguins have converged with fish-eating mammals human fatherhood. While this model delivers a rich set of origi- in body form and have lost the ability to fly. However, they nal insights, we see several directions in which it could be further still evidence male parental investment and pair bonding in extended. response to the need for biparental protection of vulnerable First, our model focuses on paternal investment in the form of eggs and young. food provisioning. Male–female and male–male complementar- ities in other domains, e.g., tool production and domestic tasks, Comparison with Other Models of Paternal Investment. In addition may be modeled using a similar approach. to the model by Gavrilets (7), there is a rich set of theoretical Second, our model disregards sexual selection. But what would models of the evolution of —both maternal and happen if females could actively select their mates? The observed paternal—or lack thereof (42–48; see ref. 49 for a survey). As polymorphic equilibrium opens the door to female choice by in our model, in these models the opportunity cost of provid- generating heterogeneity in male contributions to offspring. ing care (42) appears as lost mating opportunities (in our model, Relatedly, in our model females do not gain anything from provisioning dads have no extrapair copulations while nonpro- extrapair copulations: What if they obtained extra resources or visioning dads do). Compared to this literature, our model genetic benefits that conferred survival advantages for their off- innovates in two major ways. spring? What level of female willingness to engage in extrapair First, in almost all existing models, offspring survival depends copulations would be expected if these traits were subject to only on the sum of maternal and paternal care. By contrast, selection? The same ecological conditions that increase the fit- in our model there are female–male complementarities. While ness benefits to males from investing in offspring also increase such complementarities are also present in refs. 43–45, our the benefits to females from receiving that investment. Con- model is distinct in that it considers two types of males and also cealing ovulation is a potential female strategy that could have includes male–male complementarities in food production. Our reduced rates of male mating competition at the time of ovula- model thus sheds light on the interplay between male–female and tion, thereby reducing nonpaternity as the primary brake on male male–male complementarities in the evolution of paternal care. investment. Moreover, an unexpected insight appears, namely, that dads can Third, since our model disregards relatedness, it would be benefit from the presence of cads, which can give rise to a stable interesting to embed the male–male interaction we examine here polymorphism including both dads and cads. in a model with population structure. Moreover, since variance in Second, while we follow in the footsteps of Maynard Smith male ability and reliability in cooperation could motivate assort- (46) and use evolutionary game theory to study the evolu- ment among males, models which allow for male partner choice tion of paternal care, we do so in a different way. The orig- are warranted. inal parental care game studied a population where males Additional questions are, Would model results change if males and females are matched to interact and where males and interacted in groups of n > 2 individuals rather than in pairs? females are either a guarding type or a deserting type; the How would the presence of grandparents or other alloparents intuition was that deserting males would stand to gain more affect the key trade-offs? than deserting females (46). This modeling strategy, however, Finally, the model may also be applicable to modern, cultur- was difficult to reconcile with the Fisher condition (47), which ally variable trends in men’s parenting behavior. Both within and requires that males and females must on average have the same among populations there is significant variation in family forms, number of offspring (see refs. 17 and 48 for excellent discus- and the matrifocal family, with limited male paternal investment, sions). The Fisher condition is fulfilled in our model because is becoming increasingly prevalent in sectors of societies world- each male spends an equal amount of time with his mate, and wide. This variation invites analysis and assessment of whether this time may be spent provisioning or seducing his neighbor’s variable complementarities may help explain it. mate. This allows a straightforward definition of reproduc- tive success that does not require tracking the time spent in Data Availability. The simulation code is available to readers at and out of the mating pool. Moreover, framing the evolution- https://github.com/systemsscience/paternal. ary game as an interaction between males opens the door to studying male–male complementarities in food production and ACKNOWLEDGMENTS. I.A. acknowledges funding from the European sharing. Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant 789111; ERC Evolving Economics). I.A. and J.S. acknowledge Institute for Advanced Study in Toulouse (IAST) Directions for Future Research. We have proposed an evolution- funding from the French National Research Agency (ANR) under Grant ary game theoretic model to study the evolution of paternal ANR-17-EURE-0010 (Investissements d’Avenir program).

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ANTHROPOLOGY ANTHROPOLOGY