The Emergence of a Superorganism Through Intergroup Competition

The emergence of a superorganism through intergroup competition

H. Kern Reeve†‡ and Bert Ho¨ lldobler‡§¶

†Department of Neurobiology and Behavior, Cornell University, Ithaca, NY 14853; §School of Life Sciences, Center for Social Dynamics and Complexity, Arizona State University, Tempe, AZ 85287-4501; and ¶Biozentrum, University of Wu¨rzburg, 97070 Wu¨rzburg, Germany

Contributed by Bert Ho¨lldobler, April 16, 2007 (sent for review March 24, 2007) Surveys of insect societies have revealed four key, recurring orga- levels of altruism (with most group members foregoing direct nizational trends: (i) The most elaborated cooperation occurs in reproduction) and most intricately cooperative communication groups of relatives. (ii) Cooperation is typically more elaborate in systems, clearly occur in groups of relatives (5, 6). (ii) Cooper- species with large colony sizes than in species with small colony ation is typically more elaborate in species with large colony sizes sizes, the latter exhibiting greater internal reproductive conflict than in species with small colony sizes, the latter being charac- and lesser morphological and behavioral specialization. (iii) Within terized by greater internal reproductive conflict [manifested in a species, per capita brood output typically declines as colony size dominance hierarchies as in small polistine, ponerine, and increases. (iv). The ecological factors of resource patchiness and leptothoracine societies (7–14)] and lesser morphological and intergroup competition are associated with the most elaborated behavioral specialization (12, 13, 15, 16). (iii) Within species cooperation. Predictions of all four patterns emerge elegantly from exhibiting small to medium-sized colonies, per capita brood a game-theoretic model in which within-group tug-of-wars are output often tends to decline as colony size (number of queens nested within a between-group tug-of-war. In this individual plus workers) increases (16, 17). (iv) Intergroup competition selection model, individuals are faced with the problem of how to facilitated by the ecological factor of resource patchiness appears partition their energy between investment in intercolony compe- to be associated with the most elaborated within-group coop- tition versus investment in intracolony competition, i.e., internal eration (1, 9). A promising framework for constructing a model tugs-of-war over shares of the resources gained through inter- that potentially accommodates all of the above comparative group competition. An individual’s evolutionarily stable invest- patterns is ‘‘tug-of-war’’ theory (18). ment in between-group competition (i.e., within-group coopera- Tug-of-war theory has been used to understand evolutionarily tion) versus within-group competition is shown to increase as stable reproductive partitioning when dominants have incom- within-group relatedness increases, to decrease as group size plete control over subordinates, and group members have such increases (for a fixed number of competing groups), to increase as limited outside reproductive options that they will not receive the number of competing groups in a patch increases, and to reproductive payments to remain in the group (19). In a tug-of- decrease as between-group relatedness increases. Moreover, if war, each group member selfishly expends some fraction of the increasing patch richness increases both the number of individuals total group output to increase its share of that output. The selfish within a group and the number of competing groups, greater fraction expended is called the ‘‘selfish investment’’ or ‘‘selfish overall cooperation within larger groups will be observed. The effort.’’ Each group member’s share depends on the magnitude model presents a simple way of determining quantitatively of its selfish investment relative to the magnitude of other group how intergroup conflict will propel a society forward along a members’ selfish investments, just as the outcome of a real ‘‘superorganism continuum.’’ tug-of-war depends on the relative magnitudes of the forces generated at the two ends of the rope. Thus, an individual’s share conflict ͉ cooperation ͉ group selection ͉ tug-of-war ͉ social insects in the tug-of-war depends on the individual’s investment in the tug-of-war relative to the summed investments of the other group members (18). Using game theory, one solves for the jointly t has recently been argued that the extreme levels of cooper- optimal values of these selfish investments in the tug-of-war (18), ation exhibited by the advanced eusocial insects ultimately I i.e., for the selfish efforts that jointly maximize the group must be explained by invoking the ‘‘binding’’ force of intergroup members’ inclusive fitnesses. The tug-of-war encompasses the competition rather than by appealing to genetic relatedness, phenomenon of ‘‘mutual policing,’’ in which group members act which only amplifies ecologically driven selective forces for to increase their own share of reproduction and at the same time cooperation without causing them (1). According to the latter limit that of others (20). Game-theoretic models of evolution- view, group selection must be invoked to understand coopera- arily stable policing efforts and also the evolutionarily stable tion in insects (ref. 1 and E. O. Wilson, personal communica- resistance to policing are necessary for adequate understanding tion). However, it is easy to construct a general, purely individual of policing evolution, which is thought to play a key role in the selection model of cooperation mediated by between-group evolution of many animal societies (21). competition (2). This is not surprising, as it is now well estab- We explore the theoretical consequences of a two-tiered, but lished that trait-group selection models can be mathematically interlocking, competitive tug-of-war incorporating intergroup translated into individual selection models (including inclusive competition. First, a tug-of-war over resource share occurs fitness models), and vice versa, so the two classes of models within groups, whose members are related by r, and, second, a cannot be considered alternatives to each other (3, 4). tug-of war over the amount of resource obtained by a group The truly interesting problem is to determine (with either occurs between groups, which are related to each other by rЈ (Fig. inclusive fitness or equivalent trait-group selection models) how intergroup competition can increase the extent to which social groups can be viewed as coherent vehicles for gene propagation, Author contributions: H.K.R. designed research; B.H. analyzed data; and H.K.R. and B.H. i.e., ‘‘superorganisms’’. We present an individual selection model wrote the paper. that incorporates intergroup competition and appears to explain The authors declare no conflict of interest. all of the major trends in insect societies. A survey of insect ‡To whom correspondence may be addressed. E-mail: [email protected] or bertholl@ societies reveals at least four key, recurring organizational asu.edu. trends: (i) The most elaborated cooperation, i.e., the highest © 2007 by The National Academy of Sciences of the USA

9736–9740 ͉ PNAS ͉ June 5, 2007 ͉ vol. 104 ͉ no. 23 www.pnas.org͞cgi͞doi͞10.1073͞pnas.0703466104 Downloaded by guest on October 2, 2021 accounting for the fact that a fraction r of the individual’s fellow group members will also display its own mutant value of the competitive investment because of shared kinship. The competitiveness of this group is equal to the sum of all individuals’ investments in the group competitiveness, multiplied by some constant g. We assume a linear group competitiveness function for simplicity and to show how diminishing per capita final group output with increasing group size emerges despite such a linear combination of the individual investments. The mutant’s group thus has an overall group-level competitiveness equal to

G ϭ g͓͑1 Ϫ f ͒t ϩ r͑n Ϫ 1͒͑1 Ϫ f ͒t ϩ ͑1 Ϫ r͒͑n Ϫ 1͒͑1 Ϫ f *͒t͔ [2] A group not containing the mutant has a competitiveness equal to

G* ϭ g͓n͑1 Ϫ f *͒t͔ [3]

A group’s competitiveness determines that group’s share of the contested resource of total value r that results from the between- Fig. 1. The nested tug-of-war. Individuals engage in a selﬁsh tug-of-war over group tug-of-war. In particular, the mutant’s group share of the resource shares within groups, and, simultaneously, groups engage in a resource is equal to tug-of-war with each other. The within-group tug-of-war reduces a group’s G ability to win the between-group tug-of-war. S ϭ [4] b G ϩ rЈ͑N Ϫ 1͒G ϩ ͑1 Ϫ rЈ͒͑N Ϫ 1͒G* Ј 1). The two competitive tug-of-wars are interlocking because a where r is the relatedness between groups, i.e., the fraction of group’s ability to outcompete other groups declines the more groups that have a genetic composition like the mutant’s own total energy its group members expend in the within-group group, with respect to the locus of interest. (To see the latter, tug-of-war. For example, the group’s competitive ability in- suppose that the mutant is related to other group members by r. creases as the individual invests more time and energy in In such a case, a fraction r of group members will have the relevant allele when it is rare. If the mutant had the same cooperative foraging, brood care, nest defense, and between-

relatedness to a competing group, the latter group also would EVOLUTION group interference competition; in contrast, the individual’s have a fraction r of group members possessing the allele. If only share of resources won increases if it instead invests its time and a fraction q of competing groups were as closely related to the energy in resource hoarding and aggressive competition with mutant as members of its own group, then rЈϭqr.) fellow group members over the resources won in intergroup Thus, the mutant’s overall amount of resource obtained W, competition. We show that the four major organizational at- after both within-group and between-group competition, is tributes of insect societies (and possibly those of many vertebrate equal to societies) emerge naturally as predictions of this simple ‘‘nested’’ ͑ ͒ ϭ tug-of-war model. W f, f * SbSw R [5] Suppose that there are n individuals in a cooperative group and that N cooperative groups are competing for a resource of We assume that W is positively correlated to the mutant’s fitness total value R. Each individual is faced with the following [because this fitness is modulated by interactions with relatives, decision: Of a private prior energy store t, what fraction f of this it is Hamiltonian ‘‘neighbor-modulated fitness’’ and thus the private store should be invested in a selfish tug-of-war over model is equivalent to a generalized inclusive fitness model (5)]. resource share within the group, with the remaining fraction 1 Ϫ The mutant’s evolutionary stable fractional selfish investment in increasing its within-group share is found by solving f being used to increase group competitiveness? For example, the Ϫ private store could be an energy store, a fraction of which (1 lW f) will be allocated to performing tasks that help its group   ϭ 0 [6] lf outcompete neighboring groups for a limiting resource, and the fϭf * remaining fraction ( f) of which will be devoted to selfishly enhancing the individual’s share of the resource won by its group. in terms of f*. This equation mathematically expresses the We refer to f as simply the ‘‘selfish fraction.’’ condition that the evolutionarily stable investment should be the one yielding the highest fitness in a population of individuals We now use f to represent the selfish fraction for a rare mutant exhibiting that same investment; thus, no alternative mutant in a population, and we let f* represent the population value of strategy can invade the population (22). The solution, which this selfish fraction. The mutant’s selfish investment in within- ϭ corresponds to a maximum in neighbor-modulated individual group competition is x ft and in between-group competition is fitness, is equal to (1 Ϫ f)t, with x* and (1 Ϫ f*)t representing the corresponding population values of these investments. Thus, the mutant’s N͑n Ϫ 1͒͑1 Ϫ r͒ f * ϭ [7] within-group fraction of whatever resource is won in between- Nn Ϫ 1 Ϫ r͑n Ϫ 1͒ Ϫ ͑N Ϫ 1͒rЈ͓1 ϩ r͑n Ϫ 1͔͒ group competition is equal to (That the latter is a fitness maximum is verified by Ѩ2w/Ѩf 2 Ͻ 0 x ϭ S ϭ [1] at f f*.) As the number of group members becomes larger, f* w x ϩ r͑n Ϫ 1͒x ϩ ͑1 Ϫ r͒͑n Ϫ 1͒x* rapidly converges to N(1 Ϫ r)/[N Ϫ r Ϫ rrЈ(N Ϫ 1)]. If groups are

Reeve and Ho¨lldobler PNAS ͉ June 5, 2007 ͉ vol. 104 ͉ no. 23 ͉ 9737 Downloaded by guest on October 2, 2021 and we can allow for variable between-group competition intensity by modifying Eq. 4 to become

Gz S ϭ [9] b Gz ϩ rЈ͑N Ϫ 1͒Gz ϩ ͑1 Ϫ rЈ͒͑N Ϫ 1͒Gz*

where z is the between-group competition intensity. With these generalizations, the new evolutionarily stable selfish effort becomes just

wN͑n Ϫ 1͒͑1 Ϫ r͒ f * ϭ [10] z͑N Ϫ 1͓͒1 ϩ r͑n Ϫ 1͔͒͑1 Ϫ rЈ͒] ϩ wN͑n Ϫ 1͒͑1 Ϫ r͒

The important prediction that emerges is that the selfish effort declines as within-group competition intensity decreases relative to between-group competition intensity. In fact, if within-group competition intensity is very small relative to that between Fig. 2. Fractional investment in group competitiveness. (Upper) Individual’s groups, the individual is favored to invest virtually all of its effort evolutionarily stable investment in group competitiveness (equals the degree in between-group competition, regardless of the relatedness of superorganismness) as a function of between group relatedness (rЈ) and among group members (i.e., f 3 0asw/z 3 0). within-group relatedness (r)(n ϭ 100; n ϭ 4; z ϭ w). (Lower) Individual’s In advanced eusocial colonies, f appears to be close to zero. In evolutionarily stable investment in group competitiveness as a function of such advanced social organizations, the colony effectively be- group size (n) and number of competing groups (N)(rЈϭ0; r ϭ 1/2; z ϭ w). comes the target of selection, i.e., it is a coherent ‘‘extended phenotype’’ (23) of the genes within colony members. Selection large and there are many competing groups, f* converges to just therefore optimizes caste demography, patterns of division of (1 Ϫ r)/(1 Ϫ rrЈ). If there are no competing groups (n ϭ 1), f is labor (15), and communication systems at the colony level (9). just 1. [Note that in this mathematical model, f can be interpreted For example, colonies that employ the most effective recruit- either as the proportion of energy that each individual invests in ment system to retrieve food, or that exhibit the most powerful intracolony conflict or as the proportion of individuals that will colony defense against enemies and predators, will be able to devote all (versus none) of their energy to intracolony conflict. raise the largest number of reproductive females and males every On the latter interpretation, the proportion of individuals de- year and, thus, will have the greatest fitness within the population voting all their energy to within-colony cooperation, and none to of colonies (24). personal reproduction, will be 1 Ϫ f*, and thus the reproductive Thus, a striking characterization of f* is that it precisely skew will increase as f* decreases. However, we focus in this measures a society’s position along a ‘‘superorganism contin- paper on the implications of the model for the average level of uum.’’ At one extreme, f* ϭ 1, group members invest all of their cooperation regardless of which skew-related interpretation is energy in within-group competition, and there is really no taken.] cooperative group at all. At the other extreme, f* ϭ 0, group As can be verified by checking the derivatives of f* with respect members invest all of their energy in within-group cooperation to each of the contained variables, the individual’s fractional to outcompete other groups, and the society can be regarded as effort in selfish within-group competition increases as its group a ‘‘superorganism,’’ an analogy to a metazoan organism. For size n increases, as the number of competing groups N decreases, values in between these two extremes, the society can be viewed as within-group relatedness r decreases, and as the between- as having both selfish and superorganismal features. group relatedness rЈ increases (Fig. 2). In other words, intragroup cooperation will increase as (i) the group size decreases, (ii) the Discussion number of competing groups increases, (iii) the within-group Our model predicts an individual’s evolutionarily stable, frac- relatedness increases, and (iv) the between-group relatedness tional investment in between-group competition (equal to with- decreases (all other variables held constant in each of these in-group cooperation) versus within-group competition, the analyses). These relationships are numerically presented in Fig. latter undermining its success in between-group competition. 2. We note that the model encompasses both intraspecific and This cooperative investment, 1 Ϫ f*, and thus the degree of interspecfiic competition; in interspecific competition, the value group ‘‘superorganismness,’’ increases as within-group related- of the between-group relatedness is just rЈϭ0. ness increases, decreases as group size increases (number of The nested tug-of-war model can be generalized to encompass competing groups held constant), increases as the number of variable intensities of competition in the following way. We competing groups in a patch increases, decreases as between- assumed that an individual investing, say, twice as much as group relatedness increases, and increases as the intensity of another group member in the within-group tug-of-war will between-group competition increases relative to the intensity of receive twice as much resource as will that other group member. within-group competition. But suppose an individual investing an amount h versus another The latter predictions bear directly on the four organizational who invests j gets hw/jw as much resource, where w measures the attributes of insect societies, which we discuss in turn: intensity of competition. If w ϭ 0, the two individuals get the (i) The most elaborated cooperation, i.e., the highest levels of same amount of resource no matter how each invests. If w is altruism and most intricately cooperative communication sys- infinite, then the individual investing even slightly less gets tems, will tend to occur in groups of relatives. As predicted by essentially no resource. Thus, to incorporate variable within- our model, the selfish investment declines, and investment in the group competition intensity, we can modify Eq. 1 to become group increases, as within-group relatedness increases. Thus, within-group genetic relatedness powerfully modulates the de- w x gree of cooperation, as is observed in nature, contrary to claims S ϭ [8] w xw ϩ r͑n Ϫ 1͒xw ϩ ͑1 Ϫ r͒͑n Ϫ 1͒xw* that genetic relatedness is a secondary (or even unimportant)

9738 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0703466104 Reeve and Ho¨lldobler Downloaded by guest on October 2, 2021 booster of cooperation in insect societies. We assumed a uniform the number of directly competing groups N, which seems very and symmetrical relatedness r among group members. If group likely to be the usual case. members are full-sibling offspring of the dominant breeder, and Thus, as patch richness increases, both colony size increases the sex ratio is equal or males are as genetically valuable as and the number of competing colonies increases, with the net females, tug-of-war theory predicts that there will be no selfish result that the degree of cooperation increases (f* decreases), investment at all in the within-group tug-of-war, regardless of the because f* is more sensitive to the number of competing groups intensity of between-group competition (18). In this case, which than it is to group size for medium to large groups. In other encompasses many eusocial societies, the r is effectively 1.0, words, species that typically inhabit richer patches will typically because siblings are, on average, as valuable as offspring (25). have larger colonies and also greater cooperation, as is observed. Likewise, in our model, a within-group relatedness of 1 leads to Greater cooperation in large colonies may also be reflected by f* ϭ 0. Multiple mating by queens, multiple queens, and the enhanced work tempo of workers in larger colonies (15, 16, intercolony mixing will, in effect, lower the average r within such 28), on the assumption that worker inactivity reflects enhanced groups, leading to increasing selfish fraction f* in our model. Thus, increasing genetic heterogeneity will tend the lower the selfishness (e.g., unwillingness to assume the costs of foraging degree of group superorganismness, in accordance with the view chores). that variation in relatedness within groups has a ‘‘dissolutive’’ (iii) Within a species, per capita group output typically de- effect in reducing group reproductive harmony (1). However, a clines as colony size increases (number of competing colonies large number of competing groups and/or a strong intensity of fixed). As f* increases, the per capita colony output decreases. between-group competition can overcome low levels of related- This occurs because larger group size means that individuals can ness to yield a society that scores high on the superorganism increasingly parasitize the cooperative efforts of other group continuum. members, a common feature of many multiperson cooperative Although our model predicts that relatedness predisposes games. Because f* increases as colony size increases (values of within-group cooperation, it does not predict that relatedness is other variables held constant), the nested tug-of-war correctly necessary for high levels of within-group cooperation. It follows therefore predicts that within-species comparisons will tend to from Eq. 7 that if within-group and between-group relatedness show a negative correlation between per capita group output and are both 0, the investment in within-group cooperation 1 Ϫ f* group size. The result is predicted to hold only if patch size and becomes (N Ϫ 1)/(Nn Ϫ 1), which will be Ͼ0 as long as there is the number of competing groups are controlled in the analysis, some intergroup competition (n Ͼ 1). For example, if the which will usually be the case for within-species comparisons if ϭ number of competing groups is large and z w, then the the analysis is carried out on conspecific colonies from the same within-group investment in cooperation becomes 1/n. Intrigu- site. ingly, this may compactly explain why 1 of n unrelated found- (iv) Intergroup competition facilitated by ecological factors of resses in desert ant (Acromyrmex versicolor) foundress associa- resource patchiness is associated with the most elaborated tions becomes an altruistic forager in the face of raiding threats cooperation. The nested tug-of-war model predicts that coop- from many surrounding colonies (26). Alternatively, if the eration increases (f* decreases) as the number of competing

intensity of between-group competition is much greater than EVOLUTION that of within-group competition (z ϾϾ w), as when resources are groups (and between-group competition intensity) increase, distributed in locally rich, but sparse, patches, then the within- because greater cooperation increases group competitiveness group cooperation approaches 1.0 regardless of relatedness. The and a greater number of competing groups increases the pres- latter result has the potential to explain cooperation among sure of between-group competition. Thus, the model predicts the nonrelatives in human societies and may even be relevant to fourth organizational principle of insect societies. unraveling the mystery of unicolonial ant populations, in which The utility of the nested tug-of-war model may not be re- nearly unrelated workers in multiple nests of a ‘‘supercolony’’ stricted to social insects, but also may elucidate cooperation living in a saturated habitat appear to frequently tolerate and whenever competition is structured within and between groups, even cooperate with each other (27). as, for example, is certainly the case in humans. Future tests of (ii) Cooperation is typically more elaborate in species with the model should focus on experimental manipulation of N, n, large colony sizes than in species with small colony sizes, the z, w, r, and rЈ with subsequent observation in the frequency and latter being characterized by greater internal reproductive con- intensity of within-group conflict. Particularly intriguing is the flict and lesser morphological and behavioral specialization. This prediction that within-group cooperation will decline as be- attribute may seem to contradict the prediction that cooperation tween-group relatedness increases. For example, the model will decline as group size n increases, number of competing predicts that within-group cooperation should be more elabo- groups held constant (which directly explains attribute iii,as rated in species with long-distance dispersal of reproductives discussed below). However, in between-species comparisons, than in species with limited dispersal of reproductives, because colony size and number of competing groups are likely to be the latter will more often be competing with rival groups that are confounded. That is, attribute ii is predicted if larger colonies related. Moreover, the model predicts that interspecific compe- also tend to be in competition with a larger number of colonies: tition will more effectively promote superorganismness (low f*) Suppose that insect colonies occur within resource patches in than will intraspecific competition, because rЈ must be 0 in the patchy environments, as supported by evidence that sociality latter case. commonly arises in association with resource patchiness (9). The greater the richness of the patch, the greater is expected to be When ecological and genetic factors advance a society to near both the number of colonies per patch (N) and the number of the upper extreme of the superorganism continuum, subsequent individuals per colony (n). For example, suppose that N ϭ aR selection may result in complete loss of costly physiological and n ϭ bR, where R is the resource patch richness, and a and structures involved in within-group competition. Thus, our b are constants. That is, suppose that the number of colonies and model specifies the conditions leading to a ‘‘point of no return’’ the number of individuals per colony both increase linearly as the in eusocial evolution, i.e., a point at which the capacity for patch richness increases. How does f* change as patch richness selfishness has become insignificant because the underlying R, and thus colony size, increases? The derivative df*/dR is organs (e.g., ovaries and spermatheca) important for within- negative if r Ͼ [1 ϩ n(N Ϫ 2)]/(n Ϫ 1)2, which is essentially just group competition degenerate or become completely lost (1). the permissive condition r Ͼ 0 if group size n is much larger than Once such organs become obsolete through progressive selective

Reeve and Ho¨lldobler PNAS ͉ June 5, 2007 ͉ vol. 104 ͉ no. 23 ͉ 9739 Downloaded by guest on October 2, 2021 elimination, they are unlikely to be restored in a single muta- cooperation, and of cooperation among genes within a genome tional step. Thus, our model makes the testable prediction that and among cells within multicellular organisms. worker sterility should have been most likely to evolve when intergroup competition was most intense and/or relatedness was We thank Jessie Barker, Michelle Cilia, Lee Dugatkin, Tom Seeley, exceptionally high. Sheng-Feng Shen, David S. Wilson, and Ed Wilson for comments on an This model underlines the crucial role of intergroup compe- earlier draft of this manuscript. This work was supported by the Andrew tition in forcing within-group cooperation (1). It is probably also D. White Professorship program of Cornell University, the Arizona State a potentially useful model for explaining the evolution of human University Foundation, and the German Science Foundation (SFB 551).

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