The emergence of a superorganism through intergroup competition

It has recently been argued that the extreme levels of cooperation exhibited by the advanced eusocial insects ultimately must be explained by invoking the “binding” force of intergroup competition rather than by appealing to genetic relatedness, which only amplifies ecologically driven selective forces for cooperation without causing them (1). According to the latter view, group selection must be invoked to understand cooperation in insects (ref. 1 and E. O. Wilson, personal communication). However, it is easy to construct a general, purely individual selection model of cooperation mediated by between-group competition (2). This is not surprising, as it is now well established that trait-group selection models can be mathematically translated into individual selection models (including inclusive fitness models), and vice versa, so the two classes of models cannot be considered alternatives to each other (3, 4).

The truly interesting problem is to determine (with either 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, i.e., “superorganisms”. We present an individual selection model that incorporates intergroup competition and appears to explain all of the major trends in insect societies. A survey of insect societies reveals at least four key, recurring organizational trends: (i) The most elaborated cooperation, i.e., the highest levels of altruism (with most group members foregoing direct reproduction) and most intricately cooperative communication systems, clearly occur in groups of relatives (5, 6). (ii) Cooperation is typically more elaborate in species with large colony sizes than in species with small colony sizes, the latter being characterized by greater internal reproductive conflict [manifested in dominance hierarchies as in small polistine, ponerine, and leptothoracine societies (7–14)] and lesser morphological and behavioral specialization (12, 13, 15, 16). (iii) Within species exhibiting small to medium-sized colonies, per capita brood output often tends to decline as colony size (number of queens plus workers) increases (16, 17). (iv) Intergroup competition facilitated by the ecological factor of resource patchiness appears to be associated with the most elaborated within-group cooperation (1, 9). A promising framework for constructing a model that potentially accommodates all of the above comparative patterns is “tug-of-war” theory (18).

Tug-of-war theory has been used to understand evolutionarily stable reproductive partitioning when dominants have incomplete control over subordinates, and group members have such limited outside reproductive options that they will not receive reproductive payments to remain in the group (19). In a tug-of-war, each group member selfishly expends some fraction of the total group output to increase its share of that output. The selfish fraction expended is called the “selfish investment” or “selfish effort.” Each group member's share depends on the magnitude of its selfish investment relative to the magnitude of other group members' selfish investments, just as the outcome of a real tug-of-war depends on the relative magnitudes of the forces generated at the two ends of the rope. Thus, an individual's share 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 optimal values of these selfish investments in the tug-of-war (18), i.e., for the selfish efforts that jointly maximize the group members' inclusive fitnesses. The tug-of-war encompasses the phenomenon of “mutual policing,” in which group members act to increase their own share of reproduction and at the same time limit that of others (20). Game-theoretic models of evolutionarily stable policing efforts and also the evolutionarily stable resistance to policing are necessary for adequate understanding of policing evolution, which is thought to play a key role in the evolution of many animal societies (21).

We explore the theoretical consequences of a two-tiered, but interlocking, competitive tug-of-war incorporating intergroup competition. First, a tug-of-war over resource share occurs within groups, whose members are related by r, and, second, a tug-of war over the amount of resource obtained by a group occurs between groups, which are related to each other by r′ (Fig. 1). The two competitive tug-of-wars are interlocking because a group's ability to outcompete other groups declines the more total energy its group members expend in the within-group tug-of-war. For example, the group's competitive ability increases as the individual invests more time and energy in cooperative foraging, brood care, nest defense, and between-group interference competition; in contrast, the individual's share of resources won increases if it instead invests its time and energy in resource hoarding and aggressive competition with fellow group members over the resources won in intergroup competition. We show that the four major organizational attributes of insect societies (and possibly those of many vertebrate societies) emerge naturally as predictions of this simple “nested” tug-of-war model.

Suppose that there are n individuals in a cooperative group and that N cooperative groups are competing for a resource of total value R. Each individual is faced with the following decision: Of a private prior energy store t, what fraction f of this private store should be invested in a selfish tug-of-war over resource share within the group, with the remaining fraction 1 − f being used to increase group competitiveness? For example, the private store could be an energy store, a fraction of which (1 − f) will be allocated to performing tasks that help its group outcompete neighboring groups for a limiting resource, and the remaining fraction (f) of which will be devoted to selfishly enhancing the individual's share of the resource won by its group. We refer to f as simply the “selfish fraction.”

We now use f to represent the selfish fraction for a rare mutant in a population, and we let f* represent the population value of this selfish fraction. The mutant's selfish investment in within-group competition is x = ft and in between-group competition is (1 − f)t, with x* and (1 − f*)t representing the corresponding population values of these investments. Thus, the mutant's within-group fraction of whatever resource is won in between-group competition is equal to

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

A group not containing the mutant has a competitiveness equal to

A group's competitiveness determines that group's share of the contested resource of total value r that results from the between-group tug-of-war. In particular, the mutant's group share of the resource is equal to

where r′ is the relatedness between groups, i.e., the fraction of groups that have a genetic composition like the mutant's own group, with respect to the locus of interest. (To see the latter, suppose that the mutant is related to other group members by r. 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 relatedness to a competing group, the latter group also would have a fraction r of group members possessing the allele. If only a fraction q of competing groups were as closely related to the mutant as members of its own group, then r′ = qr.)

Thus, the mutant's overall amount of resource obtained W, after both within-group and between-group competition, is equal to

We assume that W is positively correlated to the mutant's fitness [because this fitness is modulated by interactions with relatives, it is Hamiltonian “neighbor-modulated fitness” and thus the model is equivalent to a generalized inclusive fitness model (5)].

The mutant's evolutionary stable fractional selfish investment in increasing its within-group share is found by solving

in terms of f *. This equation mathematically expresses the condition that the evolutionarily stable investment should be the one yielding the highest fitness in a population of individuals exhibiting that same investment; thus, no alternative mutant strategy can invade the population (22). The solution, which corresponds to a maximum in neighbor-modulated individual fitness, is equal to

(That the latter is a fitness maximum is verified by ∂²w/∂f² < 0 at f = f *.) As the number of group members becomes larger, f * rapidly converges to N(1 − r)/[N − r − rr′(N − 1)]. If groups are large and there are many competing groups, f* converges to just (1 − r)/(1 − rr′). If there are no competing groups (n = 1), f is just 1. [Note that in this mathematical model, f can be interpreted either as the proportion of energy that each individual invests in intracolony conflict or as the proportion of individuals that will devote all (versus none) of their energy to intracolony conflict. On the latter interpretation, the proportion of individuals devoting all their energy to within-colony cooperation, and none to personal reproduction, will be 1 − f*, and thus the reproductive skew will increase as f* decreases. However, we focus in this paper on the implications of the model for the average level of cooperation regardless of which skew-related interpretation is taken.]

As can be verified by checking the derivatives of f* with respect to each of the contained variables, the individual's fractional effort in selfish within-group competition increases as its group size n increases, as the number of competing groups N decreases, as within-group relatedness r decreases, and as the between-group relatedness r′ increases (Fig. 2). In other words, intragroup cooperation will increase as (i) the group size decreases, (ii) the number of competing groups increases, (iii) the within-group relatedness increases, and (iv) the between-group relatedness decreases (all other variables held constant in each of these analyses). These relationships are numerically presented in Fig. 2. We note that the model encompasses both intraspecific and interspecfiic competition; in interspecific competition, the value of the between-group relatedness is just r′ = 0.

The nested tug-of-war model can be generalized to encompass variable intensities of competition in the following way. We assumed that an individual investing, say, twice as much as another group member in the within-group tug-of-war will receive twice as much resource as will that other group member. But suppose an individual investing an amount h versus another who invests j gets h^w/j^w as much resource, where w measures the intensity of competition. If w = 0, the two individuals get the same amount of resource no matter how each invests. If w is infinite, then the individual investing even slightly less gets essentially no resource. Thus, to incorporate variable within-group competition intensity, we can modify Eq. 1 to become

and we can allow for variable between-group competition intensity by modifying Eq. 4 to become

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

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 groups, the individual is favored to invest virtually all of its effort in between-group competition, regardless of the relatedness among group members (i.e., f → 0 as w/z → 0).

In advanced eusocial colonies, f appears to be close to zero. In such advanced social organizations, the colony effectively becomes the target of selection, i.e., it is a coherent “extended phenotype” (23) of the genes within colony members. Selection therefore optimizes caste demography, patterns of division of labor (15), and communication systems at the colony level (9). For example, colonies that employ the most effective recruitment system to retrieve food, or that exhibit the most powerful colony defense against enemies and predators, will be able to raise the largest number of reproductive females and males every year and, thus, will have the greatest fitness within the population of colonies (24).

Thus, a striking characterization of f* is that it precisely measures a society's position along a “superorganism continuum.” At one extreme, f* = 1, group members invest all of their energy in within-group competition, and there is really no cooperative group at all. At the other extreme, f* = 0, group members invest all of their energy in within-group cooperation to outcompete other groups, and the society can be regarded as a “superorganism,” an analogy to a metazoan organism. For values in between these two extremes, the society can be viewed as having both selfish and superorganismal features.