Abstract: From a theoretical perspective, individuals are expected to sacrifice their welfare only when the benefits outweigh the costs. In nature, however, the costs of altruism and spite can be extreme, as in cases of irreversible sterility and self-destructive weaponry. Here we show that “extraordinary” self-sacrifice—in which actors pay costs that exceed the benefits they give or the costs they impose on recipients—can evolve in structured populations, where social actions bring secondary benefits to neighboring kin. When given information about dispersal, sedentary actors evolve extraordinary altruism towards dispersing kin. Likewise, when given information about dispersal and kinship, sedentary actors evolve extraordinary spite towards sedentary nonkin. Our results can thus be summed up by a simple rule: extraordinary self-sacrifice evolves when the actor’s neighbors are close kin and the recipient’s neighbors are not.
We find that individuals can evolve to value others’ fitness more than their own. Specifically, selection favors extraordinary altruism when sedentary actors interact with dispersing kin (Fig. 3f,l), and it favors extraordinary spite when sedentary actors interact with sedentary nonkin (Fig. 3o). Because extraordinary self-sacrifice entails C>|B|, the sum of the effects on the actor and recipient is always negative (B−C<0), leading overall to a secondary decrease in competition that can benefit kin. Under limited dispersal, the actor’s neighboring kin benefit secondarily when the actor remains on the natal island. Likewise, the actor’s neighboring kin benefit secondarily from spite when the recipient remains on the actor’s natal island. Finally, in the case of altruism, it is nonkin that pay the price when the recipient arrives on their island. Taken together, we arrive at a simple rule: extraordinary self-sacrifice evolves when an actor’s neighbors are close kin and the recipient’s neighbors are not.
The effects of dispersal and kinship among actors, recipients, and neighbors also become apparent when we consider the conditions of our model that fail to favor the evolution of extraordinary self-sacrifice, even when dispersal is limited (d→0) and neighborhood consanguinity is high (q→1). First, extraordinary self-sacrifice in general does not evolve with a dispersing actor (Fig. 3b,d,e,h–k), because, by dispersing to a new island, the actor gives the secondary benefit of its sacrifice (in the form of reduced competition) to neighbors who are not kin and who therefore bear rival alleles. Second, extraordinary altruism does not evolve with a recipient that is not kin (Fig. 3i,k,m), because this provides a primary benefit to a recipient bearing a rival allele. Third, extraordinary altruism does not evolve with a sedentary recipient (Fig. 3a,c,e,g,j,k,n), because, by remaining on the natal island, the recipient imposes a secondary cost (in the form of increased competition) on neighbors who are the actor’s kin and who therefore bear copies of the focal allele. Fourth, extraordinary spite does not evolve with a recipient that is likely or known to be kin (Fig. 3a–e,g,h,j,n), because this imposes a primary cost on a recipient bearing a copy of the focal allele. Finally, extraordinary spite does not evolve with a dispersing recipient (Fig. 3d,h,i,m), for the same reason that it does not evolve with a dispersing actor: because, by dispersing to a new island, the recipient gives the secondary benefit of the spiteful action (in the form of reduced competition) to neighbors who are not the actor’s kin and who therefore bear rival alleles.
We are aware of two other models that report conditions under which extraordinary self-sacrifice can evolve. The first, by Krupp and Taylor23, was briefly discussed above. It also used an inclusive fitness approach set in an island structure, wherein actors could use a signal matching mechanism to distinguish between “native” individuals, whose parents were born on the focal island, and “migrant” individuals, whose parents were born elsewhere. Although actors had no information about dispersal status in their model, dispersal was generally assumed to be rare (d→0), causing native actors to be close kin with their neighbors and causing both actors and recipients to be sedentary. Given the close parallels between these conditions and our own (represented in Fig. 3o), it is no surprise that they found that extraordinary spite can evolve among native actors interacting with migrant recipients. Our model extends their analysis, separating the effects of actor and recipient dispersal and making them explicit.
The second model, by McAvoy et al.33, used a game theoretic approach set in a heterogeneous social network of N individuals, each of whom plays either a “producer” strategy that pays a cost to give a benefit or a “non-producer” strategy that pays no cost and gives no benefit. (Because their approach differs significantly from our own, we have changed their notation and description to better correspond to ours.) One set of games entailed proportional benefits but fixed costs (“pf goods”), wherein a new benefit is given to each connected recipient without additional cost to the actor. Thus, if actor i is connnected to ni recipients, then in games with pf goods, i pays ci>0 only once to give a benefit bi>0 to each of the ni recipients. McAvoy et al. found that ci>bi can evolve in games with pf goods when there are more connections among individuals in the network than there are individuals themselves. However, this implies that C<B, because the net benefit B=bini grows with the number of connections whereas the net cost C=ci does not. Consequently, these results do not meet the definition of extraordinary self-sacrifice.
Another set of games in the McAvoy et al. model entailed fixed benefits and fixed costs (“ff goods”), wherein the benefit is divided equally among all connected recipients. Thus, in games with ff goods, the actor pays ci only once to give a benefit bi/ni to each of the ni recipients. McAvoy et al. found that ci>bi can evolve in games with ff goods within “rich-club” networks consisting of a central group of m individuals who are connected to each other as well as to a peripheral group of l individuals who are connected only to the members of the central group. Under these circumstances, the producer strategy works well for the central group but poorly for the peripheral group; nevertheless, the peripheral group evolves to play the producer strategy. We suspect, however, that this exploitative state of affairs is maintained by a peculiarity of the updating mechanisms of the model, which require individuals to imitate the strategy of better-performing connections, even if it is to their detriment. By playing the producer strategy, the central group causes the peripheral group to play the producer strategy as well: central producers have higher payoffs than peripheral non-producers, so peripheral non-producers must update their strategy to produce—despite the fact that it leaves them worse off—because they are connected strictly to better-performing central producers. As the authors show, the central group benefits greatly from this arrangement, particularly as the size of the peripheral group increases, while the peripheral group suffers losses. On the one hand, this implies that C<B for the central group, because the initial cost ci of the producer strategy to central individuals is more than repaid by the benefits bil/m it receives in return for causing peripheral individuals to produce as well; that is, the net cost C=ci−bil/m to a central producer is negative, meaning that it is actually a benefit. On the other hand, this also implies that C>B for the peripheral group, because the net cost to a peripheral producer is C=ci and the net benefit it gives is B=bi. Thus, production at the periphery would seem to meet the definition of extraordinary self-sacrifice. We wonder, then, if selection would still favor extraordinary self-sacrifice under these conditions if individuals were not powerless to play the strategy that worked best for them, irrespective of the strategy played by their connections.
Hamilton4 initially proposed that limited dispersal (in the form of “viscous” populations) would foster the evolution of altruism, because it would give kin the opportunity to interact. Conversely, he suggested that spite would most likely evolve in “dwindling panmictic species”5. With the benefit of hindsight, however, we can see that both claims are in need of refinement. From an inclusive fitness perspective, a cost to the actor must be compensated by a benefit to kin, being either the recipient or a neighbor. But limited dispersal also puts these parties in competition with one another, turning altruistic benefits to the former into costs to the latter9,11,13,34. As we find here, however, the dilemma of limited dispersal is resolved if the recipient—but not the actor or neighboring kin—can be expected to disperse after the interaction, providing a primary benefit to a consanguineous recipient and imposing a secondary cost on nonkin elsewhere (much as predicted by [9]). Indeed, the high degree of kinship that limited dispersal brings to a neighborhood is essential to the evolution of extraordinary altruism.
Likewise, spite profits not from panmixia but from population structure, because the primary costs to both the actor and the recipient are returned as secondary benefits to the actor’s neighboring kin. However, since limited dispersal increases the chances that individuals interact with kin, actors cannot simply be spiteful to anyone3. Rather, actors should discriminate along genealogical lines and, although they may not be strictly necessary, kin recognition mechanisms can be helpful in this regard.
Our model makes use of learned kin recognition systems, which are widespread in nature35,36,37,38,39. To the extent that kin recognition can operate via other routes, however, our results are not limited to organisms capable of cognition. While there are known theoretical obstacles to the evolution of genetic kin recognition40,41, for example, systems such as this have been identified and characterized in several species (e.g.42,43,44). Indeed, allorecognition is common, predates multicellularity, and has independently evolved numerous times45.
Notably, our study departs from previous theoretical work on the evolution of self-sacrifice under dispersal and kinship, largely because we ask not only whether individuals might discriminate as a function of kinship but also as a function of both actor and recipient dispersal (see also [22]). Plausibly, sedentary and dispersing types can evolve different degrees of self-interest, such that sedentary individuals generally give more than their dispersing counterparts. This should occur when the actions of sedentary individuals are systematically “funnelled” towards dispersing individuals as a function of organismal physiology or species ecology. In some cases, actors may even cause recipients to develop a dispersing phenotype—for example, by influencing caste determination46.
However, our findings also suggest the possibility that, alongside mechanisms of kin recognition, species may have evolved adaptations to estimate the spatial scale of competition47,48,49, such as mechanisms of dispersal recognition. That is, organisms might identify cues of their probability of future competition with social partners or neighboring kin and discriminate accordingly. Certainly, the eusocial insects already provide ample evidence that sedentary and dispersing individuals behave differently. For example, workers of most such species act altruistically (or, in some cases, spitefully) and are sedentary whereas reproductives act selfishly and disperse to found new colonies19. Yet, it is unclear whether some mechanism of competition estimation is the cause of such differences. If so, we might expect that individuals can predict the probability of partner dispersal by cues of future dispersal status, such as by chemical signal (e.g.50), location within the colony, presence of wings, or body size.
Though this is a knottier problem than we can address here, our results also suggest that aspects of multicellular and colony evolution, such as the division of labor between cell lines and self/nonself discrimination, are a consequence of dispersal patterns and their attendant secondary effects. Sedentary cells may sacrifice themselves to assist dispersing cells in reproducing elsewhere, as can be seen in the social amoeba Dictyostelium discoideum which, when starved, aggregates with kin to form a sterile stalk and a reproductive fruiting body51. Interestingly, individuals that starve earlier are more likely than those that starve later to become spores52. This presents the possibility that signals produced by early starvers to aggregate are attended to because they predict that these same individuals will disperse and compete elsewhere—signals that may be kept honest by virtue of the fact that starvation itself imposes pressure to disperse to find new food sources.
Moreover, sedentary individuals may serve as soldiers or enforcers, ensuring the integrity of the body or colony. For instance, the ascidian Botryllus schlosseri operates under limited dispersal, fusing with kin to create a colony with a shared vasculature53. However, when individuals encounter nonkin, they produce an immune response that causes damage at the interaction site42,54 which, arguably, is a spiteful response to a foreign competitor. Likewise, clones of the polyembryonic parasitoid wasp Copidosoma floridanum develop into two distinct castes: soldiers and reproductives. Soldiers grow quickly, spitefully attacking unrelated competitors with specialized mandibles and dying in the host body, whereas reproductives grow more slowly, eventually dispersing to parasitize new hosts55,56.
Of course, extraordinary self-sacrifice may evolve more or less easily in the wild than our model suggests. For instance, beyond the assumptions that actors use information about kinship and dispersal, we also assumed diminishing returns of the actor’s behavior, which can make the evolution of extraordinary self-sacrifice more difficult than might some other kinds of cost-benefit relationship. While there are many cases of social systems with diminishing returns32, it is possible that some interactions yield linear or even accelerating returns, improving the conditions for extraordinary self-sacrifice. Likewise, whether social goods entail proportional or fixed costs and benefits33 may also affect the ease with which extraordinary self-sacrifice evolves.
Even if each of the assumptions made here is met, other factors (such as sexual reproduction) may reduce consanguinity within the neighborhood, working against the evolution of extraordinary self-sacrifice. More generally, extraordinary self-sacrifice may cause significant but rare evolutionary events. This is because the conditions required to support it are themselves likely to be rare, as evidenced by the many scenarios of our model (represented in Fig. 3a–e,g–k,m,n) in which extraordinary self-sacrifice is not evolutionarily stable. Thus, while our model has been productive in demonstrating when and where extraordinary self-sacrifice might arise, further work establishing its prevalence, both theoretical and empirical, is certainly needed. In particular, complementary approaches, such as direct fitness and evolutionary game theoretic methods, may reveal further insights and applications.
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