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The Elusive Calculus of Insects’ Altruism and KinSelectionHow the ultra-cooperative behavior of ants, bees and other social insects could have evolvedcontinues to challenge formal analysis. But a new theory that includes hedging bets against nature’sunpredictability may help to change the math and shift the debate.

By Jordana Cepelewicz

bug eye

These ants are working together to transport their colony’s pupae from their original nest to a new location.(Immature ants can sometimes be bigger than the workers they will eventually become.) Such cooperative acts,even at the price of the workers’ individual fertility, are a hallmark of ant behavior.

In 1964, the evolutionary biologist William D. Hamilton seemingly explained one of the greatestparadoxes in biology with a simple mathematical equation. Even Charles Darwin had called the

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problem his “one special difficulty” a century earlier in On the Origin of Species, writing that it madehim doubt his own theory.

The paradox in question is the altruistic behavior exhibited most famously by social insects. Ants,termites, and some bees and wasps live in highly organized colonies in which most individuals aresterile or forgo reproduction, instead serving the select few who do lay eggs. Yet such behaviorseemed to clearly violate the concept of natural selection and survival of the fittest, if “fittest” meansthe individual with the greatest reproductive success. The insects’ compulsory altruism — a form ofextreme social behavior called eusociality — made little sense.

But that changed when Hamilton came up with his equation and formalized the theory known as kinselection: the idea that producing fewer offspring of one’s own might be worth it if cooperationincreases the offspring of relatives, who share some of one’s genes. (The biochemist J.B.S. Haldane,who pioneered this theory in the 1930s, is often credited with quipping, “I would gladly lay down mylife for two brothers or eight cousins.”) Hamilton’s elegant formulation of that insight balanced thecosts (c) that one individual incurs by helping another against the benefits (b) that the otherreceives, weighted by the relatedness of the two (r). Known as Hamilton’s rule, it states that when rb> c, a gene responsible for promoting a social behavior will spread. The rule became thecornerstone of “inclusive fitness theory,” in which fitness can be calculated as a metric of geneticsuccess based on measures of relatedness.

Little did Hamilton know that his rule would also become the center of a volatile debate amongtheorists studying social behavior.

When Hamilton presented his rule, he demonstrated its cogency by showing that it predicted thebehavior of the ants, bees and wasps of the Hymenoptera order, which were primed for eusocialityby their strange genetics. The Hymenoptera have an unusual “haplodiploid” system for determiningthe sex of individuals: Unfertilized eggs become males, and fertilized eggs become females. Oneconsequence of this arrangement is that full sisters on average share all their father’s genes and halfof their mother’s. The r value between sisters is therefore ¾, while the r value of offspring to theirmother is only ½. Hamilton pointed out that it made evolutionary sense, then, for a worker ant topass on her genes by helping her mother produce more sisters, rather than by reproducing herself.

The Hymenoptera stood for years as the textbook example of kin selection’s potency, and manybiologists got on board with it.

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Courtesy of Patrick Kennedy

Wasps nesting on a palm frond in Panama raise the colony’s offspring collectively.

But there were problems. Even though the haplodiploidy hypothesis is still associated with the studyof evolved social behaviors, it has been out of favor with experts since 1976, when Robert Triversand Hope Hare showed how males factor into relatedness. While haplodiploid females are moreclosely related to their sisters than to their offspring, they still share more genes with their offspringthan with their brothers (r is ¼). The evolutionary burden of raising low-value brothers wouldtherefore offset the advantages of rearing high-value sisters.

The theory had an even worse problem when it came to termites and other social species outside theHymenoptera — because they aren’t haplodiploid. Haplodiploidy couldn’t be the driving forceunderlying the evolution of those insects’ eusociality.

The hypothesis’s fall from grace put the first crack in what has become a giant rift in scientists’thinking about inclusive fitness theory and Hamilton’s rule. Because kin selection is still thedominant theory in the field, many biologists continue to base their work on its ideas. Others,however, argue for methods that are not informed by that conceptual framework at all. The debatebetween the two sides has often been vitriolic, with each one calling the other “cultlike” for itsunwillingness to budge.

One of the latest contributions to research in this area, published last month in Nature, offers anovel approach that takes into consideration the effects of nature’s fundamental unpredictability onevolutionary strategies. It also addresses some of the issues at the root of the disagreement amongevolution theorists — a disagreement that’s morphed greatly since Hamilton first proposed hisformula.

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Knowing When the Rules ApplyHamilton’s rule was never meant to apply to eusocial insect colonies alone. It should describe allsocial organisms that act cooperatively, such as the ground squirrels that sound off to warn theirpeers of a nearby predator (at the risk of drawing the predator to themselves) and the scrub jaysthat devote themselves to raising the offspring of others. There are even some species, such ascertain bees, that are “facultatively social,” meaning they only sometimes engage in social behavior,often in response to specific ecological or environmental conditions, and otherwise stay solitary.

How well Hamilton’s rule can account for all these different forms of altruism has been the subjectof a debate that can be traced back to the 1960s, when the fight revolved around levels of selection.Hamilton’s rule favors cooperation through the relatedness of individual kin. In contrast, anothertheory called multilevel selection (or group selection) expands that approach to apply to interactionswithin and between entire groups of organisms. Many biologists don’t think selection betweengroups can be strong enough in nature to promote adaptations. The orthodoxy in evolutionarybiology is that selection acts mostly within groups, with between-group selection reserved only forvery special cases.

In recent years, however, several groups of researchers have demonstrated that kin selection andmultilevel selection can be mathematically equivalent: The two concepts merely represent differentways of breaking down the correlation between heritable traits and fitness into “bite-sizedcomponents,” said Andrew Gardner, a biologist at the University of St. Andrews in Scotland. “For kinselection, that’s direct versus indirect benefits. For multilevel selection, it’s within groups versusbetween groups.”

Those developments might suggest that inclusive fitness theory is on a roll. But all is not well with itas an explanation for altruism, or even for eusociality, according to critics like Martin Nowak, aprofessor of biology and mathematics at Harvard University. Nowak doesn’t just disagree aboutwhether kin selection and multilevel selection are equivalent; he says that the broad mathematicalstrokes of using Hamilton’s rule to judge fitness are misleading.

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Sharona Jacobs Photography

Martin Nowak, a professor of biology and mathematics at Harvard University, has been a vocal opponent of bothinclusive fitness theory and the formulation of Hamilton’s rule most commonly used today.

The seeds of the dispute were planted in 2010 with the publication of a controversial paper inNature. Its authors, Nowak, Corina Tarnita and E.O. Wilson, all at Harvard at the time, argued thatinclusive fitness theory could not be applied to actual interactions that occur in the wild. Accordingto the authors, it made too many assumptions, most problematically that the benefits and costs ofaltruism were additive and could be modeled linearly. Hamilton’s rule couldn’t predict the outcome,for instance, if two or more helpers needed to cooperate to confer benefits on an individual.

More than 100 biologists fiercely defended inclusive fitness theory in response to the paper. Theconflict gradually came to focus on Hamilton’s rule: While the Nature paper criticized theinaccuracies of a more specific version, the opposing scientists argued that a more general form ofthe equation would not have the same problems.

Since then, with only the more general version of Hamilton’s rule under consideration, the battlelines of the debate have shifted further. Although “to some extent, they don’t disagree as much asthey think they do,” said Jonathan Birch, a philosopher specializing in social evolution and thebiological sciences at the London School of Economics and Political Science. When biologists debateHamilton’s rule today, it’s largely over what they think Hamilton’s rule can tell them, and when touse which models.

Nowak and others claim that the general version of the formula is a tautology that can’t be testedempirically. To them, Hamilton’s rule is essentially just a statistical truism about the relative

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evolutionary fitness of different groups that lacks explanatory value. “It’s not a statement aboutbiology or natural selection,” Nowak said. “It’s just about statistics, a relationship in mathematics.Like saying 2 plus 2 is equivalent to 4.”

Benjamin Allen, an assistant professor of mathematics at Emmanuel College in Boston, agreed. “Thisformulation of the rule can only rationalize observations after the fact,” he said. “It can’t predict.There’s no way to see how one observation can systematically lead to the next.”

He and Nowak instead prefer to use models based on population structure, which are often detailed,causal and case-specific. Rather than putting relatedness front and center, they focus on the costsand benefits of the cooperative acts and ask specific questions about factors such as mutations,inheritance and interactions. In the case of the 2010 Nature paper, for example, Nowak, Tarnita andWilson argued that natural selection favored the rise of eusociality among social insects becausesurvival strategies that enabled the queen to live longer and lay more eggs were advantageous tosmall colonies.

But others think the simplifications and generalizations of Hamilton’s rule can still be informative.The framework of inclusive fitness theory provides a good way to envision the role played by kinselection and relatedness. According to Birch, it’s too much to expect that a three-variable equationcan be a precise predictor of evolutionary dynamics. Rather, it should be understood as a way toorganize scientists’ thinking about the causes of social evolution, enabling them to draw a distinctionbetween direct and indirect fitness and know which follow-up questions to ask.

Usman Bashir

When conditions are harsh, the social amoebas of the species Dictyostelium discoideum mass together. Some ofthem then sacrifice their own reproductive futures by forming stalks that can elevate the others while they releasespores.

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He cites Dictyostelium discoideum, a species of social amoebas, by way of example. When theirenvironment turns inhospitable, the single-celled animals aggregate and reproduce by collectivelyreleasing hardy spores into the air from an elevated stalk. But in the process, 20 percent of theamoebas sacrifice themselves to become that stalk instead of making spores, purely to theadvantage of the other 80 percent.

To understand the evolutionary logic of this behavior, Birch said, Hamilton’s rule is essential as astarting point for examining how related the stalk and body cells are. “Hamilton’s rule tellsresearchers on the ground where to look first,” he said. “Then they can move beyond it andconstruct a more precise model that includes ecological parameters relevant to the particular case.”

But a new paper may have taken a step toward bridging the gap between the general, relatedness-centered approach and the ecological one, with its focus on costs and benefits.

How Uncertainty Favors AltruismResearchers have noticed counterintuitive examples of cooperation in nature that don’t seem to fitHamilton’s rule: helpers coming to the aid of individuals that aren’t close relations, for example,instead of having their own offspring. Sometimes the altruistic behavior comes across as incrediblywasteful and doesn’t even seem to improve the survival of their siblings’ offspring all that much, if atall. In one bee species described as facultatively social (meaning that the individuals can choosewhether or not to live in colonies), researchers found that the lifetime reproductive success ofsolitary nesters was almost double that of social ones.

Many of these altruistic situations seem to occur in unpredictable or hostile environments. So a teamof researchers, led by Seirian Sumner, a behavioral ecologist at University College London, andPatrick Kennedy, a graduate student at the University of Bristol, sought to extend Hamilton’s rule toaccount for these exceptions by interweaving it with a concept known as bet hedging. Bet hedging isa risk management strategy that hadn’t previously been formally linked to mathematical models ofhelping behavior.

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Pieter Botha; courtesy of Patrick Kennedy

Patrick Kennedy, a graduate student at the University of Bristol, and his colleagues recently published a paper thatunpacked the mathematics describing costs and benefits within Hamilton’s rule. Here he is pictured at a field site inPanama, where he studied cooperation among tropical wasps for his doctorate.

Sumner and Kennedy’s key insight was that when scientists use Hamilton’s rule, they usually basetheir fitness calculations simply on the mean number of offspring that individuals would produce, asmeasured in the wild. But that model ignores the fact that random variations in the environmentmake the actual numbers of offspring volatile. When conditions fluctuate dramatically — if food isscarce one year and abundant the next, or if brood parasites sweep through an entire population orthe weather oscillates between extremes — the benefits of cooperation vary, too. A better yardstickfor judging fitness might therefore be the variance in the numbers of offspring produced.

In other words, it can be more important for an individual’s reproductive success to be consistent onaverage, rather than simply higher than that of others. In an uncertain environment, the bet-hedgingvalue of helping others starts to look much more appealing as a strategy: It improves the odds thatsome shared genes will survive even if an individual’s own lineage dies out. Allocating some energyto helping others, even at the expense of further reproductive success, then works as an insurancepolicy.

Sumner, Kennedy and their colleagues found that, all by itself, uncertainty in the environment couldlower the threshold at which individuals need to begin cooperating. “The genes that win out in thelong run might not lead to the most number of offspring on average,” Kennedy said, “but in a

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reduced variance in that number.”

Sheng-Feng Shen, an associate research fellow at Academia Sinica in Taiwan, believes that Sumnerand Kennedy’s results will help future inclusive fitness models resemble models based on populationdynamics. “This paper shows perfectly why the debate between the two exists,” he said: Sumner andKennedy have brought Hamilton’s rule more into line with the biological and ecologicalconsiderations that critics of inclusive fitness theory have called for.

Empirical field work will be needed to test which environments most favor cooperative behavior, andto what extent it’s driven by environmental unpredictability. But Shen also says the theory needs tobe expanded further. For example, the model as it currently stands assumes that generations do notoverlap. That assumption works for microbial communities, biofilms and similar organisms, but itneeds to be honed to describe vertebrate cooperation accurately.

The new model could even be applied to research on kin selection in plants. Susan Dudley, anevolutionary ecologist at McMaster University in Canada, pointed to the Great Lakes sea rocket, aplant that produces seeds with different dispersal mechanisms: Some of its offspring end up alone,but others settle into groups that may consist of relatives or unrelated plants. “It would be a nicesystem [in which] to think about bet hedging and kin selection together,” she said.

And while this extension of Hamilton’s rule focuses on what might drive organisms toward socialbehavior, it might also provide further insights into how the much more stringent eusocial behaviorof bees, ants and other insects emerged.

The Importance of MonogamyAlthough the haplodiploidy hypothesis was debunked, researchers have continued to draw onrelatedness and Hamilton’s rule as explanations for eusociality among the social insects. Today, thedominant theory, formulated by Jacobus Boomsma, an evolutionary biologist at the University ofCopenhagen, holds that it was strict lifetime female monogamy that actually caused eusociality tooccur. In ants, bees and wasps, for instance, the colony’s queen mates with just one male: She isable to store sperm from one “wedding flight” for use throughout her reproductive life. Termites,which can’t store sperm, keep a king alongside their colony’s queen instead.

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Javier Ábalos Alvarez

Termites evolved eusociality 50 million years before ants, bees and wasps did. Recent research shows that theirsocial behaviors may have developed along similar pathways despite major differences between their biology andthat of other social insects.

Because all the members of a colony or hive have the same parents, individuals on average share asmany genes with their siblings as they would with any offspring of their own: In Hamiltonian terms,r has a mean value of ½ in both cases (for haplodiploid organisms, this remains true, since the rvalues of ¾ and ¼ for sisters and brothers, respectively, average out to ½). Consequently, even theslightest benefit from acting altruistically is enough to tilt the scales toward social evolution andcastes that rear siblings instead of offspring. “Only strict lifetime commitment between parents ispredicted to have ever bred unconditional commitment to reproductive altruism,” Boomsma wrote inan email.

So far, this monogamy theory has been supported by research into the evolutionary histories ofeusocial organisms: The ancestors of modern eusocial ants, wasps and bees — as well as thepredecessors of eusocial snapping shrimp that dwell in coral reefs off the shores of Belize — weremonogamous.

But even so, “there are a lot of subtleties within how those dominance hierarchies form and howthose societies maintain stability,” said Sandra Rehan, a biologist at the University of NewHampshire. “It’s much more nuanced than just saying ‘something is social,’ or ‘something iseusocial.’”

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Perhaps relatedness alone isn’t always enough to explain eusociality. The monogamy hypothesispredicts the conditions needed to turn simple cooperative behavior into eusociality and hierarchiesof individuals that never mate. But what makes certain species ripe for that irreversible transition?This is where Kennedy’s work might help advance understanding. Kennedy thinks it would beenlightening to examine how ecological volatility might affect the costs and benefits involved in theevolution of eusociality. It could be that random changes in the environment push primitiveeusociality; he thinks it might be possible to find out by examining those facultatively social speciesthat still have a choice about whether to cooperate. “Not all monogamous [ants, bees and wasps]have evolved eusociality,” Gardner said. “These kinds of volatility considerations could in principleexplain why.”

The Chemistry of Social CohesionHamilton’s rule still plays a strong and expanding role in guiding research on social and eusocialpopulations, even if it does have its limitations. But it can’t stand alone. Just as Shen discussedintegrating aspects of population dynamics into the framework of inclusive fitness, other directionsof research add to the story.

Such work does not probe just the origin of eusociality; it also explores the genomic events thatcemented eusociality’s details after its foundation was laid. A paper in Nature Ecology & Evolutionin February, for example, analyzed the genomes of termites and cockroaches, the termites’ non-eusocial ancestor. It found that when cockroaches evolved, the number of genes they carried for aspecific class of proteins called gustatory receptors hugely expanded. Then, when the termitesevolved, they gave these receptors new jobs. Previously just a tool for perceiving chemical cues inthe environment, the receptors gained more specific functions for sensing signals associated withtermite activities, such as feeding, laying eggs or aggressive behavior.

Ants, bees and wasps evolved eusociality 50 million years after the termites, but previous researchshows that they did something very similar with a different class of proteins called odorantreceptors. “Social evolution has evolved independently twice in the insects, and it went down a verysimilar path,” said Erich Bornberg-Bauer, a molecular biologist at the University of Münster inGermany and one of the study’s authors. That similarity shows how much social behavior depends onchemical recognition, at least in insects.

At the moment, this kind of work on the nuts and bolts of what enables social behavior remainsseparate from the research by Kennedy and others unpacking the evolutionary pressures thattriggered it. For instance, it remains unclear whether the termites’ chemosensory ability evolvedbecause it was useful specifically for helping relatives. “That’s not something we can determine fromsimple genomic comparisons,” said Xavier Bellés, a biologist at the Institute of Evolutionary Biologyin Barcelona and another author of the paper. He noted that the cockroach genome they analyzedcould produce twice as many proteins as the genomes of the termites they sequenced, even thoughtermites are socially far more complex.

An enormous obstacle to scientists’ understanding of social evolution revolves around how to unitethose insights. By connecting larger evolutionary forces to the smaller forces that shape changes inthe genome — a goal still a long way off — researchers might finally solve the mystery of eusociality.For now, honing a more unified mathematical description seems like a good first step.