But there were problems. Even though the haplodiploidy hypothesis is still associated with the study of evolved social behaviors, it has been out of favor with experts since 1976, when Robert Trivers and Hope Hare showed how males factor into relatedness. While haplodiploid females are more closely related to their sisters than to their offspring, they still share more genes with their offspring than with their brothers (r is ¼). The evolutionary burden of raising low-value brothers would therefore 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 the Hymenoptera — because they aren’t haplodiploid. Haplodiploidy couldn’t be the driving force underlying 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 the dominant 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 debate between the two sides has often been vitriolic, with each one calling the other “cultlike” for its unwillingness to budge.

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

Knowing When the Rules Apply

Hamilton’s rule was never meant to apply to eusocial insect colonies alone. It should describe all social organisms that act cooperatively, such as the ground squirrels that sound off to warn their peers of a nearby predator (at the risk of drawing the predator to themselves) and the scrub jays that devote themselves to raising the offspring of others. There are even some species, such as certain 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 subject of 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, another theory called multilevel selection (or group selection) expands that approach to apply to interactions within and between entire groups of organisms. Many biologists don’t think selection between groups can be strong enough in nature to promote adaptations. The orthodoxy in evolutionary biology is that selection acts mostly within groups, with between-group selection reserved only for very special cases.

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

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

The seeds of the dispute were planted in 2010 with the publication of a controversial paper in Nature. Its authors, Nowak, Corina Tarnita and E.O. Wilson, all at Harvard at the time, argued that inclusive fitness theory could not be applied to actual interactions that occur in the wild. According to the authors, it made too many assumptions, most problematically that the benefits and costs of altruism 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. The conflict gradually came to focus on Hamilton’s rule: While the Nature paper criticized the inaccuracies of a more specific version, the opposing scientists argued that a more general form of the equation would not have the same problems.

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

Nowak and others claim that the general version of the formula is a tautology that can’t be tested empirically. To them, Hamilton’s rule is essentially just a statistical truism about the relative evolutionary fitness of different groups that lacks explanatory value. “It’s not a statement about biology 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. “This formulation 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 costs and 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 and Wilson argued that natural selection favored the rise of eusociality among social insects because survival strategies that enabled the queen to live longer and lay more eggs were advantageous to small 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 kin selection and relatedness. According to Birch, it’s too much to expect that a three-variable equation can be a precise predictor of evolutionary dynamics. Rather, it should be understood as a way to organize scientists’ thinking about the causes of social evolution, enabling them to draw a distinction between direct and indirect fitness and know which follow-up questions to ask.