Pity people who become icons. Once they represent an important idea in the minds of others, they can't change their iconic status, even when they change their own minds.

Such was the fate of William D. Hamilton, the legendary founder of inclusive fitness theory, which was dubbed kin selection by John Maynard Smith (see T&R VIII). Hamilton became world famous for explaining how altruism can evolve according to the rule br - c >0, where b is the benefit that the altruist gives a recipient, c is the cost to the altruist, and r is the chance that the recipient shares the same altruistic gene through a common ancestor. At least that was the original interpretation of r; eventually, it morphed into something different, as we shall see.

Why was Hamilton's theory regarded as so important? After all, multilevel selection already provided a framework for studying altruism. Hamilton's theory was regarded as a breakthrough because it seemed to explain altruism without invoking group selection. That was the whole point of Maynard Smith's haystack model (see T&R VIII and IX), which claimed to show that group selection didn't work and that Hamilton's theory provided a viable alternative. Thanks to Hamilton, the perspective of Wynne-Edwards (see T&R III) and everything else associated with group selection could be rejected in favor of his elegant rule, which predicted that altruism should be doled out in direct proportion to genealogical relatedness.

Hamilton's rule also enabled altruism to be interpreted as a form of self-interest. After all, the altruist maximizes its own inclusive fitness by helping its genes in the bodies of others. No more foolish "for the good of the group" thinking! Inclusive fitness theory made evolution seem just like economics, in which everything can be explained as a form of utility maximization at the individual level.

With the benefit of hindsight, we can see that comparing the two theories is not so straightforward. Multilevel selection theory shows how altruism can evolve, despite being selectively disadvantageous within groups. Inclusive fitness theory shows how altruism can evolve but it isn't obvious from Hamilton's rule what happens within single groups. It's not as if groups are absent; social interactions always take place within groups and the coefficient of relatedness specifies how groups are formed in the case of interactions among relatives, as we saw with Athena's class exercise (see T&R XII). Hamilton's rule correctly predicts when altruism evolves in the total population, given the assumptions of the model, but if we want to know if it is an alternative to group selection, we need to figure out what goes on within single groups.

Hamilton himself didn't figure this out until he encountered another rule formulated by another theoretical biologist named George Price. The Price equation is not as famous as Hamilton's rule among the general public, but theoretical biologists regard it as a work of art. I won't print it here, because some readers are so afraid of math that a formula only slightly more complicated than Hamilton's rule might cause them to lose bladder control, but I will describe it in words. On one side of the equation, the term ΔP shows whether a given gene evolves in the total population. On the other side of the equation, two sets of terms show the contributions of within- and between-group selection. The Price equation is regarded as beautiful precisely because it so cleanly splits evolution into its components. There is a term that looks much like r in Hamilton's rule, but it does not stand for the probability of sharing a gene identical by descent. Instead, it stands for the importance of between-group selection relative to within-group selection.

When Hamilton examined his own theory through the lens of the Price equation, he saw that altruism is selectively disadvantageous within each group of relatives containing both types, making his theory a confirmation of group selection rather than an alternative to group selection. Only then did Hamilton realize what students can learn in an afternoon through the kin selection version of Athena's exercise (see T&R XII).

It is fascinating to read Hamilton's own account of his revelation, which he wrote in his collection of autobiographical essays. Here is how he describes his first encounter with the Price equation.

A manuscript did eventually come from him but what I found set out was not any sort of new derivation or correction of my 'kin selection' but rather a strange new formalism that was applicable to every kind of natural selection...His voice was squeaky and condescending, rather guarded on the phone...He spoke of his formula as "surprising for me too--quite a miracle"..."Have you seen how my formula works for group selection?" I told him, of course, no, and may have added something like: "So you actually believe in that do you?" Up to this contact with Price, and indeed for some time after, I had regarded group selection as so ill-defined, so woolly in the uses made by its proponents, and so generally powerless against selection at the individual and genic levels, that the idea might as well be omitted from the toolkit of a working evolutionist.

This passage shows with crystal clarity how thoroughly group selection had been rejected by the late 1960s, by Hamilton along with everyone else. Now here is how he describes his reaction to the Price equation, shortly before Price, a tragic figure, committed suicide.

I am pleased to say that, amidst all else that I ought to have done and did not do, some months before he died I was on the phone telling him enthusiastically that through a "group-level" extension of his formula I now had a far better understanding of group selection acting at one level or at many than I had ever had before.

Three aspects of Hamilton's account are worth noting. First, why did both Price and Hamilton find it so easy to recognize group selection in the Price equation? It is extremely abstract and can be used to describe many different kinds of groups, but neither man fretted over details. The reason is that in all cases, the Price equation reveals the selective disadvantage of altruism within groups, which is the essence of the group selection controversy. As US President Bill Clinton might have put it, "It's the Original Problem, stupid!"

Second, why did Hamilton fail to see group selection in his original formulation? Precisely because it did not showcase what happens at a local scale on its way toward showing what evolves in the total population. You can't see the need for group selection unless you note a discrepancy between what is favored locally and what evolves in the total population.

Third, neither Price nor Hamilton were prejudiced against group selection. It was not Hamilton's goal to explain the evolution of altruism without invoking group selection. His goal was to explain the evolution of altruism and he was happy to acknowledge group selection's essential role as soon as it was revealed to him through the Price equation.

Let's pause to savor this moment in the history of evolutionary thought. Group selection had been thoroughly rejected in favor of inclusive fitness theory, which seemed to explain altruism as a form of self-interest. Then it emerged that inclusive fitness theory is not an alternative to group selection after all; the role of group selection was merely obscured by the way it was formulated. Hamilton, who had become an icon as the originator of inclusive fitness theory, happily changes his mind. What happens next?

Here's what should have happened. The whole field should have revisited the consensus formed only a few years earlier, concluding that group selection can be important after all and that there is no alternative explanation for the evolution of altruism, in contrast to what inclusive fitness theory seemed to provide.

Here's what did happen. Theoretical biologists began to take notice of the Price equation, while the rest of the field continued to treat group selection as a heresy and inclusive fitness theory as a wondrous alternative. Poor Hamilton had become an icon and it didn't matter that the person had changed his mind.

I recently had the opportunity to demonstrate this sad state of affairs in an e-mail dialogue that I organized among theoretical biologists titled "If the theorists can't agree...", meaning that if those who understand the models in intimate detail can't achieve a new consensus, then there is little hope for everyone else interested in evolutionary theory. Steven Frank, a distinguished theorist and authority on the Price equation, stated toward the end of the dialogue that:

[S]tarting with Hamilton and Price... we have the only framework that really exists. The 1960s don't count, because almost no one even cited Hamilton's work in that decade.

Steve was referring to his fellow theorists. I promptly did a citation analysis for all scientific publications, showing that Hamilton's first formulation (represented by his 1964 article) and second formulation (represented by his 1975 article) are cited in a 15:1 ratio with no trend whatsoever for the 1975 paper to become more frequently cited over the decades. And this is the scientific literature!

When I give academic seminars on this subject, I ask my colleagues in the audience to predict the result of my citation analysis before presenting the answer. Usually they guess it right, noting that most people who cite the 1964 paper haven't read either one. That gets a laugh, but what does it really say about the study of evolution as a scientific discipline? It means that science as practiced is often a far cry from science as idealized. Certitudes are passed unquestioningly from teachers to students, especially when they confirm cultural biases, in a way little different than the transmission of religious dogmas.

Even worse, it turns out that the theorists can't agree. Core differences remain among the experts, even after they agree on the details of any particular model. The group selection controversy is like a battle that moves among battlegrounds. The claims that caused group selection to be rejected in the first place are no longer defended, but other claims are defended just as fiercely.