Truth and Reconciliation for Group Selection XIII: Hamilton Speaks

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 controversy over 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 even 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 1960's, 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 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.

To be continued.

Comments

[William Tatum]

Dude i've just finished reading several of your posts and you totally blow my mind. Honestly i just read a post of yours from 2007 about stealth religions and i had seriously never thought of it that way and i appreciate that.

As per this post I had never heard of Hamilton or Price though i will be looking into them in the future, im really into the idea of evolutionary biology, psychology, sociology etc. I look forward to reading more of your posts.

On a side note some of us new athiests don't worship at the altars of Dawkins and Hitchens, though the idea behind Memetics really gets me going.

[royniles]

Nice commentary here from Dan Agin. And again on the subject of mathematics, your comment about such requires the inference that it was a necessary element in reaching the truth, or at least accuracy, of your hypotheses. And correct me if I'm mistaken, but you appear to be using mathematical induction as the method of testing these hypotheses. But I would argue the best that can be done with that method is to demonstrate the results of the exercise have a certain consistency with the assumptions, but are not in any sense a proof of their accuracy.
Mathematical induction is not to be confused with the inductive reasoning by which we ordinarily produce these hypotheses. Your assumptions have not been proved right - you have simply been demonstrating they have passed the first test of consistency. Your modeling has not been constructed to test the assumptions themselves against possibilities of there being at least equally valid counter-as­sumptions.

[riemannzeta]

It is also striking how similar the relationship between mean field theory models of dynamics and the Hamilton equation seem to have in common. One has to assume that fluctuations are small around equilibrium and treat local dynamics as representative of the whole by symmetry arguments in order to get exact solutions, for example, to the Ising model:

http://en.wikipedia.org/wiki/Mean_field_theory

In general (as Price realized) if the fluctuations (i.e., variations) are larger the symmetries may be broken and the dynamcis of the system split into a variety of local symmetries, the exception being for certain fixed points associated with zero temperature, infinite temperature, and critical temperature.

[Dan Agin - Huffpost Blogger]

Do you really think the Hamiltonian of theoretical physics has anything to do with Hamilton's equation in evolutionary biology? Can you spell this out, please.? Certainly the two Hamilton's are not the same, one a 19th century mathematical physicist and the other a 20th century biologist.

[riemannzeta]

Not the Hamiltonian per se, but the approximation that permits you to solve the macroscopic dynamics from the Hamiltonian.

In the 1D Ising Model, one has to assume that the dynamics at each point in the lattice are symmetrical throughout the lattice -- i.e., that a mean field approximation applies -- in order to obtain an exact solution. In general, the dynamics are not the same at each point in the lattice. The broken symmetries, in higher dimensions, result in different local dynamical structure.

I don't know where your background is, so I don't know if I'm getting through. I do know that Bar-Yam has made a similar observation, although I can no longer remember in what context I saw it.

[Dan Agin - Huffpost Blogger]

To riemannzeta:

I'm sorry, but I disagree completely with your post below and above. The Hamiltonian in physics has absolutely nothing to do with Hamilton's equation in evolutionary biology. The two Hamiltons are different people and the two equations have no relation to each other apart from the name "Hamilton"­..

[riemannzeta]

Here you are, Mr. Agin. Here's another paper laying out the same point nicely.

http://www.necsi.edu/research/evoeco/EvolutionBeyondNeoDarwin1.pdf

[riemannzeta]

It's truly remarkable that the exact same equation appears in a foundational case in tort law decided by Judge Learned Hand:

http://en.wikipedia.org/wiki/United_States_v._Carroll_Towing_Co

Judge Posner points to this case as one of the origins of law and economics. Perhaps neoclassical economic theory is too flat a description of how norms evolve in the same way that kin selection was too flat a description of how biological trails evolve.

[royniles]

"- some readers are so afraid of math" perhaps because they have found mathematics to be one of the greatest facilitators of confirmation bias extant.

And also look at this excerpt from Stanford Encyclopedia of Philosophy, Biological Altruism:
"Another popular misconception is that kin selection theory is committed to ‘genetic determinism’, the idea that genes rigidly determine or control behaviour. Though some sociobiologists have made incautious remarks to this effect, evolutionary theories of behaviour, including kin selection, are not committed to it. So long as the behaviours in question have a genetical component, i.e. are influenced to some extent by one or more genetic factor, then the theories can apply. When Hamilton (1964) talks about a gene which ‘causes’ altruism, this is really shorthand for a gene which increases the probability that its bearer will behave altruistically, to some degree. This is much weaker than saying that the behaviour is genetically ‘determined’, and is quite compatible with the existence of strong environmental influences on the behaviour's expression. Kin selection theory does not deny the truism that all traits are affected by both genes and environment. Nor does it deny that many interesting animal behaviours are transmitted through non-genetical means, such as imitation and social learning (Avital and Jablonka 2000)."

[royniles]

Theorists can't agree on who is correct sometimes because it's neither or none of them, when, as in tis situation, all have models based on the same incorrect assumptions.
Some of this is much too reminiscent of the behaviorists, and their theorizing - observing, rationalizing, testing, hypothe-sizing more or less in that order - with less concern for the why of the matter than the what.
Such as when first they assume altruism must be genetic, then find what appear to be "sacrificial" genes in microbes - and while they haven't found the same in humans, the assumption is that where there is sacrificial behavior, the genes must be there.
But microbes can evolve almost at will with strategies fitted to, or activating, small differences in physiology, resulting in one such strategic form of the species carrying out specific duties that benefit the survival of the species as a whole - the choice of carrying out the needed and specific assignments not being an option. The version of this dynamic in insects takes longer to evolve, and with more distinctive differences in the physiological aspects of these strategies, often with a main or central physiological entity carrying the gene pool that reproduces all the rest.
And microbes and insects don't know or anticipate their fates in advance!!
What we, with our multiple choice short and long term stratagems, may see as sacrifice will be faced as simply a duty for the strategic entity that risks destruction as part of its