The Price of Altruism

George Price was a remarkable man who came to judge his own life a failure, and had many reasons to do so. The legacy that may or may not buoy up that judgment consists of a handful of obscure mathematical papers that purport to make contributions to evolutionary biology. Price himself doubted their value, and biologists still use his work, but there remains an ambivalence about its meaning and significance. In The Price of Altruism, Oren Harman tells the story of evolutionary debates over altruism versus selfishness from The Origin of Species to the present day, and interweaves it with biographical material. Both strands are rich and complex, and their interplay creates a stirring book that will reward many readers with an intelligent interest in altruism.

George Price was an enigmatic figure in life, and remains so 25 years after his suicide in London. An American, he was involved in the Manhattan Project and worked for IBM, and more than once he claimed to have invented or, better, to be on track to invent, a grand new machine. One example was his “Design Machine,” in which one could specify any three-dimensional shape, and it would produce an object with that shape. It would have been very useful for manufacturing parts, and such a device may or may not exist today, but in 1956 it was far beyond the realm of the feasible. George publicised his “invention,” and appeared heroically in November of that year in Fortune magazine. He also contacted many famous figures, not hesitating to use his considerable intellectual and rhetorical skills to interest Hubert Humphrey in his ideas about winning the Cold War, and to walk into B. F. Skinner’s lab and discuss “Teaching Machines” with him. Thus he started on his life as an uncertain mixture of visionary and charlatan-showman, of profound thinker and intellectual gadfly and self-publicist, which Harman documents very engagingly.

The reader of this book meets Prince Kropotkin, J. B. S. Haldane, John von Neumann, R. A. Fisher, Bill Hamilton, John Maynard Smith, C. A. B. Smith, and many more characters relevant to the development of evolutionary biology. A reasonably knowledgeable reader will have heard of these people, but not know much about most of them, and Harman gives very entertaining accounts. (There are inaccuracies, however; for example, W. D. Hamilton did not have a research post at Silwood Park in the 1960s, but a university lectureship. Indeed, the undergraduates complained each year about his teaching of population genetics, and appealed for marks from that course not to count towards their degree results.)

While in complaining mode, I may as well get off my chest irritation with the bizarre and distracting convention adopted in the book of following a colon with an upper-case letter, as though it were the beginning of a new sentence. And the more entertaining of the typos include a “compliment of chromosomes” and someone having “too much on their palate.” The endnotes refer to manuscript sources such as GPP (George Price Papers), but to find what GPP means, it turns out the reader must find the first reference to that source in the endnotes. Nor is it obvious where to find these manuscript sources, so the academic good intentions of the endnotes are not fully carried through.

But the central claim to interest of George Price, in connection to altruism, is the famous “Price Equation.” I forebear to repeat it here in any of its many forms, but I need to set the scene by saying that (a simple form of) the Price Equation shows how a change in gene frequency from one generation to the next can be understood in terms of statistical associations across individuals in the parental generation, between a number of quantities: each individual’s gene frequency, the number of gametes each individual succeeds in contributing to making offspring, and the difference in gene frequency of those successful gametes from the individual’s own gene frequency. The Price Equation is remarkable in that it applies to sexual, asexual, and mixed populations, to cases with overdominance and epistasis, to arbitrary mating systems, and to haploidy, diploidy and to mixed ploidies too.

The equation applies to selection of all traits, and allows some very neat analytic manipulations. The book focuses on altruism because social traits were the first application, in Hamilton’s 1970 paper, and because it is currently used in the yawningly long-lasting debate on group selection. However, it is also useful in studying the sex ratio, and in my own current research, for capturing selection on an arbitrary trait when discussing the link between gene frequencies and fitness optimisation.

Harman explains the equation in the text and in an appendix, but not very sharply, and the result is probably satisfactory for the non-technical reader interested in the personal side of the story; but it will frustrate and disappoint a biologist or mathematician who wants to understand the central scientific issue. This vagueness is not accidental. Price himself was ambivalent about the value of this contribution, and biologists working today with the Price Equation do have different understandings of it. Price enjoyed teasing Bill Hamilton with the implications of his work, but seemed to have doubts about whether what we now call the Price Equation belonged to his profound or charlatan side. There is a certain wonderment in imagining Price having employed his unquestioned intelligence and inter-personal skills to have written his papers to run rings around succeeding generations of biologists.

I myself believe there is indeed a profound value in the Price Equation, but let’s look first at a positive and negative aspect that Harman neglected. On the positive side, the Price Equation deals with individuals and not, as most population genetic formalisms, with genes or genotypes. This chimes with how most biologists think conceptually about animal behaviour and design, and also with how most field biologists conduct their research. (It is not quite true, but almost, that there is no biologically interesting trait of which the genetics is known, so the emphasis on individuals is usually necessary as well as desirable.)

The negative side, neglected by Harman and not mentioned by Price, is dynamic insufficiency. Most population geneticists feel a methodological obligation to work with systems that model a population right through from one generation to the next, and in such a way that the model can pick up and repeat itself so that successive generations unfold. The Price Equation requires detailed knowledge of the parental generation, but then produces only a population average for the offspringgeneration, so that there is insufficient information to “crank the handle.”

This dynamic insufficiency is the precise cost paid for the vast generality, and so useful applications of the Price Equation are likely to be found where the generality is really important and the dynamic insufficiency acceptable. It is true that the assumptions of the Price Equation are themselves dynamically insufficient, but even strong advocates of the Price Equation differ on whether it can become dynamically sufficient if enough further assumptions are made.

In conclusion, The Price of Altruism is a very readable and entertaining popular book, with flatteringly academic-like qualities. It ranges widely, and if there is some uncertainty in the book’s resolution of central issues, that is at least partly because the Price Equation is still at the centre of continuing, sometimes fierce debates in biology. I’d like to think that a new edition in ten years’ time could have a coda with settled answers to questions of altruism and selfishness, but that may be too optimistic.

Alan Grafen is Professor of Theoretical Biology at the University of Oxford, and a keen user of the Price Equation since 1983.