Featured image: Worker bees in a hive work for the collective good but don’t have a chance to pass their genes on to future generations. Photo: Todd Huffman/Wikimedia Commons, CC BY 2.0.
It is difficult to introduce George Price. Perhaps we can start with the end.
When George Price, aged 52, died in 1975, his funeral was attended by about a dozen people. Most of these people were squatters with whom he had shared the last part of his life. Also among the attendees were two of the brightest evolutionary biologists of the time, John Maynard Smith and William Hamilton.
An American chemist who had worked on the Manhattan Project, Price had a habit of dabbling in different areas and trying to make a significant contribution. His scientific career and personality were perhaps prophesied when he was interviewed for admission in Harvard University. After selecting him, the committee commented that Price “may go haywire but will never be humdrum”.
After an operation on the thyroid gland in 1967 that left him with a bad shoulder and arm, Price, then 45, decided to move to London and make his foray into yet another area: theoretical biology.
Soon after his move, he submitted a paper to the journal Nature on why we don’t see escalated retaliation among animals when fighting. The two referees for the paper were unable to ascertain the value of the contribution, and the manuscript was sent to Maynard Smith, who strongly recommended publication.
In 1971, when Smith was building on Price’s idea, he couldn’t locate the paper he had so positively recommended. Curious about the whereabouts of the man he had never heard of before then, he requested Nature for Price’s address, and was astonished that the idea had come from an unemployed American living in London! Smith and Price subsequently jointly published a simple and elegant paper in 1973 that introduced game theory into biology.
Around the same time, Price was interested in the question of the origins of altruism. Why is it that certain members of a species indulged in behaviour that was to the benefit of others, often at personal cost? For example, worker bees in a hive work for the collective good but don’t have a chance to pass their genes on to future generations. This is in stark contrast to Darwinian selection, which says that only traits that maximise an individual’s fitness get transferred to subsequent generations. So where did altruism come from?
Charlies Darwin had thought about this problem as well. His solution had been the idea that if altruistic behaviour helped the group that an organism cohabited with, it could flourish. In the 20th century, William Donald Hamilton proposed that altruism could have a biological basis if altruistic behaviour benefited individuals related to the altruist more than the cost the altruist incurred while engaging in altruism.
He captured this idea in an equation, which says altruism prevails when `rB > C`. Here, B is the benefit for the recipient of altruistic behaviour, C is the cost to the altruist and r is the degree of relatedness between the altruist and the recipient. For example, a mother and a daughter have r = 0.5, since they share half the genes (the other half coming from the father). Siblings have r = 0.5 as well. Altruistic behaviour that favours one’s kin is called kin selection.
The British-Indian scientist J.B.S. Haldane popularised this idea when he said, “I would lay down my life for two brothers or eight cousins.” That is, if I were to lay my life down to save two of my siblings, with whom I share half my DNA, hence r = 0.5, then the total DNA saved is two times 0.5, which equals one. Therefore, as far as my genes are concerned, it doesn’t matter whether I survive or if two of my siblings survive. But with cousins, r = 0.125, so it would only make sense to lay one’s life down if one’s could save eight of them.
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Anyway, Price – a novice in the area of theoretical biology – arrived at an equation that succinctly described the action of natural selection both at an individual level and at the level of a group or kin. He hadn’t come across anything like his result in the scientific literature, so he showed his work to a statistician at University College London. The college had been home to scientific luminaries since the 19th century, and it speaks of the quality of what Price had found that by the time he concluded his meetings, he was offered a position there.
His result is now known as Price’s equation. It describes the action of natural selection, the agent of evolutionary change, in its most general and fundamental form.
∆Z = Cov(wi,zi)Z
The left side of the equation, ΔZ, refers to the change in a trait like height or altruism in a population over one generation. The term on the right links the trait value (zi) with an individual’s fitness (wi) using the covariance between them – that is, how the trait value and fitness of an individual correlated. (The equation has one more term not shown here. The complete equation with its derivation and significance can be found here.)
Price’s framework widened the scope of the evolution of altruism and freed it from depending solely on relatedness. Earlier this year, to commemorate 50 years of the equation, the Royal Society published a series of articles about Price’s work and life.
However, this moment of professional triumph came at great personal agitation to Price. He started wondering that of all the luminaries in evolutionary biology, why should he – a novice – have been the one to have arrived at the equation. Dwelling more on this, he came to the only conclusion that made sense to him: that he had been chosen by a deity. He found no other reason that explained his life, and so, a fierce atheist was transformed to a believing Christian.
This realisation also prompted Price to think of the philosophical connotations of his equation. The fact that he could explain the evolution of altruism as a trait meant the trait itself was never pure, as in that altruism couldn’t ever be entirely unselfish. Selfish interests influenced its development in nature. However, Price was also unsatisfied with this damning conclusion and set out to prove himself wrong.
He changed his behaviour and started giving away his possessions to those in need, and invited homeless people to his place. In a letter to Maynard Smith, he wrote, “I am now down to exactly 15p. … I look forward eagerly to when the 15p will be gone.” This was Price’s fight against his own equation – to show that altruism could be borne out of pure goodness of the heart.
Soon enough, Price was left with nothing and was out on the street himself. Hamilton and Smith, perhaps the only two who recognised the importance of Price’s work but who between them were not on speaking terms, tried to ‘save’ him. Sadly, early in 1975, Price ended his life. Although his death may have been the result of his refusal to take thyroid medication, in a scientific sense, his decision to end his life also summarised his quest to answer one question: How can altruistic behaviour evolve and survive?
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Price was, by all accounts, a difficult man. He had married a devout Christian woman and the couple had had two daughters. The marriage ended with a divorce in 1955, and Price rarely saw his daughters. Though aware of his mortality, he often wrote to them and kept them abreast of developments in his life. In 2016, Laura Farnworth, a theatre director, put together a play entitled ‘Calculating Kindness’ in London. For one of the shows, she invited Price’s daughters to watch.
Oren Harman, Price’s biographer, wrote that though Price’s life ended on a grey note, his life itself was about recognising that “there is a point where the filopodia of science end, and cannot crawl any further”. Harman also quoted the philosopher Ludwig Wittgenstein: “Even if all possible scientific questions be answered, the problems of life have still not been touched at all. Of course there is then no question left, and just this is the answer.”
Supreet Saini is an associate professor in the department of chemical engineering at IIT Bombay.