By Dylan Matthews

What the late biologist George Price can teach us about the price of altruism.

Sunday, January 6, is the 44th anniversary of the death of someone whose life I think about a lot: evolutionary biologist George Price.

Price is perhaps most famous for his namesake Price equation, which takes many forms but is perhaps most easily understood in its “simple” form:

wΔz=cov(wi,zi)

“It captured the essence of evolution by natural selection in one simple formula,” the science journalist Michael Regnier explains. “It describes how in a population of reproducing individuals, be they people, plants or self-replicating robots, any trait (z) that increases fitness (w) will increase in the population with each new generation; if a trait decreases fitness, it will decrease.”

Here “fitness” is meant in the technical, biological sense: the degree to which a trait improves the reproductive success of an organism.

You can find a blunter explanation in the 2007 horror movie WΔZ (which takes its name from the left half of the equation), in which a biologist played by Paul Kaye explains it to our heroes Melissa George and Stellan Skarsgård:

The Price equation is useful for describing natural selection in general, but it’s especially interesting in explaining a particularly puzzling biological phenomenon: altruism.

As early as Darwin, the existence of self-sacrificing organisms that are willing to give up their own lives, and their own ability to reproduce, for the sake of others, posed a puzzle for evolutionary theory. Regnier offers the example of worker ants, which “are sterile and so have literally zero fitness.” How do those continue to exist, if they, by design, cannot produce offspring sharing their traits?

In trying to answer that question, Price was inspired by an earlier equation by another pivotally important mid-century evolutionary biologist, W.D. Hamilton, who argued that altruism could come about when organisms act in support of their genetic relatives.

The horror movie biologist above offers one good, if oversimplified, example. Suppose you have a group of monkeys in a large cage, then add a monkey-eating snake to the cage. One of the monkeys then lures the snake away to a corner of a cage, so that the snake eats it, giving the other monkeys time and room to work together and kill the snake.

That, of course, prevents the devoured monkey from having any more offspring. But because the dead monkey is related to living monkeys, the dead monkey’s genes are actually more prevalent because of her sacrifice. Those genes include genes connected to self-sacrifice, creating a reinforcing cycle causing future generations of monkeys to also be more altruistic than if the first altruistic monkey hadn’t sacrificed herself.

Hamilton’s rule, as it is now known, formalized this phenomenon as:

rB > C

Broken down, the formula suggests that genes for altruism will evolve if the cost (C) of them to the altruist are offset by the reproductive benefits (B) to those helped, multiplied by the probability (r) that the beneficiaries share the altruistic genes.

Since r is necessarily much higher for blood relatives, the equation explains the origins of altruism as an outgrowth of sacrifice for the sake of one’s kin. Even before Hamilton’s formulation, the evolutionary biologist J.B.S. Haldane reportedly quipped that he would give his life to save two brothers or eight cousins, which captures the same central idea.

How Price’s life fell apart

Price’s work suggested a different way for altruism to spread. His equation did not privilege genetic similarity.

“Natural selection is indifferent to why individuals end up together in groups,” historian Oren Harman explains in his punnily titled biography of Price, The Price of Altruism. “Whether it’s due to common descent, or similarity in traits, or any other pretext doesn’t matter.” If a group of people with altruistic genes found each other, then sacrificing on behalf of each other would spread the gene for altruism, for exactly the same reason that sacrificing for blood relatives made sense under Hamilton’s rule.

But the finding also disturbed Price. If altruism can spread when altruists cluster together, then its opposite — spite, or harming another organism even when one gains no individual benefit from it — can also spread if spiteful organisms cluster together. “What determined whether a living being should act kindly or with malice had nothing to do with an ‘essence’ or ‘inner core’ — both, after all, resided within us,” Harman writes. “Instead, if the surrounding creatures were similar altruism could evolve; if they were different, spite was the solution. Pure unadulterated goodness was a fiction.”

Deriving the equation got Price a job at University College London. (He showed the equation to John Maynard Smith, another eminent biologist there, and within 90 minutes Smith and the department chair had given him an office and an honorary appointment.)

It also, arguably, helped ruin his life.

Around the same time that he discovered the equation, Price became an incredibly devout Christian. Initially this took the form of increasingly intense biblical hermeneutics — notably including a quest to find out the “true” date of Easter, which he thought most churches had gotten wrong — but a vision of God he claimed to have experienced in 1972 transformed his faith, convincing him he had been too literal and insufficiently humanistic.

In 1973, he started to invite a large number of homeless people he met around Soho Square and Euston Station in London to live in his home. After his lease ran out, he became homeless himself. Around this time, he published a paper with Smith that made the cover of Nature.

Eventually he and a homeless buddy, who went by Peg Leg Pete (I swear all of this is in Harman’s book, I am if anything downplaying it), joined a squatters’ house together. Price would hop from squatters’ home to squatters’ home until he died. “Price was probably experiencing psychotic delusions, paranoia and hallucinations beyond his visions of Jesus, not to mention depression exacerbated by thyroid hormone deficiency,” Regnier writes. “For him, the most rational explanation available was that he had been chosen by …read more

Read more here: The scientist who tried to be as selfless as possible, until it killed him

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