W. D. Hamilton

Based on Wikipedia: W. D. Hamilton

The Man Who Explained Why You'd Die for Your Family

In the summer of 1963, a disheveled graduate student sat alone in London parks and railway stations, scribbling mathematical equations that would eventually reshape our understanding of life itself. His supervisors didn't understand his work. The journals kept rejecting it. He was, by all accounts, deeply depressed. Yet William Donald Hamilton was working out something that had puzzled biologists since Darwin: why would any creature sacrifice itself for another?

The answer he discovered was elegant, mathematical, and slightly unsettling. It would make him, in Richard Dawkins's estimation, "the greatest Darwinian of my lifetime."

The Altruism Problem

Here's the puzzle that haunted evolutionary biology for a century. Natural selection should favor selfishness. An organism that helps others at cost to itself should, over time, be outcompeted by organisms that don't bother with such generosity. Yet everywhere we look in nature, we see apparent altruism. Worker bees die defending the hive. Ground squirrels give alarm calls that attract predators to themselves while allowing relatives to escape. Human soldiers throw themselves on grenades.

Darwin knew this was a problem. So did the great twentieth-century geneticists Ronald Fisher and J.B.S. Haldane. Haldane famously quipped that he would lay down his life for two brothers or eight cousins. It was a joke, but it contained the seed of the answer.

Hamilton figured out why that math actually works.

From Cairo to Kent

Hamilton was born in 1936 in Cairo, Egypt, the second of seven children in a remarkable New Zealand family. His father was an engineer, his mother a physician. Of his siblings, two sisters became doctors (one invented the alternating pressure mattress used in hospitals worldwide to prevent bedsores), one sister became a pasture scientist, and a brother became an engineer. Intellectual firepower ran in the genes—a fact Hamilton would have appreciated given his later work.

The family settled in Kent, England, and during World War II, young Bill was evacuated to Edinburgh. He became obsessed with natural history, spending his free time collecting butterflies and insects. At age ten, he discovered a book called Butterflies by E.B. Ford, part of the New Naturalist series. It introduced him to evolution by natural selection, genetics, and population genetics. The trajectory of his life was set.

Then, at twelve, he nearly ended that life prematurely.

Hamilton's father had kept explosives left over from making hand grenades for the Home Guard during the war. The boy found them, played with them, and was seriously injured in the resulting explosion. Surgeons at King's College Hospital had to perform a thoracotomy—opening his chest cavity—and amputate parts of fingers on his right hand to save his life. He needed six months to recover, and the scars remained visible for the rest of his life.

An Uninspired Undergraduate

Hamilton went to Tonbridge School and then, after two years of national service and travels in France, to St. John's College, Cambridge, to study biology. He was not impressed. The biology faculty, he later complained, "hardly seemed to believe in evolution."

This is a remarkable statement. Evolution is the central organizing principle of biology—nothing in the field makes sense without it. But in the early 1960s, many biologists treated evolutionary theory as a philosophical backdrop rather than a working tool. They described organisms, classified them, studied their physiology. What they didn't do was ask, with mathematical precision, why organisms behaved as they did.

Hamilton wanted to ask why.

The Equation That Changed Biology

After Cambridge, Hamilton enrolled in a master's program in demography at the London School of Economics. But his interests quickly turned mathematical and genetic. He began working on the problem that had tantalized Fisher and Haldane: how could natural selection favor behaviors that helped relatives at cost to oneself?

The breakthrough came when Hamilton realized that the key number falling out of his calculations was something called the coefficient of relationship—a measure developed by the geneticist Sewall Wright to quantify how genetically similar two individuals are.

Your coefficient of relationship with your identical twin is 1. You share all your genes. With a parent or child, it's 0.5—you share, on average, half your genes. With a sibling, also 0.5. With a grandparent, aunt, uncle, niece, or nephew, it's 0.25. With a first cousin, 0.125. And so on, halving with each step of separation.

Hamilton's rule, as it came to be known, can be expressed as a simple inequality: a costly action should be performed if the cost to the actor, multiplied by one, is less than the benefit to the recipient, multiplied by their coefficient of relationship.

In plain English: you should sacrifice yourself for two siblings, four half-siblings, or eight first cousins. Haldane's joke was mathematically correct.

Why the Math Matters

This might seem like abstract theorizing, but it has concrete implications. The rule doesn't describe conscious calculation—bees don't do algebra. Instead, it describes the evolutionary pressures that shape behavior over millions of years. Genes that cause organisms to behave in ways consistent with Hamilton's rule tend to spread through populations. Genes that cause organisms to sacrifice too much for distant relatives, or too little for close ones, tend to disappear.

The most striking application involves the social insects: ants, bees, and wasps. These creatures belong to an order called Hymenoptera, which has an unusual genetic system called haplodiploidy. In this system, females develop from fertilized eggs and have two sets of chromosomes, while males develop from unfertilized eggs and have only one set.

This quirk of genetics creates a strange consequence. A female worker bee shares three-quarters of her genes with her sisters, but would share only half her genes with her own daughters. From a purely genetic standpoint, she's better off helping her mother (the queen) produce more sisters than she would be reproducing herself.

Hamilton had explained, mathematically, why worker bees are sterile. They're not sacrificing their reproductive interests—they're maximizing them, in a roundabout way, by helping to raise genetically similar siblings.

Rejection and Recognition

Hamilton wrote up his findings in two papers titled "The Genetical Evolution of Social Behaviour." They were dense with mathematics. Two reviewers at the journal couldn't follow the arguments. The third reviewer, John Maynard Smith, didn't fully understand them either—but he recognized their importance.

The papers were published in 1964 in the Journal of Theoretical Biology. Almost nobody read them. For years, Hamilton's work languished in obscurity while he labored as a lecturer at Imperial College London, including a facility at Silwood Park where a building now bears his name.

Recognition came slowly, then all at once. In 1976, Richard Dawkins published The Selfish Gene, which explained Hamilton's ideas to a popular audience. The book became a sensation. Suddenly, everyone was talking about "inclusive fitness" and "kin selection"—terms Hamilton had coined. The 1964 papers began accumulating citations. Today, they're among the most referenced works in all of biology.

There was friction between Hamilton and Maynard Smith over credit. During the review process, Maynard Smith had published his own paper that briefly mentioned similar ideas. Hamilton suspected—perhaps unfairly—that Maynard Smith had delayed his work to claim priority. The two men remained professionally cordial but never warm.

Extraordinary Sex Ratios

Hamilton's work on altruism was just the beginning. In 1967, he published a paper in Science that opened an entirely new field of research: the evolution of sex ratios.

Why are there roughly equal numbers of males and females in most species? Fisher had worked this out in 1930. If males were rare, parents who produced more sons would have more grandchildren, since those sons would have many mating opportunities. This would increase the proportion of males. Conversely, if males were common, producing daughters would be advantageous. The result is an equilibrium at roughly 50-50.

But Hamilton noticed that many species don't follow this pattern. Some wasps, for instance, produce wildly skewed sex ratios. Why?

The answer involved local competition for mates. In species where brothers compete with each other for access to sisters (yes, this happens in some wasps), mothers do better by producing mostly daughters with just enough sons to fertilize them. Hamilton worked out the mathematics with characteristic rigor.

The paper also introduced something called the "unbeatable strategy"—an approach that, once established in a population, cannot be displaced by any alternative. Maynard Smith and another theorist, George Price, later developed this into the concept of the evolutionarily stable strategy, or ESS. This idea proved enormously influential not just in biology but in economics and game theory more broadly.

The Price Connection

George Price was an unusual figure in this story. An American chemist with no formal training in biology, he had independently derived a mathematical equation that described evolutionary change—and in doing so, had rediscovered Hamilton's rule from first principles.

Price came to Hamilton, and the two began collaborating. Maynard Smith peer-reviewed one of Price's papers and was so impressed that he offered Price co-authorship on his own ESS paper. This helped repair the frayed relationship between Maynard Smith and Hamilton.

Price's later life took a tragic turn. He became intensely religious, gave away his possessions, and lived among homeless people in London. He died by suicide in 1975. Hamilton and Maynard Smith were among the few mourners at his funeral.

The Red Queen's Race

In the 1980s, Hamilton turned his attention to another fundamental puzzle: why does sex exist at all?

This is a genuine mystery. Sexual reproduction is enormously costly. You have to find a mate. You have to compete for access to that mate. You can only pass on half your genes to each offspring. An asexual organism, by contrast, can reproduce alone and passes on all its genes. Asexual reproduction should dominate.

Yet sex is everywhere. Why?

Hamilton proposed what became known as the Red Queen hypothesis, named for a character in Lewis Carroll's Through the Looking-Glass. The Red Queen tells Alice that in her world, "it takes all the running you can do, to keep in the same place."

The idea is that organisms are locked in an endless evolutionary race with their parasites. Parasites evolve to exploit whatever genetic configuration is most common in the host population. Sexual reproduction, by constantly shuffling genes into new combinations, creates moving targets. Your children have different genetic vulnerabilities than you do, making it harder for parasites to track any particular lineage.

Sex, in this view, is an arms race without end. Species with sex can keep "running away" from their parasites. Asexual species eventually get caught.

Spite and Greenbeards

Hamilton also explored the dark side of social evolution. In a 1970 paper, he asked whether organisms ever harm others simply to harm them, without any benefit to themselves.

Such behavior he called spite. And he showed that it could evolve—but only under narrow conditions. If you share genes with most of your neighbors, then harming a random stranger might actually help your genes spread, because the stranger is less related to you than average. You're reducing competition for your relatives.

In practice, spite is rare and never elaborates into complex adaptations. Targets of spite tend to retaliate, and most individuals in a population are roughly equally related to each other, making it hard to find profitable targets.

Hamilton also clarified the concept of the "green beard effect"—the idea that a gene might spread if it caused organisms to recognize copies of itself in others and behave altruistically toward them. Imagine a gene that simultaneously produced a green beard, enabled recognition of green beards in others, and caused generosity toward green-bearded individuals. Such a gene could spread even in the absence of kinship.

This sounds like science fiction, but examples have been found in nature. Some social amoebae, for instance, have recognition systems that allow them to distinguish relatives from strangers.

A Difficult Man

By all accounts, Hamilton was not easy to know. He was socially awkward, prone to depression, and a notoriously poor lecturer. When he arrived at the University of Michigan in 1978 as Professor of Evolutionary Biology, students staged protests and sit-ins because of his association with sociobiology—a field many viewed as providing biological justifications for inequality and racism.

The protests were based on a misunderstanding. Hamilton's work described how natural selection shapes behavior; it did not prescribe how humans should behave. But the association persisted, and it troubled him.

His lecturing difficulties never hampered his reputation. The ideas spoke for themselves, especially after Dawkins popularized them. In 1980, Hamilton was elected a Fellow of the Royal Society, Britain's most prestigious scientific academy. In 1984, he was invited to Oxford as Royal Society Research Professor, a position he held until his death.

He married Christine Friess in 1966. They had three daughters—Helen, Ruth, and Rowena—and separated amicably after 26 years. In his final years, he found companionship with Maria Luisa Bozzi, an Italian science journalist.

Autumn Leaves and Cloud-Making Algae

Hamilton never stopped generating ideas. In the 1990s, he proposed an evolutionary explanation for autumn leaf colors. Why do trees produce bright reds and yellows as their leaves die? Hamilton suggested it was a signal to insects: "Don't lay your eggs here—this tree has strong defenses." The brightness of the colors would indicate the vigor of the tree's chemical armaments.

He also co-authored a paper proposing that marine algae release dimethyl sulfide—a chemical that acts as a seed for cloud formation—as an adaptation. Clouds help disperse algal spores around the world. The algae, in effect, manipulate the weather for their own benefit.

Both ideas remain controversial. But they illustrate Hamilton's characteristic approach: taking a familiar phenomenon, asking what evolutionary purpose it might serve, and pursuing the logic wherever it led.

The Congo and the End

In his final years, Hamilton became interested in a hypothesis about the origin of HIV—the idea that the virus might have entered human populations through contaminated oral polio vaccines used in Africa during the 1950s. The hypothesis has since been thoroughly discredited, but Hamilton found it compelling enough to write the foreword to Edward Hooper's 1999 book The River, which advanced the claim.

To gather evidence, Hamilton traveled to the Democratic Republic of the Congo in early 2000 to study natural levels of simian immunodeficiency virus in wild primates. He was 63 years old.

He returned to London on January 29, 2000, and was admitted to University College Hospital the next day. He died on March 7, having never recovered from what a coroner later determined was multi-organ failure due to gastrointestinal hemorrhage. He had contracted malaria during the expedition, but the connection to his death was indirect at best—possibly a pill taken for malarial symptoms lodged in an intestinal pouch and caused ulceration.

A secular memorial service was held at New College, Oxford, organized by Richard Dawkins. Hamilton had been an agnostic throughout his life.

A Final Wish

Hamilton was buried near Wytham Woods, outside Oxford. But he had written an essay about his "intended burial" that reveals something of his character—a strange mix of scientific precision, romantic naturalism, and dark humor:

I will leave a sum in my last will for my body to be carried to Brazil and to these forests. It will be laid out in a manner secure against the possums and the vultures just as we make our chickens secure; and this great Coprophanaeus beetle will bury me. They will enter, will bury, will live on my flesh; and in the shape of their children and mine, I will escape death. No worm for me nor sordid fly, I will buzz in the dusk like a huge bumble bee. I will be many, buzz even as a swarm of motorbikes, be borne, body by flying body out into the Brazilian wilderness beneath the stars.

The Coprophanaeus is a dung beetle—one of the creatures that had fascinated Hamilton since childhood. He wanted his body to nourish them, to become part of them, to disperse into the forest in their gleaming forms.

It was a fitting fantasy for a man who had spent his life showing that the boundaries between self and other, between individual and kin, are more porous than we imagine. Your genes don't end at your skin. They extend into your relatives, your offspring, and through them into the future.

Hamilton's rule quantified this insight with mathematical precision. But his essay about the beetles captured something the equations couldn't: the strange beauty of a world where death is not an ending but a transformation, where self-sacrifice is not tragedy but strategy, where every creature is both individual and vehicle for something larger.

Legacy

Hamilton collected numerous honors in his lifetime: the Darwin Medal of the Royal Society, the Crafoord Prize (sometimes called the Nobel Prize of biology), the Kyoto Prize, and many others. His collected papers, published under the title Narrow Roads of Gene Land, run to three volumes.

But his real legacy is the conceptual framework he built. Before Hamilton, evolutionary biology was largely about describing what organisms do. After Hamilton, it became possible to predict what they should do—to derive behavior from first principles.

Inclusive fitness theory, kin selection, evolutionarily stable strategies, the Red Queen hypothesis—these ideas now form the backbone of evolutionary ecology and animal behavior. They've been applied to everything from the social lives of bacteria to the psychology of human families.

The lonely graduate student in the London parks, wrestling with equations that no one else understood, had figured out something fundamental about the nature of life. Every act of apparent selflessness, he showed, serves the deeper selfishness of the genes. And in that insight lies not cynicism but clarity—a way of seeing the living world that makes its endless complexity, at last, comprehensible.