Why do we help others, even when it costs us something? This question has fascinated scientists for decades. A new study from the University of Amsterdam offers a breakthrough answer by updating one of the most famous ideas in evolutionary biology: Hamilton’s rule. The research was published on 12 September in the journal eLife.

Hamilton’s rule, introduced in the 1960s, says that altruism – helping others at your own expense – can evolve when the benefits to others, multiplied by how closely related they are to you, outweigh the cost to yourself. In simple terms, we’re more likely to make sacrifices for family because it helps our shared genes survive.

Not just one rule

But ever since it was proposed, scientists have disagreed about how general the rule really is. Some said it almost never applies, while others argued it’s as broad and fundamental as natural selection itself. By reworking the mathematics behind Hamilton’s rule, the new study shows that a rule that describes when altruism is or is not selected should not be just one formula. The original Hamilton’s rule is actually part of a whole family of rules, with each version of the rule applying under different circumstances, depending on how traits influence survival and reproduction.

‘For years, the debate has been about whether Hamilton’s rule is universal,’ says the study’s author, Professor Matthijs van Veelen. ‘What I show is that it’s not a single rule, but is in fact many different versions that work in different situations. That means both sides of the debate were partly right.'

A fresh mathematical foundation

The key to this discovery is an updated mathematical tool called the Generalised Price equation. The original Price equation described how traits change from one generation to the next, but it left some important gaps. The new version reconnects the math with statistics, and shows how data can help choose between different ways in which traits affect fitness – of which there are many. Every such way comes with a version of the Price equation of its own.

This new perspective reveals that the classic Hamilton’s rule is only the simplest case. More complex versions can account for things like multiple interacting traits or non-linear effects. In short, there’s no longer a need to argue about whether Hamilton’s rule “holds” or not. The real question is: which version of it applies in each situation?

Why it matters

This breakthrough could reshape how scientists study cooperation and altruism in nature. Instead of asking whether Hamilton’s rule is true in a given species – a question that turns out to be unhelpful – researchers can now focus on figuring out which version of the rule fits their data.

That shift could make studies of social behaviour much clearer, whether scientists are looking at microbes that work together, birds that share food, or humans who help strangers.

Ending the debate, opening new doors

The study provides what Van Veelen calls a “constructive solution” to a decades-old argument. Rather than taking sides, it reframes the question in a way that makes progress possible. ‘This result doesn’t just close the debate,’ he says. ‘It gives us a more powerful framework to use in future. Cooperation is everywhere in nature, and now we have a clearer picture of the many ways evolution can produce it.’

Looking ahead

By resolving one of the biggest theoretical disputes in evolutionary biology, this work opens the door to more precise and practical research. It highlights the flexibility of evolution and shows that cooperation isn’t a mystery – it can be explained, but the explanation depends on the details of each case. In other words: there’s no single path to cooperation in evolution. There are many – and now we finally have a map.