The study, published in the journal Proceedings of the Royal Society B, shows that the trend was caused primarily by evolution of larger brains within populations of individual species, but the introduction of new, larger-brained species and extinction of smaller-brained ones also played a part.
"Brain size is one of the most obvious traits that makes us human. It's related to cultural complexity, language, tool making and all these other things that make us unique," said Andrew Du, a postdoctoral scholar at the University of Chicago in the US.
"Think about the entrance to a building. You can reach the front door by walking up a ramp, or you can take the steps," said Bernard Wood, from George Washington University (GW) in the US.
"The conventional wisdom was that our large brains had evolved because of a series of step-like increases each one making our ancestors smarter," said Wood.
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"Not surprisingly the reality is more complex, with no clear link between brain size and behaviour," he said.
They saw that when the species were counted at the clade level, or groups descending from a common ancestor, the average brain size increased gradually over three million years.
Looking more closely, the increase was driven by three different factors, primarily evolution of larger brain sizes within individual species populations, but also by the addition of new, larger-brained species and extinction of smaller-brained ones.
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