Blue whales and other filter-feeding leviathans became giants when climate change introduced them to binge-eating, research has shown.
At more than 30m long, the blue whale is the largest vertebrate animal that has ever lived.
It also dwarfs its ancestors. Scientists have discovered that whales with bodies longer than 10m only made an appearance about 4.5 million years ago.
At the same time, smaller species of whale began to vanish, suggesting large size was suddenly an important advantage.
The reason for the size expansion of the blue whale and other baleen whales was food, the researchers believe.
All baleen whales have a filter in their mouth that sifts out tiny creatures known as krill.
As ice sheets covered the northern hemisphere, krill ceased to be distributed thinly throughout the oceans.
Instead, it became concentrated at certain times of year in coastal areas where runoff from the newly formed ice caps washed nutrients into the sea.
For the whales, it made sense to make the most of the seasonal abundant food by bingeing.
Filter-feeding and large body size made for more efficient eating when faced with dense accumulations of prey.
Dr Graham Slater, a member of the US team from the University of Chicago, said: "We might imagine that whales just gradually got bigger over time, as if by chance, and perhaps that could explain how these whales became so massive.
"But our analyses show that this idea doesn't hold up - the only way that you can explain baleen whales becoming the giants they are today is if something changed in the recent past that created an incentive to be a giant and made it disadvantageous to be small."
The scientists analysed fossil whale skulls at the Smithsonian Institution's National Museum of Natural History in Washington DC to estimate the size of 63 extinct species.
Among the fossils were the earliest baleen whales, which lived more than 30 million years ago.
The findings were published in the journal Proceedings of the Royal Society B.
