"My, what big eyes you have!"

There may be something to that fairy-tale line, uttered by the Big, Bad Wolf before it pounced on Little Red Riding Hood and ate her.

A new study suggests that millions of years before the first fish came crawling onto land, the size of their eyes roughly tripled — giving them a greater ability to spot potential sources of food on shore.

Using a combination of fossil measurements and computer simulations, researchers Malcolm McIver and Lars Schmitz theorize that radically expanded vision helped spur the transition from water to land about 385 million years ago.

"We found a huge increase in visual capability in vertebrates just before the transition from water to land," Malcom McIver, a neuroscientist and engineer at Northwestern University in Evanston, Illinois, said in a statement on the findings. "Our hypothesis is that maybe it was seeing an unexploited cornucopia of food on land — millipedes, centipedes, spiders, and more — that drove evolution to come up with limbs from fins."

Over the course of about 12 million years, the average size of the eye sockets in 59 fish fossils grew from around 13 millimeters (about half an inch) to 36 millimeters by the time the first vertebrates ventured out of the water.

Many invertebrate species like insects and spiders were already there. But recent scholarship indicates vertebrates' transition to land occurred about 400 million years ago, with the first land-adapted, four-footed creatures appearing about 330 million years ago.

The findings suggest these bigger-eyed fish hunted much like today's crocodiles — watching from the shallows for prey before coming out of the water to hunt.

"As the eyes got bigger, they saw further and further and had more and more selective advantage toward getting the limbs that eventually let them live full-time on land," McIver said.

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The study was published this week in Proceedings of the National Academy of Sciences. McIver said the research bolsters what he called the "Buena Vista hypothesis" of evolution, which posits that better vision helped drive aquatic vertebrates onto land before limbs evolved.

Bigger eyes weren't much of a help underwater, said Schmitz, assistant professor of biology at California's Claremont McKenna, Scripps, and Pitzer colleges. But above the surface, they expanded the visual range of those species a millionfold.

That gave those fish a massive amount of data that likely boosted their brains as well. And with better vision, they could see potential prey — or threats — further off, giving them more time to respond.

"In evolution, it often comes down to a trade-off. Is it worth the metabolic toll to enlarge your eyes?" Schmitz said. "What's the point? Here we think the point was to be able to search out prey on land."