Cooking would have made wild tubers much more nutritious to humans, he noted, “which is not to be sniffed at, especially if you’re a very hungry Pleistocene hunter-gatherer.”

Another clue to the importance of carbohydrates, Dr. Thomas said, can be found in our DNA. Chimpanzees, our closest living relatives, have two copies of the amylase gene in their DNA. But humans have many extra copies — some people have as many as 18. More copies of the amylase gene means we make more of the enzyme and are able to derive more nutrients from starches, Dr. Thomas said.

When scientists first discovered the extra genes, they hypothesized that our improved production of amylase evolved at the dawn of agriculture several thousand years ago. As wheat and other starchy crops became staples, the argument went, natural selection favored people with more amylase.

But recent studies of the DNA of preagricultural hunters from Europe reveal that people had extra copies of amylase genes long before they started farming. Dr. Thomas and his colleagues propose that the invention of fire, not farming, gave rise to the need for more amylase. Once early humans started cooking starchy foods, they needed more amylase to unlock the precious supply of glucose.

Mutations that gave people extra amylase helped them survive, and those mutations spread because of natural selection. That glucose, Dr. Thomas and his colleagues argue, provided the fuel for bigger brains.

The fossil record shows a drastic acceleration in the size of hominin brains starting roughly 800,000 years ago. Today our outsize brains use up as much as a quarter of the calories we burn.

Other experts said that Dr. Thomas and his colleagues have marshaled a lot of compelling evidence for the importance of carbohydrates in human evolution. But they were not ready to embrace the detailed scenario the scientists lay out in the new paper.