Yet evolutionarily speaking, whales are recent leviathans. After the largest dinosaurs died off, land mammals bulked up, leading to elephant-size rhinoceroses, sloths and armadillos about 35 million years ago. The ancestors of today's giant whales, meanwhile, stayed curiously small.

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“It is only since around the beginning of the so-called ice ages that whales have not just evolved to be huge, but titanic in size,” Erich M.G. Fitzgerald, a vertebrate paleontologist at Museum Victoria in Australia, said in an email. “Most baleen whales that ever lived were little fellows compared to their modern descendants.”

To Pyenson and other paleontologists, what exactly jump-started the age of aquatic giants remained a mystery. “It’s such an obvious question,” he said. “If you’re an evolutionary biologist or a paleobiologist, you want to know how it came to be that way.”

Relying on the extensive collection of fossil whale skulls at the Smithsonian, Pyenson and his colleagues tracked the evolution of baleen whale size. (Baleen whales lack teeth, instead using the mustache-like bristles that hang in their mouths to scoop up krill, fish and other tiny sea creatures.) From the skull sizes, the scientists could estimate the body lengths of about 60 species of modern and extinct whales.

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Fossils of the first baleen whales appeared about 25 to 20 million years ago. For millions of years afterward, most baleen whales remained about 15 feet long. But 3 million years in the past, the scientists reported Tuesday in the Proceedings of the Royal Society B, baleen whales underwent a dramatic size shift. The smallest baleen whales vanished. The others grew to double or triple the size.

Paleobiologist Jorge Velez-Juarbe, a marine mammal curator at the Natural History Museum of Los Angeles County who was not involved with the new study, said that experts previously proposed baleen whales grew large as a way to avoid being eaten. Even the biggest ocean predators from several million years ago — sperm whales such as Livyatan melvillei, or the shark Carcharocles megalodon — would struggle to chomp on anything larger than about 30 feet (smaller than the average humpback whale alive today). But baleen whales didn’t outgrow such carnivores until millions of years after predatory sperm whales appeared in the fossil record.

In the new study, Pyenson and his co-authors note that shoreline ecosystems changed about 3 million years ago, around the same time that baleen whales got huge. First, seasonal windy upwellings began to kick up nutrients along the coast; later, glacial runoff added to the richness of these pockets. The net results were souped-up marine ecosystems where whales could feast.

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It was not that the ocean necessarily had more krill or other whale food. But the food was more densely packed. Pyenson likened the seasonal upwellings to a bag of marbles dumped in a corner of a room, rather than the balls careening across the floor. When the marbles are clustered, it's easier to hoover them up in a single go instead of plucking the marbles one by one. For suspension feeders such as baleen whales, “the bigger you get, the more efficient you are,” Pyenson said. “It maximizes the return on density of prey.”

“A large size allows them to take a giant bite,” Velez-Juarbe said in an email, “as well as makes it easier to migrate between areas where food is concentrated.” Because the increased marine productivity changed with the seasons, the giants would have to swim vast distances to find new pockets. Locomotion as a rule gets easier the larger you are (each step of a long leg or flap of a wide fluke propels you farther). Gigantism may have allowed large baleen whales to outcompete their smaller cousins.

Fitzgerald, who was not an author of the study, called the new analysis “quite convincing,” given the fossil data and sophisticated computations used to shoot down alternative explanations. The scientists said they were able to rule out that the whales grew large by chance, for instance.

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“That being said, there are uncertainties inherent to this type of study,” Fitzgerald said, “stemming from the fact that we are reliant on what the fossil record has revealed — so far.” A “yawning hole,” he said, blanks out the baleen whale fossil record between 2 million to 3 million years ago. Or perhaps there are older titans waiting to be unearthed. “This paper lays down the gauntlet for us paleontologists to get out there and find them!”

If the food-patch hypothesis is correct, it suggests that ocean ecosystems are “much more productive than they've ever been,” Pyenson said. The implications are awesome and sobering. This means that humans are able to witness the largest critters ever. But it also means that blue whales live on a ecological knife's edge, at the mercy of oceans — increasingly warm, increasingly polluted — that must continue to stay unusually rich.