"They are complete opposites," Speakman said.
As its wing evolved, the penguin would have become a better diver and a worse flyer, until one day the prospect of flying no longer appealed.
Dive-fishing auks are black and white like penguins, but airborne too.
To test the theory the team studied auks, a family of seabirds similar to penguins, that catch fish underwater but can still fly.
Speakman was able to work out how much carbon dioxide the birds produced as they swam, flew, or sat about.
From this, he could extrapolate how much energy these activities needed.
He explained: "We found auks have exceptional diving abilities, almost as good as a penguin, but their flight costs are enormous - the highest ever measured. This matched the theory exactly."
In their ability to fly and dive they were "on the cusp" of becoming like penguins, he said. The great auk, a species hunted to extinction in the 19th century, had already lost the ability to fly, in keeping with the theory.
Had there ever been a flying penguin?
"The fossil record doesn't contain a flying penguin," he said.
"The first one we have was already flightless, and that was about 60 million years ago."
So while it seems extremely mal-adaptive to see emperor penguins wobbling kilometres across the ice to their rookeries, it stems from a trade-off far back in the evolutionary chain in which their wings adapted to their increasingly aquatic environment and they lost the ability to fly.
"When you see them swimming underwater, you truly get a sense of what they gained in return," Speakman said.
• Michael Parker is environment and energy editor at The Conversation.