A certain amount of nonsense has been written about duck-sized horses and horse-sized ducks, and it’s time to set the record straight.

In an online Q&A session back in August, President Obama was asked, “Would you rather fight 100 duck-sized horses or one horse-sized duck?” The Atlantic wrote a cheerful article about Obama’s choice (horse-sized duck), but the biologists they hastily recruited as fact-checkers were obviously operating outside their specialty. I feel it’s rather a shame Obama staffers neglected to consult me, as that question was, in essence, my PhD topic; I could have given the President better advice, and explained why his intuition—that a single giant duck would be an easier fight—is wrong, wrong, wrong.

The Fight

Ground rules: in the immortal tradition of Flash Gordon or Star Trek, the President finds himself alone in an arena, armed only with what he can improvise (“Your drones will not help you now, Mr President”). He’s faced with two doors: behind each are the opponent(s) he must defeat in order to, I don’t know, save the Earth. Which should he choose?

Horse-Sized Duck

A good-sized horse weighs 500 kg, or half a metric ton. What would a half-tonne duck look like, exactly? The problem is most people aren’t thinking of the biological scaling laws, known as allometry, that come into play when you make animals larger or smaller. While I’m sure John Eadie, the conservation ecologist quoted by The Atlantic, knows his field, he’s just wrong to imagine a giant duck would be dealing terrible blows with its enormous wings. It would be flightless, and its wings would be reduced to tiny stubs or have vanished altogether.

The closest thing to half-tonne ducks we have in the fossil record are Gastornis, sometimes known as Diatryma, from Europe and North America, and the dromornithids of Australia. Both were gigantic moa-sized birds, related to ducks and geese, with huge sturdy legs and gigantic sharp beaks. They’re sometimes thought to be scavengers or fruit-eaters, but were likely predators similar to the better-known but unrelated phorusrachids of South America. Dromornis stirtoni, one of the largest birds ever, approached 500 kg and has even been nicknamed “the demon duck of doom” by Australian paleontologists, in their playful way.

Duck-Sized Horses

What’s a typical duck? I had to measure many, many duck bones to come up with a model for estimating body mass from femur diameter. There are over 100 species of ducks, and they range from less than 300 g (10 ounces) to about 4 kg (9 lbs); the “average duck” weighs about 700 g, the same as a guinea pig. That’s smaller than you would think, but more of a bird’s volume is made up of feathers than most people realise, now that we no longer pluck our own game.

What would a duck-sized horse look like? The smallest horse that springs to mind for most people is the ancestral Eohippus, famously “fox-terrier” sized, but actually about 30 kg according to more recent models (such as MacFadden’s in his 1994 book on fossil horses), so about 40 times too large for our purposes. When we scale animals up and down in size, allometry—the laws of physics—has far more effect on their appearance than their ancestry does. A dog-sized horse has body proportions about that of a dog; a guinea-pig sized horse would look pretty much like a guinea pig.

Wouldn’t about 100 of them be fairly formidable, though? The herding behaviour of horses and other large herbivores lets them spot predators and defend themselves if necessary, but that only works if predators are roughly the same size as them. For a predator 100 times your size, the only response is not to try and swarm it, but to flee in terror.

Conclusion

President Obama weighs about 80 kg. Should he try to take down a 500 kg bird, with its powerful kick and huge razor-sharp beak, using just his bare hands? Or should he rather face 70 kg of terrified guinea pigs, which would require nothing but stout footwear? If the Earth’s fate is in the balance, the choice is clear, and it’s a specific instance of a general law I once came up with: nothing in evolution (or imaginary arena combat) makes sense except in the light of allometry.