Big antlers shouldn’t exist. This math model explains why they do

The biggest isn’t necessarily the best when it comes to deer antlers and lion manes, based on a new mathematical model from researchers at Northwestern University. The calculations address why animal ornamentation exists at all — a question that stumped evolutionary luminary Charles Darwin, who once wrote, “The sight of a feather in a peacock’s tail, whenever I gaze at it, makes me sick.”

The new research, published in Proceedings of Royal Society B, shows that ornaments straddle a divide. Some animals go big, while the rest prefer small to protect a portion of the population from the negative ramifications of showing off.

Ornaments are costly. A peacock’s colorful train, for instance, expends lots of nutrients to grow and sustain its flush of feathers, which takes away energy for foraging and hiding from predators. It’s counterintuitive, and fewer should survive to reproduce.

Yet animal ornaments are attractive to the opposite sex, meaning in these cases, natural selection or survival is at odds with sexual selection. In 1975, biologist Amotz Zahavi explained this phenomenon in a hypothesis called the handicap principle: The fitter an animal, the more he can afford to waste on costly ornaments that signal his health status to potential mates.

Mathematician Danny Abrams and his colleagues at Northwestern decided to put this concept to the test by plotting ornament sizes from fifteen species onto graphs. The researchers used data on the length of dung beetle horns, the body size of salmon, the duration of fiddler crab fights, the antlers of roe deer and other ornamentation among birds, mammals, insects and fish.

“You would expect most measurements of animal characteristics to be sort of evenly distributed,” Abrams said. Take cat ears for example. If you examined random populations of cats, their ear sizes would most likely fit on what’s called a bell curve — with fewer on each side of the spectrum and a bulge caused by more landing in the middle.

“That’s why it was very surprising that for ornaments we came up with a different distribution, with two peaks,” Abrams said.

Rather than follow a bell curve, many ornaments among the species examined in the study followed a pattern marked by two pinnacles. Those peaks represented groups with large ornaments and those with small ornaments. Few members landed in the middle, with average-sized ornaments. This pattern applied to mature lions, great tits, yellow-breasted chats, dung beetles and earwigs.

The researchers argue this “bimodal distribution” — a dataset with two peaks — might exist in nature because individuals with smaller ornaments offer contrast to the impressive size of their counterparts. Abrams likens this idea to marketing: You can either spend a lot on advertising a product, or you can have a cheaper product, but it’s bad to be in the middle.

Carl Bergstrom, a biologist at University of Washington who wasn’t involved in the study, offered an alternative rationale.

“For whatever reason, there can be a slight female preference for some kind of ornament. So then males who have that ornament do better, and then the offspring of those males also inherit their mother’s genes for having a preference for that ornament,” Bergstrom said. “The trait and the preference evolve hand in hand and become more extreme.”

So the next time you see a buck with little antlers in the woods, don’t think him inferior. He may be less attractive to females, but he might live longer–with a smaller chance of getting his antlers caught in a tree and less of a chance to ending up as a trophy on your wall.