Why the rock-paper-scissors game explains natural selection

It's time for another apparently ridiculous analogy linking together a basic facet of the natural world with a piece of pop culture ephemera! This time around, rock-paper-scissors explains why three or more competitors for the same resources can coexist forever.

There's a basic rule of thumb in ecology that, if two species are in competition for the same resource, eventually one is going to be more successful and drive the other to extinction. But this doesn't happen in more complicated situations, where anywhere from three to a thousand different species coexist in the same ecological niche. For instance, the Amazon is home to thousands of different tree species, all of which manage to somehow share the same basic resources. So how do they do it?

The answer to this conundrum can be found in rock-paper-scissors. This game is a simple example of what's known as intransitive competition, in which the participants can't actually be ordered from best to worst. For instance, if you had an ecosystem that was just rock and paper, then paper would drive rock to extinction. But adding scissors back into the mix brings them back to an impasse. This stalemate can allow the three competitors to live in harmony pretty much indefinitely.

Now researchers from the University of Chicago and UC Santa Barbara have shown that what works for three species can work for far more complex systems. Co-author Stefano Allesina explains:

"If you have two competitors and one is better, eventually one of the two will be driven extinct. But if you have three or more competitors and you use this rock-paper-scissor model, you can prove that many of these species can co-exist forever. No one had pushed it to the limit and said, instead of three species, what happens if you have 4,000? Nobody knew how. What we were able to do is build the mathematical framework in which you can find out what will happen with any number of species."

In these highly complex systems, biodiversity increases as different species compete for multiple resources. Certain species focus on certain resources, giving them a slight edge, but this is in exchange for weaknesses elsewhere that mean they can't become dominant over the other species. A few of the weakest species die out, but a larger stalemate develops, allowing potentially thousands of species to live on in eternal competition.

Co-author Jonathan Levine explains how even two limiting factors for available resources is enough to ensure the maximum amount of biodiversity:

"What we put together shows that when you allow species to compete for multiple resources, and allow different resources to determine which species win, you end up with a complex tournament that allows numerous species to coexist because of the multiple rock-paper-scissors games embedded within...It basically says there's no saturation. If you have this tradeoff and have two factors, you can have infinite species. With simple rules, you can create remarkable diversity."

And this isn't purely theoretical, as Allesina and Levine were able to successfully reverse-engineer just such a network of interrelated species from observed data sets of tropical trees and marine invertebrates. One thing that the researchers point out is that, for all the immense complexity of these systems, they still can be very fragile, and the removal of even a single species can bring the whole impasse tumbling down:

Allesina: "The fact that many species co-exist could depend on the rare species, which are more likely to go extinct by themselves. If they are closing the loop, then they really have a key role, because they are the only ones keeping the system from collapsing."
Levine:"If you're playing rock-paper-scissors and you lose rock, you're going to end up with only scissors in the system. In a more complex system, there's an immediate cascade that extends to a very large number of species."

Via PNAS.