For three weeks starting tonight, the attention of sports fans around the country will be on the brackets of the NCAA Basketball Tournament as 68 teams are methodically reduced to one champion. The process is somewhat similar to evolution, as a combination of direct competition and environmental luck (determined by a team’s seeding and the results in other games) helps whittle down the field in a survival of the fittest fashion – no wonder the bracket is initially set by the NCAA Selection Committee. Nature, it turns out, conducts its own tournaments to determine which species in a given ecosystem will live on and which will go extinct. Only in this game, it’s a little harder to keep score.
Rock-Paper-Scissors is best known as a childhood playground game, one that gets old once the players realize that no clear winner will ever emerge. But that indecisive quality attracted researchers Stefano Allesina and Jonathan Levine to the simple game as a potential explanation for one of ecology’s greatest mysteries: biodiversity. The ability of similar species to occupy similar niches within an ecosystem has long baffled ecologists, since evolutionary competition between the species should eventually produce a surviving winner and an extinct loser. But in systems like the Amazon, thousands of species appear to have struck a truce, peacefully co-existing.
Yet what looks like peace on the surface may merely be the result if constant rock-paper-scissors-like tournaments behind the scenes, Allesina and Levine report this week online at Proceedings of the National Academy of Sciences. The game is an example of an intransitive relationship, where none of the three options can achieve total dominance: rock beats scissors, scissors beats paper, and paper beats rock. That kind of relationship has been observed in nature, for trios of lizards or bacterial species. But what about intransitive relationships with more than three participants – the rock-paper-scissors-dynamite and beyond of nature?
“No one had pushed it to the limit and said, instead of three species, what happens if you have 4,000? Nobody knew how,” said Allesina, assistant professor of ecology and evolution at the University of Chicago. “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.”
Allesina and Levine built their model to simulate the outcome when different numbers of species compete for various amounts of “limiting factors” with variable success. An example, Allesina said, is a group of tree species competing for multiple resources such as nitrogen, phosphorus, light, and water. Some trees may be better at obtaining nitrogen from the soil, while others may have better access to water or light.
When such a complex model is simulated over time, some weaker species lose and go extinct. But many species remain – some common, some rare, but all balanced in a state of equilibrium. With each additional limiting factor added into the model, more species are able to survive, producing robust biodiversity despite constant competition.
“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,” said Levine, professor of ecology, evolution & marine biology at the University of California, Santa Barbara.
From running the model, the researchers discovered several interesting new rules for ecology. Most importantly, they found that biodiversity is essentially limitless with enough limiting factors; the more species they started with, the more species would survive to reach a “rock-paper-scissors” equilibrium. Even a very simple system can produce unlimited diversity. When species experience a “trade-off” in competing for limiting factors – for example, being good at collecting nitrogen makes a species bad at collecting phosphorous, and vice versa – a mere two limiting factors are required to achieve maximal biodiversity.
“It basically says there’s no saturation,” Allesina said. “If you have this tradeoff and have two factors, you can have infinite species. With simple rules, you can create remarkable diversity.”
Running the model predicts population densities for each species in a given ecosystem, and Allesina and Levine were able to backwards test their results by taking real-world population data on tropical forest trees and marine invertebrates and reverse-engineering the competition network. The next step is seeing whether the computer model can forward-predict the outcome of a pre-assembled ecosystem, an experiment Allesina will run with bacterial species thanks to a grant from the James S. McDonnell Foundation.
In the meantime, the rock-paper-scissors model proposes new ideas about the stability of ecosystems – or the dramatic consequences when only one species in the system is removed. A rare species that may hardly be noticed could in fact be a key player in preserving the ecosystem’s balance, and removing any species from the network could have dramatic consequences for the entire tournament.
“If you’re playing rock-paper-scissors and you lose rock, you’re going to end up with only scissors in the system,” Levine said. “In a more complex system, there’s an immediate cascade that extends to a very large number of species.”