A tropical rainforest hosts a diverse range of species that can coexist despite competing for the same resources. While previous work has modelled this kind of coexistence based on the rock-paper-scissors game and just three species, a new study has now applied this to a large number of competing species.
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CAMBRIDGE: A new model based on the dynamics of the ‘Rock-paper-scissors' game has been used to explain the stable coexistence of many competing species, and sheds new light on the mechanisms that maintain biodiversity, scientists report.
The new study is the first to model the coexistence of a large number of species competing for the same resources, and reveals the potential for unlimited biodiversity. The authors believe that their mathematical model, published in the Proceedings of the National Academy of Sciences, represents a “generic backbone” of coexistence mechanisms.
“Coexistence is paradoxical in some ways,” explained co-author Stefano Allesina, assistant professor of ecology and evolution at the University of Chicago. “There’s a bit of a clash between the math and the biology, and typically biology wins. So it’s nice that we have a very simple theory … but still can produce results that are very similar to what we observe in the field.”
Rock-paper-scissors explained
It has long been known that when two species compete in isolation, one always wins. But this seems to preclude the coexistence of species that require the same resources. However, when more than two species compete, there is not necessarily a superior overall competitor.
This is similar to a game of Rock-paper-scissors, where one option beats the second, but loses to the third. Previous work shows that this type of intransitive competition stabilises coexistence between species.
“But for some reason,” Allesina said, “[in] all the examples in the literature, there’s just three species competing.” The new model demonstrates that the rock-paper-scissors scenario can be extended to any number of species.
An emergent property of the community
Pairs of competing species were embedded into a network in which no species could out-compete all the others. This set up a complex interplay of rock-paper-scissors games involving random competition for several limiting factors.
After elimination of the weakest species, there was stable coexistence of the remainder; these populations fluctuated indefinitely in regular cycles.
More limiting factors allowed more species to coexist, until this saturated at half the number of the original species pool, regardless of its size. This contradicts traditional models, which predict a limit for coexistence, even when there are more species to begin with.
A new way of thinking about coexistence
Alterations in the model revealed further dynamics. When species hierarchies for different resources were no longer independent, the number of limiting factors required for maximum coexistence changed. And spatially uneven resources increased the final diversity.
The results extend the rock-paper-scissors theory and demonstrate that competitive exclusion can be incorporated into more complex systems that allow the stable coexistence of many species.
Todd Palmer, assistant professor of biology at the University of Florida who studies species coexistence of ants, is excited by the study. “I think it represents a significant advance in how we think about species coexistence,” Palmer said. “It uses a set of realistic assumptions … to show that a large number of species can coexist on a set of resources as a result of the intransitivity that clearly occurs in natural systems.”
Watching the effects of extinction
Allesina says that the model also reveals the extent of interdependence between coexisting species and the delicate balance between them.
“This approach [shows] that coexistence is not a feature of any particular species in itself, but rather it’s an emergent property of the community,” he said. “If one species goes extinct, in this framework it would cause other extinctions.”
The real test of the model is how closely it represents nature. The study showed a good fit to species abundance data from tropical forests, but Allesina plans to use bacteria to test it further. “It will be interesting to see what emerges from empirical tests,” said Palmer. “I think it's a model that has a lot of traction in terms of representing natural systems.”
