Recalculating a 40-Year-Old Ecology Riddle


By Rob Mitchum

In 1972, a physicist named Robert May tried his hand at a different scientific discipline, publishing a simple formula that inflamed the field of ecology. Scientists studying the structure of natural ecosystems had long assumed that diversity was an inherently good thing — those ecosystems stocked with thousands of species were likely more resistant to extinctions, changes in climate, or other challenges. May, with a physicist’s eye for simplicity, crafted a model that predicted the stability of an ecosystem using just the number of species and how strongly they interact with each other. But when it was used, May’s formula provided a surprising and counter-intuitive result: species-rich ecosystems, such as rain forests and coral reefs, should be too unstable to exist.

That paper, published in Nature under the title “Will a Large Complex System be Stable?” (May’s answer: No), was both a major step for computational ecology and the ignition of what came to be called the diversity-stability debate. The disagreement between May’s model and what ecologists saw in reality provoked the question of how nature rescues what should be an unstable ecosystem, allowing it to survive. Ecologists began looking for what May called “devious strategies” — the workarounds that a natural system uses to increase its species capacity without sacrificing its stability. Soon, May’s elegant formula became swollen with additions meant to reconcile the mathematical predictions with field observations.

Stefano Allesina, assistant professor of Ecology & Evolution at the University of Chicago, decided to take a different approach. Rather than building even more complex additions on to May’s model, Allesina and graduate student Si Tang, sharpened their pencils and went back to the original source, tweaking the model by thinking about the general types of ways species interact in nature. Their new model, published 40 years after the original in the same journal, adjusted May’s formula to incorporate predator-prey or consumer-resource relationships, where one species profits at the expense of another. The small changed allowed the model to describe an ecosystem where stability is possible even with an infinite number of species.

“Predator-prey relationships are stabilizing. We can fit much larger ecosystems if there’s a backbone of predator-prey interactions, and see a lot of species happily co-existing ever after,”Allesina said. “We kind of solved this one puzzle of how can we see very many species in an ecosystem. But then we open different puzzles.”

May’s original model, designed to be as general as possible, assumed random interactions between species. But in nature, two species can interact with each other in one of three general ways: as predator and prey, as competitors, or as part of a mutalistic relationship. In the predator-prey or consumer-resource relationship, one species benefits from another species’ loss, be it a lion eating a gazelle or a caterpillar eating a leaf. Competition theoretically has a negative effect on the two species fighting over the same food source, while mutualism (rarely seen in nature) can benefit both participants. By building each of these three relationships separately into May’s model, Allesina and Tang discovered that these interactions each produce very different ecosystems.

In the predator-prey condition, the stability of the ecosystem is increased such that a large number of species can be supported. In the competition and mutualism systems, the ecosystem is highly unstable and vulnerable to perturbation.

“What we are showing is that of all the types of interactions you can have, only predator-prey can support an infinite number of species,” Allesina said. “If you look in nature, there are very obvious consumer-resource relationships everywhere, and maybe this system assembles so easily because these relationships provide a lot of stability.”

But just as the revised version of May’s formula brings it in line with one natural observation, more counter-intuitive results are created. Many ecologists believe that strong interactions between species, such as when a predator relies upon only one prey species for food, make an ecosystem more vulnerable. However, the revised formula predicts that weak interactions, not strong interactions, are destabilizing to a food web.

Another discrepancy occurs when the model is applied to a realistic food-web structure, rather than the theoretical, random structure used as a default. When a commonly observed natural structure — such as the “cascade” model where each predator eats prey smaller than themselves — is tested with the model, the resulting system is less stable than that produced by a random structure.

But like May’s original formula, these disagreements between model and reality offer new opportunities to explore how nature subverts these predictions and produces diverse, stable ecosystems. Many of the “devious strategies” proposed as additions to the original model can now be tested with the revised formula as a reference point.

“I think this is a good step forward, especially because it resuscitates this result that has been so fundamental for theoretical ecology, but no one since has touched it,” Allesina said. “Everybody cited it, and kind of disproved it metaphorically, but it’s nice to go back to the original formulation and extend it.”


Allesina, S., & Tang, S. (2012). Stability criteria for complex ecosystems Nature DOI: 10.1038/nature10832

About Rob Mitchum (525 Articles)
Rob Mitchum is communications manager at the Computation Institute, a joint initiative between The University of Chicago and Argonne National Laboratory.
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