A classic model for ecological stability revised, 40 years later

February 19, 2012

A famous mathematical formula which shook the world of ecology 40 years ago has been revisited and refined by two University of Chicago researchers in the current issue of Nature.

In 1972, physicist Robert May rankled ecologists by publishing a simple model describing the relationship between diversity and stability in a theoretical ecosystem. Though ecologists had long believed that richer, more diverse environments were inherently more resistant to disruption, May's formula argued that more in fact creates more instability.

But rich exist in nature, such as those found in or rain forests. For 40 years, ecologists have attempted to expand May's formula to explain how these highly diverse natural systems persist. For the new paper, University of Chicago researchers Stefano Allesina and Si Tang returned to the original equation, and with small mathematical tweaks, reconciled the disagreement between theory and reality.

Adjusting May's formula to incorporate predator-prey or consumer-resource relationships, where one species profits at the expense of another, allows the model to describe an ecosystem where stability is possible even with an 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," said Allesina, PhD, assistant professor of Ecology & Evolution at the University of Chicago. "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, also published by Nature, sought to challenge the ecological belief that diverse ecosystems were more resistant to perturbations such as invasive species or abrupt climate change. With his physics training, May set out to create a model of the relationship between diversity and stability with the fewest possible factors, settling upon a model that used only the number of species and the strength of their interactions with each other.

The surprising result of May's model was that large or complex ecosystems were so unstable that their existence was statistically improbable. While that conclusion did not match what ecologists observe in natural systems such as rain forests, which may contain thousands of species in a single tree, the model challenged the simplistic assumption of more diversity leading to more stability.

"May made the beautiful point that nature must adopt some 'devious strategies' to cope with this fact, because if mathematically there is this impossibility of complexity, how come we then observe it in nature?," Allesina said. "It must be that nature uses some sneaky way to violate this rule."

May's article launched the "diversity-stability debate," as ecologists proposed many such "devious strategies" to explain the persistence of rich ecosystems in nature by adding complex qualifiers to his formula. Instead of following this trend, Allesina and Tang went back to the original model and made a small adjustment. They replaced the random species interactions of May's model with three general types of relationships observed between species in nature.

In the "eat-or-be-eaten" world of a predator-prey relationship, one species (the predator) benefits while another species (the prey) suffers a loss of fitness. A competitive relationship between two species can have a negative effect on both, while a relationship of mutualism produces a positive effect for the two species involved.

When each of these interactions is inputted separately into May's formula, the predicted stability for a given number of species changes from his original calculation using a random distribution of species-species interaction. 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 an ecosystem.

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 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."

Explore further: Scientists find universal rules for food-web stability

More information: The paper, "Stability criteria for complex ecosystems," will be published online February 19th by Nature at doi:10.1038/nature10832

Related Stories

Scientists find universal rules for food-web stability

August 6, 2009

The findings, published in this week's issue of Science, conclude that food-web stability is enhanced when many diverse predator-prey links connect high and intermediate trophic levels. The computations also reveal that small ...

Rock-paper-scissors tournaments explain ecological diversity

March 14, 2011

According to classical ecology, when two species compete for the same resource, eventually the more successful species will win out while the other will go extinct. But that rule cannot explain systems such as the Amazon, ...

Stability and Diversity in Ecosystems

August 3, 2007

Is biodiversity important for predicting human impacts on ecosystems? If diverse ecosystems were as a consequence more stable, the answer would be yes.

Study: Ecological effects of biodiversity loss underestimated

November 30, 2010

Children aren't the only youngsters who are picky eaters: More than half of all species are believed to change their diets -- sometimes more than once -- between birth and adulthood. And a new study by ecologists at Rice ...

Recommended for you

What humans and primates both know when it comes to numbers

January 18, 2017

For the past several years, Jessica Cantlon has been working to understand how humans develop the concept of numbers, from simple counting to complex mathematical reasoning. Early in her career at the University of Rochester, ...

Male baboons found to engage in feticide

January 18, 2017

(Phys.org)—A team of researchers from several institutions in the U.S., some with ties to the Institute of Primate Research, National Museums of Kenya, has found that male baboons in the wild at times engage in feticide. ...

'Molecular scissors' could point the way to genetic cures

January 18, 2017

Guan-En Graham is determined to find out exactly what happened to her father. When she was a child, he developed brain cancer. Since then, she has worked to understand the intricate genetic mechanisms that trigger brain diseases ...

Decoded microbial metabolism explains biofuel yield

January 18, 2017

To unravel how intricate waste biomass converts to biofuels, a Cornell professor studied the bacterium Clostridium acetobutylicum to decipher its metabolism. Understanding the bacterium's sugar-processing complexities may ...


Adjust slider to filter visible comments by rank

Display comments: newest first

3 / 5 (2) Feb 19, 2012
the article says: "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," said Allesina, PhD, assistant professor of Ecology & Evolution at the University of Chicago."

In real-time real-life ecosystems the predator-prey relationship systematically evolves into an improved hunter/hunted survival technique for both. A predator has to develop the best hunting skills including cunning, perception and adaptation to the conditions of the chase. The prey, on the other hand, also has to develop the same skills, although the skills are for the benefit of its survival and also include greater speed and subterfuge. Each side has its own strategy for accomplishing its task; the one to acquire a meal and the other to avoid becoming a meal. In real life conditions, the strategies work well for both predator and prey, even though one or the other may be unsuccessful
3 / 5 (2) Feb 20, 2012
This "theoretical ecology" that's spoken of in the article is nonsense. There are just too many variables that come into play in a proper predator/prey ecosystem whether on paper or in real life. It doesn't even mention the disruption when humans enter the ecosystem and, for example, shoot coyotes who would ordinarily prey on rats and jackrabbits just because they have killed and eaten some chickens on someone's farm. The disruption's cause and effect does more harm than good because the rats and jackrabbits will then have a population explosion with less coyotes to keep their population in check. I tend to agree more with Robert May's original formula. Too much diversity can be disastrous. A good example to prove that is the Everglades ecosystem in Florida, where pythons were introduced and have been systematically eating the natural fauna who have no survival techniques to avoid being eaten by pythons. That does not fit into any other formula that I know of, but I'm not an expert.
3.9 / 5 (7) Feb 20, 2012
This "theoretical ecology" that's spoken of in the article is nonsense. There are just too many variables that come into play in a proper predator/prey ecosystem - WhatsNewPussycat

But that's the whole idea - to reduce systemic noise and to zero in on the signal. You don't need to model the behavior of every water molecule to make useful calculations with fluid dynamics equations.
1 / 5 (4) Feb 20, 2012
Newtons laws of motion are just nonsense. They don't even begin to address the many variables that come into play in a proper physical system weather on paper or real life.

"This "theoretical ecology" that's spoken of in the article is nonsense. There are just too many variables that come into play in a proper predator/prey ecosystem whether on paper or in real life." - Pussycat

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.