Mathematically rainforests and coral reefs should be improbable.
Ecologists always thought that diverse and rich ecosystems were more stable and more resistant to disruption than simple ecosystems. Then in 1972 a model produced by physicist Robert May overturned that and stated that complex ecosystems were not just less stable but statistically should be rare.
Statistically rainforests should not exist.
The problem is that while May’s formula suggests complex ecosystems are not stable or widespread it doesn’t take much looking to see these ecosystems in nature. Coral reefs, rain-forests and even individual trees can have complex ecosystem supporting hundreds or thousands of species and they appear to flourish and be stable.
Squaring the ecological circle.
For 40 years ecologists have tried to square the circle – why does the math show one thing and the real world another?
A new study published in the current issue of Nature seeks to do just that. Researchers Stefano Allesina and Si Tang from the University of Chicago believe that many – though not all – questions raised by the discrepancy can be answered by simple tweaking of the May formula.
This ”diversity-stability debate,” among ecologist has led to the idea that nature operates a number of ‘devious strategies’ in order for it to form complex and improbable ecosystems. This method of dealing with the discrepancy has led to complex qualifiers being used in May’s formula to justify the complexity of ecosystems studied.
“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.“
Revising the May Formula for ecological stability.
What the two researchers did though was rather than add on qualifiers to the formula they took a closer look at the formula itself. They then added a simple adjustment to take into account predator-prey relationships and discovered that this amended formula allows stability in ecosystems with 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,” 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.”
The adjustment to the ecological formula the researchers made was to replace the random distribution of species-species interaction with three general types of relationships observed between species in nature.
Only predator – prey species interactions support complex ecosystems.
The different relationships that were put into the formula and tested individually were:
- predator – prey,
- competition,
- mutualism.
The results were clear. If the original random species interaction was replaced by either competition or mutualism then the ecosystem became highly unstable. When the original random species interaction was replaced by predator-prey relationships then the ecosystem could grow and remain stable.
“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.”
Revised formula raises questions as well as answers them.
While the new adapted formula answers one major riddle of the original theoretical ecosystem model it does raise other questions that ecologists need to answer.
While most ecologists believe that if predators rely on only one prey species – a strong relationship – then the ecosystem is more vulnerable the revised model indicates the opposite. It suggests that strong inter-species relationships make an ecosystem more stable and weak species relationships make a system vulnerable.
Another issue that needs further refinement is about food webs. When the revised formula is tested using real world food web models such as the cascade model – where predators eat smaller species than themselves - it produces less stable ecosystems than when using a random theoretical food web.
“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.”
External web sites:
Nature: Stability criteria for complex ecosystems.
