Ecosystems need maths to survive

Scientists have discovered a previously unknown mathematical property which is behind one of nature's greatest mysteries – how ecosystems survive.

Researchers led by the University of Warwick in UK found that Trophic Coherence is a universal, mathematical property found in each and every ecosystem.

Trophic Coherence is a measure of how plant and animal life interact within the food web of each ecosystem - providing scientists with the first ever mathematical understanding of their architecture and how food webs are able to grow larger while also becoming more stable.

Researchers said Trophic Coherence demonstrates that ecosystems are less random and more structured than had previously been thought.

"Buildings require structural supports, such as the metal or timber frames around which they are then built. For the building to remain standing though these supports need to comply with the laws of mathematics and physics; if the roof is too heavy for the frame, the building collapses," said Dr Samuel Johnson, from Warwick's Mathematics Institute.

"The frames also need flexibility to adapt to conditions, if they are too rigid they become fragile and, for instance, unable to cope with difficult weather.

"The same is true of natural ecosystems; they need support and structure. Trophic Coherence seems to play a similar role in ecosystems as supporting frames of buildings - it is a structural property that helps ecosystems survive, and is common to all the ones we have analysed.

It provides them with essential support and structure," Johnson said.
Although coherence appears to be crucial to ecosystem survival, the researchers argued that this does not imply it was selected by the forces of nature for this purpose.
"Most animals will eat whatever they can, whether or not this is good for their ecosystem," Johnson said.

"But, luckily, coherence emerges from the fact that species tend to consume others which have certain things in common, such as their diet.

"Observed in nature these interactions, which comprise an ecosystem's food web, can look totally random, but if they were truly so then they would collapse.

"In reality, beneath this random facade lays a fundamental mathematical property that helps the ecosystem to survive - this is Trophic Coherence," said Johnson.

"As mathematicians we aim to uncover the underlying patterns in the natural world and ecosystems had been puzzling mathematicians for decades - how can something, which appears to be random and should not be able to survive, actually do so?

"Trophic Coherence allows food webs to become larger while maintaining stability, a bit like flying buttresses were the element needed for cathedrals to do likewise," Johnson said.

The research is published by the Proceedings of the National Academy of Sciences