# Ecosystems need maths not random nature to survive

A previously unknown mathematical property has been found to be behind one of nature's greatest mysteries – how ecosystems survive.

Found in nature and common to all the property, 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.

Identified by researchers led by the University of Warwick, Trophic Coherence's identifiers argue that it demonstrates that ecosystems are less random and more structured than had previously been thought. Trophic Coherence was found to be a universal, mathematical property found in each and every ecosystem.

Dr Samuel Johnson, from Warwick's Mathematics Institute, explains:

"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. 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 ; 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".

Although coherence appears to be crucial to ecosystem survival, the researchers argue 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. 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 façade lays a fundamental mathematical property that helps the ecosystem to survive – this is Trophic Coherence", says Dr 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".

Knowing whether a given ecosystem is likely to become more or less stable if it lost certain species is, the researchers argue, important for conservation efforts. The results may also find potential application in fields such as finance and engineering, where understanding the relation between size and stability in interconnected systems is often paramount.

The research, titled Trophic determines stability, is published by the Proceedings of the National Academy of Sciences (PNAS).

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Dec 22, 2014
You mention finance as another potential field of application. Might I also suggest the more general field of economics as what we are working with now, capitalism, is not working very well- it is generally unstable, tends to concentrate rather than disperse/distribute resources thereby undermining renewal and making it not particularly sustainable because of growing inequities, a type of metastasis I have heard it called. To those who say the last 100 - 200 years demonstrates otherwise, also recall that that is nothing more than a blink in the geological time scale which is relevant to species survival, let alone our civilization.

Dec 22, 2014
capitalism, is not working very well- i

Because it is NOT capitalism. It is socialism and socialism has been demonstrated to fail.

Just as Trophic Coherence, will be shown to fail.

Deterministics keep looking for the magic formula that can predict all.

"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"."

That's because engineers didn't know any better at the time. Not a great analogy.

Dec 23, 2014
Great theoretical work

Right, THEORY.

The Limist to Growth was a failed theory, too.

Knowing whether a given ecosystem is likely to become more or less stable if it lost certain species is, the researchers argue, important for conservation efforts.

Like the Models of Doom, the purpose of this theory is to justify more govt 'action' to 'save the planet'.

The results may also find potential application in fields such as finance

Matlab was being used in the financial world leading up to the collapse of the real estate market. That theory didn't hold up well for most of us.

Dec 25, 2014
capitalism, is not working very well- i

Because it is NOT capitalism. It is socialism and socialism has been demonstrated to fail.

Has there ever been any economic system that was actually implemented which you would consider to be capitalism? Because if not, then there are two possibilities:
1) Capitalism is just a Platonic ideal to you, which would work if it were ever tried, definitely, but nobody has ever had the guts. That is the same claim that die-hard socialists make about socialism.
2) This is a case of the no true Scotsman fallacy. You wait to see whether an economic system fails your standards, and if it does, you declare it socialism.

Just as Trophic Coherence, will be shown to fail.

Finally, a claim with scientific content, IF you have an argument. Do you?

Dec 25, 2014
Matlab was being used in the financial world leading up to the collapse of the real estate market. That theory didn't hold up well for most of us.

MatLab is a software package, not a scientific theory. There is a bit of a difference.

Dec 25, 2014
The closest to capitalism in the USA was occurring in the later half of the 1800s.

There are market segments in the US that have been able to escape the regulatory state, for a time, and have created great wealth.
The computer industry has been one of those and has escaped partly because it moves so quickly.
We are now seeing capitalism and the regulatory state clashing with the new online ride sharing companies.

Dec 25, 2014
MatLab is a software package

Most who use Matlab are engineers.
As the govt promoted housing bubble began to inflate, Matlab experts were enticed into analyzing and predicting the risks of securitized mortgages and attempting to quantify and mitigate that risk.
But, with all computer code, garbage in, garbage out and that garbage out provides a false sense of security, until reality hits.

Dec 25, 2014
"Before the collapse, Carnegie Mellon's alumni in the industry were telling me that the level of complexity in the mortgage-backed securities market had exceeded the limitations of their models. The bridge was cantilevered out way too far, and the quants knew it. But in most banks, the quants are not the decision-makers. When they issue warnings that stand in the way of profits, they are quickly brushed aside. Furthermore, in addition to better engineering, the bridge must not be built this time with the shoddy construction material of no-documentation mortgage applications and a network of unscrupulous mortgage originators."
"the surest way to repeat this disaster is to trust the models blindly while taking large-scale advantage of situations where they seem to provide trading strategies that would yield results too good to be true. "
http://www.forbes...eve.html

Biologists have discovered 'quants'.

Dec 26, 2014
The closest to capitalism in the USA was occurring in the later half of the 1800s.

So what made that closest to capitalism, how did that contribute to success, and what is your measure of success?

And what does any of this have to do with trophic coherence? You remember, the topic of the article you commented on? What you said would fail? Surely you had a reason for saying so?

Dec 26, 2014
MatLab is a software package

Most who use Matlab are engineers.
As the govt promoted housing bubble began to inflate, Matlab experts were enticed into analyzing and predicting the risks of securitized mortgages and attempting to quantify and mitigate that risk.

Expertise in using MatLab is not the relevant expertise. If these analysts had written their code in C++ or Phython or even Fortran, then if their code implemented the same equations or simulations, the output would have been the same. Do you honestly claim you can't see the difference between the programming environment used and what is being programmed?

Dec 26, 2014
"Before the collapse, Carnegie Mellon's alumni in the industry were telling me that the level of complexity in the mortgage-backed securities market had exceeded the limitations of their models. The bridge was cantilevered out way too far, and the quants knew it. But in most banks, the quants are not the decision-makers.

Previously you wrote
That theory didn't hold up well for most of us.

Now you say the theory was fine in that it was clear where its limits were, but the managers chose to ignore those limits. What incentives made them do so? I trust you are not telling me it was a market failure.

Dec 26, 2014
So what made that closest to capitalism,

Limited government interference in the market.
the output would have been the same

Sure, but Matlab is convenient to use.
the theory was fine

The theory was not fine.
Too many will assume a computer model IS theory (AGWites, etc.) without understanding its limits. Especially if the results are what they want to hear.

Dec 26, 2014
Why do I suggest trophic coherence is wrong?
This analogy:

"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".

And this:

"The fact that large, complex ecosystems are particularly robust is mysterious in the light of mathematical arguments that suggest they should be unstable;"

http://www.pnas.o...abstract

"better statistical predictor of linear stability "
Why only 'linear stability'?

Dec 26, 2014
One other annying bit is the hubris of the headline.
'Ecosystems need maths'?
Ecosystems don't need maths and have done what they have done for billions of years without the invention of maths.
(Unless the authors suggest that God has been the underlying 'maths' behind ecosystems.)

Why won't the authors state the reality? "Maths have failed to model ecosystems and now, maybe, this new model may do a better job."
Why is it so difficult for 'science' to acknowledge inadequacy?

Dec 28, 2014
So what made that closest to capitalism, how did that contribute to success, and what is your measure of success?

Because the state was not plundering wealth and directing research, development and ingenuity, individuals were able to invent and create new industries that enabled hundreds of millions of people to create wealth and rise out of poverty.

What new industry has been created in the past few decades that did not have its origin in the later half of the 1800s?

Nuclear energy may be the only industry that was invented in the 20th century, but because it has been under the control of the state, it has not been allowed to grow.

Heavier than air craft first flew in early 20th century, invented by two bicycle mechanics powered by fossil fueled internal combustion engines.

Why did it take over 100 years for a private individual to build a plane that could go into space?

Dec 28, 2014
Why won't the authors state the reality? "Maths have failed to model ecosystems and now, maybe, this new model may do a better job."

This does make sense inasmuch as math is a construct of human mind... the forest is the real thing...

Dec 28, 2014
Heavier than air craft first flew in early 20th century, invented by two bicycle mechanics powered by fossil fueled internal combustion engines.

Might want to back-check with Wikipedia on that statement...

Dec 28, 2014
Heavier than air craft first flew in early 20th century, invented by two bicycle mechanics powered by fossil fueled internal combustion engines.

Might want to back-check with Wikipedia on that statement...

Which part?

Dec 28, 2014
Who is trying to make 'unobtainium'? The movie, The Core, must have been written by an engineer as the 'ship' used to travel to the core was made of 'unobtainium'.
If someone could make a material lighter, stronger,...better and cheaper that could replace steel, titanium, aluminum, beryllium, ....and at lower cost, say 'unobtanim', and refused to patent the process and kept it proprietary, and captured most of the world market, what would govts do?
As Ayn Rand speculated in 'Atlas Shrugged' with Rearden metal, the govt finally resorted to blackmail to force Rearden to sign away his rights to his invention.
The US govt punished Rockefeller for capturing the kerosene market by making a better, cheaper product.
Govt power during the late 1800s in the US was limited enabling inventors like Bell, Edison and Tesla to create and profit from their inventions.
Today, the state's power to confiscate wealth and inventions punish those who risk and innovate.

Dec 29, 2014
Heavier than air craft first flew in early 20th century, invented by two bicycle mechanics powered by fossil fueled internal combustion engines.

Might want to back-check with Wikipedia on that statement...

Which part?

And unobtainium was also what they wanted to mine in "Avatar".

Dec 29, 2014
Which part of 'powered flight'?

Why not address the point, WG?

And if you can't figure out the point, I will be explicit, socialism destroys innovation.

Dec 29, 2014
Which part of 'powered flight'?

Why not address the point, WG?

And if you can't figure out the point, I will be explicit, socialism destroys innovation.

just that it wasn't the first powered flight.
And it doesn't destroy it - just maybe slows it down some...
so that people don't pay for a new innovation on Tuesday and have to buy a new one by the following Tuesday. Reads kinda like capitalism, doesn't it...

Dec 29, 2014
Depends upon what source you use to define powered, heavier than air flight.
The Smithsonian credits the Wright Brothers.

Dec 30, 2014
Actually.... Random systems don't need maths...
Maths need random systems to find coherence in...

Dec 31, 2014
@Sigh

"Alfred N. White­head said in his Dialogues, "One of the happiest times in the his­tory of mankind was the 30 years roughly from 1880 to 1910." That was surely about the peak of lib­erty and contentment for Ameri­cans."
http://fee.org/fr...progress

Dec 31, 2014
@Sigh

"Alfred N. White­head said in his Dialogues, "One of the happiest times in the his­tory of mankind was the 30 years roughly from 1880 to 1910." That was surely about the peak of lib­erty and contentment for Ameri­cans."

So... the main portion of his adult years.... Well, at least HE was happy for that time...
Cept for the divorce, car accident, bankruptcy and ungrateful kids, I think it was the forty years from 1976 to 2014...

Anyway... Happy New Year, all !