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201505Jan20:08

Ecosys­tems need math­e­mat­i­cal struc­ture, not ran­dom nature, to survive

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pub­lished 05 Jan­u­ary 2015 | mod­i­fied 05 Jan­u­ary 2015
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Marine ecosystemA pre­vi­ously unknown math­e­mat­i­cal prop­erty has been found to be behind one of nature’s great­est mys­ter­ies — how ecosys­tems sur­vive. The appli­ca­tion of this knowl­edge is expected to be impor­tant for future con­ser­va­tion efforts accord­ing researchers led by the Uni­ver­sity of Warwick .

Found in nature and com­mon to all ecosys­tems 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 the math­e­mat­ics researchers, Trophic Coher­ence 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 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”.

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 coher­ence deter­mines food-​web sta­bil­ity, is pub­lished online before print on 2 Decem­ber by the Pro­ceed­ings of the National Acad­emy of Sci­ences (PNAS).




(Source: Uni­ver­sity of War­wick press release, 22.12.2014)


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