Mathematically speaking , the way a tiger charges a herd of antelope resembles a white line of descent cadre assail a colony of bacteria . That ’s the conclusion ofa new paperby an international team of physicists , just published in Journal of Physics A : Mathematical and Theoretical .
This , in turning , could shed light on the intricate dynamics of animal conduct , as well as how bacterial invader can evade attack and survive despite the proficient travail of the immune system . “ We would anticipate this to be a fairly just estimation for many animals , ” go author Ralf Metzler , of the University of Potsdam in Germany , said in a command .
predatory animal / prey mathematical models are much a workhorse in fields like ecology , biological science , and epidemiology , render a ready to hand means of studying how nature maintains an ecological residue . For lesson , members of the ill-famed Cordyceps kinfolk of fungi — over 400 dissimilar metal money in all — targetvarious worm populations(ants , mosquito hawk , cockroaches , aphids , or mallet , ordinarily ) .

The fungus strewing spores into the aviation , which commonwealth on a legion ’s body , work its way within and sprouting long tendril reaching into the host ’s brain . Then it releases chemicals that turn the poor host into the fungi ’s zombie slave . The fungus slowly eat up the brainiac , until itbursts through the host ’s head , scattering even more spore into the air to infect more unsuspecting host . It ’s pretty horrible , particularly for this pathetic bullet ant :
But Cordyceps serves an important purpose : controlling the population of various pests . The dynamics play out something like this . If , say , an ant universe grows so much that it peril to drown the uncommitted resourcefulness to get the colony , the fungus universe will also come out to increase , gradually thinning out the herd , so to speak . The ant population begins to diminish , meaning there are few host for the fungi to infect , so their numbers also decrease . Then the ants start multiply , and the whole bicycle start all over again .
That ’s one edition of a vulture / quarry model . Metzler and his colleaguesopted for a different version : that of a single marauder hunting a herd of prey . Think of a lion or Panthera tigris chasing after an antelope herd , or a wolf charging a muckle of sheep — or even a white blood jail cell homing in on a settlement of bacteria .

Their analysis revealed two different phases of the hunting process . At first , the predator ’s motion is best identify by a so - calledrandom pass , as it explore for its prey . This involvessearching a bit in one place , then moving to another potential situation nearby and searching there , and so on . This is also a good foraging strategy for the fair game .
Once the marauder has pick out the prey , however , the dynamics transfer to more of a ballistic flight : the Panthera tigris now wants to exit the distance between itself and its target as chop-chop as potential , while the target wish to evade the attack , start evasive simulated military operation in response .
The researchers found that the appoint tiger and the quarry now move as if connect by a spring ( see top image ) . Chances are you larn aboutHooke ’s Lawin skill class : the force take to pass or squeeze a spring by a given distance is proportional to that length . The Panthera tigris commission , the antelope start to zigzag and scatter to bilk the attack , and when the Panthera tigris finally closes the space , an antelope falls .

credit line of sight turns out to be pretty key to how those moral force play out — the best the prey is capable to spy encroach predators , the better its chances of survival . So the physicist added this element to their model . astonishingly , they found that the predator ’s eyesight is n’t as critical . piranha do good more from poor seeing of the quarry than from any improved visual modality of their own .
And sometimes particularly large herds can get in each other ’s way as they clamber to escape a charging predator . Other studies have found that herds can increase their selection odds by clustering in ways that optimize potential escape road . Maybe that ’s how certain bacterial colonies manage to make it a white blood mobile phone ’s attack .
It ’s just one more example of the mightiness of mathematics to tease out hidden connexion between systems that seem on the Earth’s surface to have nothing in common at all .

[ Journal of Physics A : Mathematical and Theoretical ]
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