(Not  too)  few  but  capable    

   The  scarcity  of  “knowledgeable  elders”  may  have  devastating  consequences    March  20,  2104  

 Small  changes  in  a  population  may  lead  to  dramatic  consequences,  like  the  disappearance  of  the  migratory  route  of  a  species.  A  study  carried  out  in  collaboration  with  the  SISSA  has  created  a  model  of  the  behaviour  of  a  group  of  individuals  on  the  move  (like  a  school  of  fish,  a  herd  of  sheep  or  a  flock  of  birds,  etc.)  which,  by  changing  a  few  simple  parameters,  reproduces  the  collective  behaviour  patterns  observed  in  the  wild.  The  model  shows  that  small  quantitative  changes  in  the  number  of  knowledgeable  individuals  and  availability  of  food  can  lead  to  radical  qualitative  changes  in  the  group’s  behaviour.    

 Until  the  ’50s,  bluefin  tuna  fishing  was  a  thriving  industry  in  Norway,  second  only  to  sardine  fishing.  Every  year,  bluefin  tuna  used  to  migrate  from  the  eastern  Mediterranean  up  to  the  Norwegian  coasts.  Suddenly,  however,  over  no  more  than  4-­‐5  years,  the  tuna  never  went  back  to  Norway.  In  an  attempt  to  solve  this  problem,  Giancarlo  De  Luca  from  SISSA  (the  International  School  for  Advanced  Studies  of  Trieste)  together  with  an  international  team  of  researchers  (from  the  Centre  for  Theoretical  Physics  -­‐  ICTP  –  of  Trieste  and  the  Technical  University  of  Denmark)  started  to  devise  a  model  based  on  an  “adaptive  stochastic  network”.  The  physicists  wanted  to  

simulate,  simplifying  it,  the  collective  behaviour  of  animal  groups.  Their  findings,  published  in  the  journal  Interface,  show  that  the  number  of  “informed  individuals”  in  a  group,  sociality  and  the  strength  of  the  decision  of  the  informed  individuals  are  “critical”  variables,  such  that  even  minimal  fluctuations  in  these  variables  can  result  in  catastrophic  changes  to  the  system.    “We  started  out  by  taking  inspiration  from  the  phenomenon  that  affected  the  bluefin  tuna,  but  in  actual  fact  we  then  developed  a  general  model  that  can  be  applied  to  many  situations  of  groups  “on  the  move”,  explains  De  Luca.      The  collective  behaviour  of  a  group  can  be  treated  as  an  “emerging  property”,  that  is,  the  result  of  the  self-­‐organization  of  each  individual’s  behaviour.  “The  majority  of  individuals  in  a  group  may  not  possess  adequate  knowledge,  for  example,  about  where  to  find  rich  feeding  grounds”  explains  De  Luca.  “However,  for  the  group  to  function,  it  is  enough  that  only  a  minority  of  individuals  possess  that  information.  The  others,  the  ones  who  don’t,  will  obey  simple  social  rules,  for  example  by  following  their  neighbours”.      More  in  detail    The  tendency  to  comply  with  the  norm,  the  number  of  knowledgeable  individuals  and  the  determination  with  which  they  follow  their  preferred  route  (which  the  researchers  interpreted  as  being  directly  related  to  the  appeal,  or  abundance,  of  the  resource)  are  critical  variables.  “When  the  number  of  informed  individuals  falls  below  a  certain  level,  or  the  strength  of  their  determination  to  go  in  a  certain  direction  falls  below  a  certain  threshold,  the  migratory  pathway  disappears  abruptly”.      “In  our  networks  the  individuals  are  “points”,  with  interconnections  that  form  and  disappear  in  the  course  of  the  process,  following  some  established  rules.  It’s  a  simple  and  general  way  to  model  the  system  which  has  the  advantage  of  being  able  to  be  solved  analytically”,  comments  De  Luca.      So  what  ever  happened  to  the  Norwegian  tuna?  “Based  on  our  results  we  formulated  some  hypotheses  which  will,  however,  have  to  be  tested  experimentally”,  says  De  Luca.  In  the’50s  Norway  experienced  a  reduction  in  biomass  and  in  the  quantity  of  herrings,  the  main  prey  of  tuna,  which  might  have  played  a  role  in  their  disappearance.    “This  is  consistent  with  our  model,  but  there’s  more  to  the  story.  In  a  short  time  the  herring  population  returned  to  normal  levels,  whereas  the  tuna  never  came  back.  Why?”    One  hypothesis  is  that,  although  the  overall  number  of  Mediterranean  tuna  has  not  changed,  what  has  changed  is  the  composition  of  the  population:  “The  most  desirable  tuna  specimens  for  the  fishing  industry  are  the  larger,  older  individuals,  which  are  presumably  also  those  with  the  greater  amount  of  knowledge,  in  other  words  the  knowledgeable  elders.”  concludes  De  Luca.    Another  curious  fact:  what  happens  if  there  are  too  many  knowledgeable  elders?  “Too  many  know-­‐alls  are  useless”,  jokes  De  Luca.  “In  fact,  above  a  certain  number  of  informed  individuals,  

the  group  performance  does  not  improve  so  much  as  to  justify  the  “cost”  of  their  training.  The  best  cost-­‐benefit  ratio  is  obtained  by  keeping  the  number  of  informed  individuals  above  a  certain  level,  provided  they  remain  a  minority  of  the  whole  population”.      

IMAGE:  

• Tuna  specimens  (credits:  Takashi  Hososhima  -­‐  http://bit.ly/1mu5px4)    

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