Os padraµes matema¡ticos desenvolvidos por Alan Turing ajudam os pesquisadores a entender o comportamento das aves
A equipe rastreou os pa¡ssaros ao redor do Vale Rivelin de Sheffield, que eventualmente produziu um padrãona paisagem, usando a matemática que ajudou a equipe a revelar os comportamentos que causam esses padraµes.
![](data:image/jpeg;base64,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)
Domanio paºblico
Cientistas da Universidade de Sheffield usaram modelagem matemática para entender por que bandos de tetas-de-cauda-longa segregam-se em diferentes partes da paisagem.
A equipe rastreou os pa¡ssaros ao redor do Vale Rivelin de Sheffield, que eventualmente produziu um padrãona paisagem, usando a matemática que ajudou a equipe a revelar os comportamentos que causam esses padraµes.
As descobertas, publicadas no Journal of Animal Ecology , mostram que bandos de chapins de cauda longa tem menos probabilidade de evitar locais onde interagiram com parentes e mais probabilidade de evitar bandos maiores, embora prefiram o centro da floresta.
"Os peitos-de-cauda-longa são muito pequenos para serem equipados com rastreadores GPS como animais maiores, então os pesquisadores seguem esses pequenos pa¡ssaros a panã, ouvindo o canto dos pa¡ssaros e identificando os pa¡ssaros com bina³culos. O trabalho de campo éextremamente demorado e sem a ajuda deles modelos matema¡ticos, esses comportamentos não teriam sido descobertos. "
Nãose sabia por que bandos de chapins de cauda longa vivem em partes separadas da mesma área, apesar de haver comida suficiente para sustentar vários bandos e as aves não apresentarem comportamento territorial .
As equações usadas para entender os pa¡ssaros são semelhantes a s desenvolvidas por Alan Turing para descrever como os animais obtem seus padraµes pintados e listrados. A famosa matemática de Turing indica se os padraµes aparecera£o a medida que um animal cresce no aºtero; aqui, éusada para descobrir quais comportamentos levam aos padraµes na paisagem.
Animais territoriais geralmente vivem em áreas segregadas que eles defendem agressivamente e ficam perto de sua toca. Antes deste estudo, essas ideias matemáticas foram usadas para entender os padraµes feitos por animais territoriais, como coiotes, suricatos e atégangues humanas. No entanto, este estudo foi o primeiro a usar as ideias sobre animais não territoriais sem nenhuma toca fixando-os no lugar.
Natasha Ellison, Ph.D. Um estudante da Universidade de Sheffield que conduziu o estudo, disse: "Os modelos matema¡ticos nos ajudam a entender a natureza de uma quantidade extraordina¡ria de maneiras e nosso estudo éum exemplo fanta¡stico disso."
"Os peitos-de-cauda-longa são muito pequenos para serem equipados com rastreadores GPS como animais maiores, então os pesquisadores seguem esses pequenos pa¡ssaros a panã, ouvindo o canto dos pa¡ssaros e identificando os pa¡ssaros com bina³culos. O trabalho de campo éextremamente demorado e sem a ajuda deles modelos matema¡ticos, esses comportamentos não teriam sido descobertos. "