Nature

[Alexandre Galvão Patriota <patriota@ime.usp.br>]

Caros,

Na edição do dia 25/10/2007 do periódico NATURE, físicos (alguns brasileiros)
estudaram o comportamento das caminhadas e trajetórias realizadas por albatrozes
viajantes, abelhas e outras espécies biológicas. Talvez esse seja um exemplo
interessante para ser abordado em sala sobre aplicações da distribuição Gamma.

O artigo pode ser acessado em: http://www.if.ufal.br/~fidelis/nature06199.pdf

Aos interessados, boa leitura.

Segue o resumo:

The study of animal foraging behaviour is of practical ecological
importance, and exemplifies the wider scientific problem of
optimizing search strategies. Le´vy flights are random walks, the
step lengths of which come from probability distributions with
heavy power-law tails, such that clusters of short steps are connected
by rare long steps. Le´vy flights display fractal properties,
have no typical scale, and occur in physical3?5 and chemical6
systems. An attempt to demonstrate their existence in a natural
biological system presented evidence that wandering albatrosses
perform Le´vy flights when searching for prey on the ocean
surface7. This well known finding2,4,8,9 was followed by similar
inferences about the search strategies of deer10 and bumblebees10.
These pioneering studies have triggered much theoretical work in
physics (for example, refs 11, 12), as well as empirical ecological
analyses regarding reindeer13, microzooplankton14, grey seals15,
spider monkeys16 and fishing boats17. Here we analyse a new,
high-resolution data set of wandering albatross flights, and find
no evidence for Le´vy flight behaviour. Instead we find that flight
times are gamma distributed, with an exponential decay for the
longest flights. We re-analyse the original albatross data7 using
additional information, and conclude that the extremely long
flights, essential for demonstrating Le´vy flight behaviour, were
spurious. Furthermore, we propose a widely applicable method
to test for power-law distributions using likelihood18 and Akaike
weights19,20. We apply this to the four original deer and bumblebee
data sets10, finding that none exhibits evidence of Le´vy flights, and
that the original graphical approach10 is insufficient. Such a graphical
approach has been adopted to conclude Le´vy flight movement
for other organisms13?17, and to propose Le´vy flight analysis
as a potential real-time ecosystem monitoring tool17. Our results
question the strength of the empirical evidence for biological Le´vy
flights.


Alexandre Galvão Patriota
Instituto de Matemática e Estatística - USP
email: patriota@ime.usp.br