Quote: Current computer models assume that each bird interacts with all birds within a certain distance. But the new observations, however, show that each bird keeps under control a fixed number of neighbours - seven other starlings - irrespective of their distance, which is the secret of how they stick together.I'd love to read the actual paper that this article was based on. Anyone with uni access have a citation? -me
New data on Flocking of Starlings
Author
Cool article for those of us who play around with flocking behaviors:
http://www.telegraph.co.uk/earth/main.jhtml;jsessionid=X2TAPSYKVGGJ5QFIQMFSFFWAVCBQ0IV0?view=DETAILS&grid=&xml=/earth/2008/01/29/scistarling129.xml
The key point:
http://www.pnas.org/cgi/content/full/105/4/1232 is the full article.
Interesting. I'd like to see a good demo of this in action.
Interesting. I'd like to see a good demo of this in action.
I'm in the midst of searching up references for my own thesis, so I can oblige by tracking down that paper for you [smile].
I think this is the paper you're looking for: Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study (PDF link)
Abstract:
I think this is the paper you're looking for: Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study (PDF link)
Abstract:
Quote:Numerical models indicate that collective animal behaviour may emerge from
simple local rules of interaction among the individuals. However, very little is
known about the nature of such interaction, so that models and theories mostly
rely on aprioristic assumptions. By reconstructing the three-dimensional position
of individual birds in airborne flocks of few thousands members, we prove that the
interaction does not depend on the metric distance, as most current models and
theories assume, but rather on the topological distance. In fact, we discover that
each bird interacts on average with a fixed number of neighbours (six-seven),
rather than with all neighbours within a fixed metric distance. We argue that a
topological interaction is indispensable to maintain flock’s cohesion against the
large density changes caused by external perturbations, typically predation. We
support this hypothesis by numerical simulations, showing that a topological
interaction grants significantly higher cohesion of the aggregation compared to a
standard metric one.
That is very interesting if each bird is only looking at approximately 6 or 7 others in the flock of thousands. Assuming that their choices of other birds to look at is random, then the internal "interaction/follow" topology may not be fully connected and the flock may actually consist of multiple "topological" sub-flocks. This inference is based on the paper "The Number of Neighbors Needed for Connectivity of Wireless Networks" where the authors found that to guarantee connectivity in a randomly deployed sensor network, each node needs to be connected to at least 5.1774*(log n) neighboring nodes (where n is the total number of nodes deployed). So, in the case of a random flock of 1000 birds, to guarantee the internal "interaction/follow" topology is fully connected, each bird would really have to look at at least 15 others instead of 6 or 7.
Have you noticed that flocks often do break apart into sub-flocks and reform, particularly when external influences are present (look at the way sheep respond to a sheep dog, or how small fish respond to larger predators as examples). I think the point is that nature wants there to be only a weak coupling throughout the flock so that it can break apart when needed, but reform when appropriate, irrespective of the distance. If, when breaking apart, all birds/fish/sheep went their own way (i.e., they ignored their rules governing interactions) each individual would be at higher risk. Having a flock break into two when a predator comes calling guarantees survival for at least one group!
Anyway, a very interesting article... 8)
Cheers,
Timkin
Anyway, a very interesting article... 8)
Cheers,
Timkin
Author
The other limiting factor (or related anyway) is the "digit span" of birds. Like humans, other mammals can only focus on a limited number of things at a time. For humans that's about 7-10, birds is ~7, fish is 3-5. The authors note this in their article as one of the things that led them towards and/or reinforced their hypothesis (don't quite remember/too lazy to find the quote).
This model finds that the birds only cared about ~7 other birds; other cognitive studies have shown that a bird can only focus on ~7 object at a time. That's a very suggestive parallel (and perhaps obvious in retrospect [smile])
The one thing I couldn't get from the paper was whether the 7 chosen links were permanent or whether they shifted through time. i.e. am I just trying to stay with my friends, or am I trying to stay with any random 7 birds of the moment? Staying with a fixed 7 might suggest interesting things about their social structure; certainly in a human mob, you try to stay with your buddies as you move with the herd.
-me
This model finds that the birds only cared about ~7 other birds; other cognitive studies have shown that a bird can only focus on ~7 object at a time. That's a very suggestive parallel (and perhaps obvious in retrospect [smile])
The one thing I couldn't get from the paper was whether the 7 chosen links were permanent or whether they shifted through time. i.e. am I just trying to stay with my friends, or am I trying to stay with any random 7 birds of the moment? Staying with a fixed 7 might suggest interesting things about their social structure; certainly in a human mob, you try to stay with your buddies as you move with the herd.
-me
Quote:Original post by WeirdoFu
This inference is based on the paper "The Number of Neighbors Needed for Connectivity of Wireless Networks" where the authors found that to guarantee connectivity in a randomly deployed sensor network, each node needs to be connected to at least 5.1774*(log n) neighboring nodes (where n is the total number of nodes deployed). So, in the case of a random flock of 1000 birds, to guarantee the internal "interaction/follow" topology is fully connected, each bird would really have to look at at least 15 others instead of 6 or 7.
The value of 5.1774 is what the authors of that paper rigorously prove will result in connectivity, but they also provide simulation results that suggest values above 1.5 are sufficient. Following just 6 neighbors should be sufficient for even a flock of up to 10,000 individuals, to keep the flock topologically connected.
Quote:Original post by VorpyQuote:Original post by WeirdoFu
This inference is based on the paper "The Number of Neighbors Needed for Connectivity of Wireless Networks" where the authors found that to guarantee connectivity in a randomly deployed sensor network, each node needs to be connected to at least 5.1774*(log n) neighboring nodes (where n is the total number of nodes deployed). So, in the case of a random flock of 1000 birds, to guarantee the internal "interaction/follow" topology is fully connected, each bird would really have to look at at least 15 others instead of 6 or 7.
The value of 5.1774 is what the authors of that paper rigorously prove will result in connectivity, but they also provide simulation results that suggest values above 1.5 are sufficient. Following just 6 neighbors should be sufficient for even a flock of up to 10,000 individuals, to keep the flock topologically connected.
That is true, which would further reinforce why birds only need to look at ~7 neighbors, as it is sufficent for their purpose.
Quote:Original post by Palidine
The one thing I couldn't get from the paper was whether the 7 chosen links were permanent or whether they shifted through time. i.e. am I just trying to stay with my friends, or am I trying to stay with any random 7 birds of the moment?
Apart from bird friendship, changing the tracked neighbours from time to time would have a benefical effect from a flocking point of view: fluctuations like the random segregation suggested by WeirdoFu wouldn't last enough to affect the flock seriously.
It seems plausible for birds to elect more suitably placed buddies to follow when those they are tracking are too far or too near or too clustered; they might also lose track of their buddies spontaneously, e.g. when another bird occludes them.
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