Topological or metric interactions in animal groups
In plain words
A bird could respond to all neighbors within a fixed distance, or to a fixed number of nearest neighbors whatever their distance. Field data favor the second for starlings, but why the number is about seven, and whether this holds across species, is open.
Precise statement
Infer from 3D trajectory data the interaction kernel of birds, fish and insects: metric (range $r_c$), topological ($n_c$ nearest neighbors; $n_c \sim 6\ \mathrm{to}\ 7$ in starlings, Ballerini and co-workers, 2008) or visual-field based, using maximum-entropy or force-inference methods with model selection. Determine $n_c$ across species and the mechanism (perceptual limits, group-cohesion optimization) that sets it.
What would settle it
Model selection on large trajectory data sets from several species showing which kernel fits and the measured $n_c$ or $r_c$ with uncertainties.
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