Flocks of starlings exhibit a remarkable ability to maintain cohesion as a
group in highly uncertain environments and with limited, noisy information.
Recent work demonstrated that individual starlings within large flocks respond
to a fixed number of nearest neighbors, but until now it was not understood why
this number is seven. We analyze robustness to uncertainty of consensus in
empirical data from multiple starling flocks and show that the flock
interaction networks with six or seven neighbors optimize the trade-off between
group cohesion and individual effort. We can distinguish these numbers of
neighbors from fewer or greater numbers using our systems-theoretic approach to
measuring robustness of interaction networks as a function of the network
structure, i.e., who is sensing whom. The metric quantifies the disagreement
within the network due to disturbances and noise during consensus behavior and
can be evaluated over a parameterized family of hypothesized sensing strategies
(here the parameter is number of neighbors). We use this approach to further
show that for the range of flocks studied the optimal number of neighbors does
not depend on the number of birds within a flock; rather, it depends on the
shape, notably the thickness, of the flock. The results suggest that robustness
to uncertainty may have been a factor in the evolution of flocking for
starlings. More generally, our results elucidate the role of the interaction
network on uncertainty management in collective behavior, and motivate the
application of our approach to other biological networks.Comment: 19 pages, 3 figures, 9 supporting figure