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Abstract |
Collective behaviour is found in a startling variety of biological systems, from
clusters of bacteria and colonies of cells, up to insect swarms, bird flocks, and
vertebrate groups. A unifying ingredient is the presence of strong correlations:
experiments in bird flocks, fish schools, mammal herds, insect swarms, bacterial
clusters and proteins, have found that the correlation length is significantly
larger than the microscopic scales. In the case of natural swarms of insects
another key hallmark of statistical physics has been verified, namely dynamic
scaling: spatial and temporal relaxation are entangled into one simple law, so
that the relaxation time scales as a power of the correlation length, thus
defining the dynamical critical exponent, z. Within statistical physics, strong
correlations and scaling laws are the two stepping stones leading to the
Renormalization Group (RG): when we coarse-grain short-scale fluctuations, the
parameters of different models flow towards one common fixed point ruling their
large-scale behaviour. RG fixed points therefore organize into few universality
classes the macroscopic behaviour of strongly correlated systems, thus providing
parameter-free predictions of the collective behaviour. Biology is vastly more
complex than physics, but the widespread presence of strong correlations and the
validity of scaling laws can hardly be considered a coincidence, and they rather
call for an exploration of the correlation-scaling-RG path also in collective
biological systems. However, to date there is yet no successful test of an RG
prediction against experimental data on living systems. In this talk I will apply
the renormalization group to the dynamics of natural swarms of insects. Swarms of
midges in the field are strongly correlated systems, obeying dynamic scaling with
an experimental exponent z~1.2, significantly smaller than the naive value z = 2
of equilibrium overdamped dynamics. I will show that this anomalous exponent can
indeed be reproduced by an RG calculation, provided that off-equilibrium activity
*and* inertial dynamics, are both taken into account; the theory gives z=1.3, a
value closer to the experimental exponent than any previous theoretical
determination. This successful result is a significant step towards testing the
core idea of the RG even at the biological level, namely that integrating out the
short-scale details of a strongly correlated system impacts on its large-scale
behaviour by introducing anomalies in the dimensions of the physical quantities.
In the light of this, it is fair to hope that the renormalization group, with its
most fruitful consequence -- universality -- may have indeed an incisive impact
also in biology. |
