  Collective biological systems display power laws for macroscopic quantities
and are fertile probing grounds for statistical physics. Besides power laws,
natural insect swarms present strong scale-free correlations, suggesting
closeness to phase transitions. Swarms exhibit {\em imperfect} dynamic scaling:
their dynamical correlation functions collapse into single curves when written
as functions of the scaled time $t\xi^{-z}$ ($\xi$: correlation length, $z$:
dynamic exponent), but only for short times. Triggered by markers, natural
swarms are not invariant under space translations. Measured static and dynamic
critical exponents differ from those of equilibrium and many nonequilibrium
phase transitions. Here, we show that: (i) the recently discovered
scale-free-chaos phase transition of the harmonically confined Vicsek model has
a novel extended critical region for $N$ (finite) insects that contains several
critical lines. (ii) As alignment noise vanishes, there are power laws
connecting critical confinement and noise that allow calculating static
critical exponents for fixed $N$. These power laws imply that the unmeasurable
confinement strength is proportional to the perception range measured in
natural swarms. (iii) Observations of natural swarms occur at different times
and under different atmospheric conditions, which we mimic by considering
mixtures of data on different critical lines and $N$. Unlike results of other
theoretical approaches, our numerical simulations reproduce the previously
described features of natural swarms and yield static and dynamic critical
exponents that agree with observations.
