  We explain how event-by-event fluctuations of particle ratios can constrain
and falsify the statistical model of particle production in heavy ion
collisions, using $K/\pi$ fluctuations as an example. We define an observable
capable of determining which statistical model, if any, governs freeze-out in
ultrarelativistic heavy ion collisions. We calculate this observable for
$K/\pi$ fluctuations, and show that it should be the same for RHIC and LHC
energies, as well as independent of centrality, if the Grand-Canonical
statistical model is an appropriate description and chemical equilibrium
applies. We describe what happens in case of deviations from this scenario,
such as light quark chemical non-equilibrium, strange quark over-saturation and
local conservation (canonical ensemble) for strange quarks. We also introduce a
similar observable capable, together with the published $K^*/K$ measurement, of
ascertaining if an interacting hadron gas phase governs the system between
thermal and chemical freeze-out, and of ascertaining its duration and impact on
hadronic chemistry
