  In this article we derive and test the fluctuating hydrodynamic description
of active particles interacting via taxis and quorum sensing, both for
mono-disperse systems and for mixtures of co-existing species of active
particles. We compute the average steady-state density profile in the presence
of spatial motility regulation, as well as the structure factor and
intermediate scattering function for interacting systems. By comparing our
predictions to microscopic numerical simulations, we show that our fluctuating
hydrodynamics correctly predicts the large-scale static and dynamical
properties of the system. We also discuss how the theory breaks down when
structures emerge at scales smaller or comparable to the persistence length of
the particles. When the density field is the unique hydrodynamic mode of the
system, we show that active Brownian particles, run-and-tumble particles and
active Ornstein-Uhlenbeck particles, interacting via quorum-sensing or
chemotactic interactions, display undistinguishable large-scale properties.
This form of universality implies an interesting robustness of the predicted
physics but also that large-scale observations of patterns are insufficient to
assess their microscopic origins.
