Constraints on UHECR sources and their environments, from fitting UHECR spectrum and composition, and neutrinos and gamma-rays.*

We perform high-precision joint fitting of the Auger extragalactic spectrum and composition with IceCube astrophysical neutrino spectrum and upper limits, and Fermi-LAT extragalactic gamma-ray spectrum to constrain the properties of UHECR sources, the source environments, source evolution and distance to nearest source. At present, the largest source of uncertainty comes from LHC-tuned hadronic event generators, limiting the ability to derive decisive conclusions on all of the above topics. Nonetheless, we can obtain interesting constraints on UHECR, neutrino and gamma-ray sources.