When ultra-high-energy cosmic rays (UHECRs) propagate through the universe they produce secondary neutrinos as well as photons, electrons and positrons (initiating electromagnetic cascades) in different kinds of interactions. These neutrinos and electromagnetic cascades are detected at Earth as isotropic extragalactic fluxes. The level of these fluxes can be predicted and used to constrain UHECR source models.

The public astrophysical simulation framework CRPropa 3, designed for simulating the propagating extraterrestrial ultra-high energy particles, is ideally suited for this purpose. CRPropa includes all relevant UHECR interactions as well as secondary neutrino and electromagnetic cascade production and propagation. It is designed for high-performance computing and provides the flexibility to scan large parameter ranges of UHECR models.

The expected cosmogenic neutrino and gamma-ray spectra depend strongly on the evolution with redshift of the UHECR sources and on the chemical composition of UHECRs at injection. The isotropic diffuse gamma-ray background measured by Fermi/LAT is already close to touching upon a model with co-moving source evolution and with the chemical composition, spectral index and maximum acceleration energy optimized to provide the best fit to the UHECR spectrum and composition measured by the Pierre Auger Collaboration. Additionally, the detectable fraction of protons present at the highest energies in UHECRs is shown as a function of the evolution of UHECR sources for a range of sensitivities of neutrino detectors at an energy of $\sim1$ EeV.

Neutrino and gamma-ray measurements are starting to constrain realistic UHECR models. Current and future neutrino experiments with sensitivities in the range of $\sim 10^{-8}$ - $10^{-10}$ GeV cm$^{-2}$ s$^{-1}$ sr$^{-1}$ for the single-flavor neutrino flux at $\sim1$ EeV will be able to significantly constrain the proton fraction for realistic source evolution models.