Interactions of ultra-high-energy cosmic rays with background photons set a limit to the distance cosmic rays reaching us above a certain energy can originate from, making measurements of their fluxes insensitive to properties of sources at high redshifts. On the other hand, the secondary PeV–EeV neutrinos produced in UHECR propagation can reach the Earth even from very high redshifts, and electromagnetic cascades initiated by secondary photons and electrons/positrons contribute to the diffuse gamma-ray background. Therefore, a multi-messenger analysis combining UHECR, neutrino, and gamma-ray data can still provide information about the cosmological evolution of UHECR sources. In this work, we compare predicted particle fluxes from Monte Carlo simulations in various scenarios with recent experimental data, and discuss the conclusions that can be drawn about UHECR sources and their cosmological evolution.