The origin of ultra-high energy cosmic rays is an open question. Detailed simulations of the propagation through extragalactic and galactic space are needed in order to connect theories about the cosmic-ray origin with the available measurements. For this purpose the simulation software CRPropa 3 was developed. The software is presented with its new modular simulation structure and the implementation of all physical processes relevant for the propagation of ultra-high energy cosmic-ray hadrons. This includes cosmological effects, deflections in magnetic fields, interactions with the photon background and the production of secondary particles.Using CRPropa 3 a simple astrophysical scenario of extragalactic sources accelerating a mixed composition of cosmic-rays with a power-law spectrum and a rigidity dependent cutoff is investigated.A method is presented to compare the predicted energy spectrum and the mass-sensitive Xmax distributions from these simulations to the measurements by the Pierre Auger Observatory for energies above 10^18.7 eV. A Bayesian analysis is performed to calculate the probability distributions of the source model parameters given the measurements, and the impact of the main systematic uncertainties of simulation and measurement is investigated. The resulting scenarios are characterized by low maximum acceleration energies and by emission spectra that are significantly harder than expected for Fermi-type accelerators. The scenarios are discussed in terms of expected anisotropies in the arrival directions, and fluxes of cosmogenic photons and neutrinos, finding no additional constraints from these observables.
