We present simulations of the propagation of ultra-high energy cosmic rays (UHECR) in three-dimensional space, including realistic assumptions about the extragalactic magnetic field (EGMF) and taking into account interactions of the UHECR with the cosmic microwave background and extragalactic background light as well as the cosmological evolution of the universe. On this basis, we study which energy spectrum and chemical composition of the UHECR must be assumed at their sources to obtain an energy spectrum and a chemical composition of the UHECR arriving at Earth that are in best agreement with the measurements by the Pierre Auger Observatory. We find that the best-fitting energy spectrum and chemical composition parameters depend strongly on the properties of the EGMF, showing that the EGMF must be carefully taken into account. Furthermore, we address the dependence of these parameters on the source evolution.