  We use a kinetic-equation approach to describe the propagation of ultra high
energy cosmic ray protons and nuclei and calculate the expected spectra and
mass composition at the Earth for different assumptions on the source injection
spectra and chemical abundances. When compared with the spectrum, the
elongation rate $X_{max}(E)$ and dispersion $\sigma(X_{max})$ as observed with
the Pierre Auger Observatory, several important consequences can be drawn: a)
the injection spectra of nuclei must be very hard, $\sim E^{-\gamma}$ with
$\gamma\sim 1-1.6$; b) the maximum energy of nuclei of charge $Z$ in the
sources must be $\sim 5Z\times 10^{18}$ eV, thereby not requiring acceleration
to extremely high energies; c) the fit to the Auger spectrum can be obtained
only at the price of adding an {\it ad hoc} light extragalactic component with
a steep injection spectrum ($\sim E^{-2.7}$). In this sense, at the ankle
($E_{A}\approx 5\times 10^{18}$ eV) all the components are of extragalactic
origin, thereby suggesting that the transition from Galactic to extragalactic
cosmic rays occurs below the ankle. Interestingly, the additional light
extragalactic component postulated above compares well, in terms of spectrum
and normalization, with the one recently measured by KASCADE-Grande.
