  We present numerical simulations on the propagation of UHE protons with
energies of $(10^{19.5}-10^{22})$ eV in extragalactic magnetic fields over 1
Gpc. We use the ORS galaxy sample, which allow us to accurately quantify the
contribution of nearby sources to the energy spectrum and the arrival
distribution, as a source model. We calculate three observable quantities,
cosmic ray spectrum, harmonic amplitude, and two point correlation function
from our data of numerical simulations. With these quantities, we compare the
results of our numerical calculations with the observation. We show that the
three observable quantities including the GZK cutoff of the energy spectrum can
be reproduced in the case that the number fraction $\sim 10^{-1.7}$ of the ORS
galaxies more luminous than -20.5 mag is selected as UHECR sources. In terms of
the source number density, this constraint corresponds to $10^{-6}$ Mpc$^{-3}$.
However, since mean number of sources within the GZK sphere is only $\sim 0.5$
in this case, the AGASA 8 events above $10^{20.0}$ eV, which do not constitute
the clustered events with each other, can not be reproduced. On the other hand,
if the cosmic ray flux measured by the HiRes, which is consistent with the GZK
cutoff, is correct and observational features about the arrival distribution of
UHECRs are same as the AGASA, our source model can explain both the arrival
distribution and the flux at the same time. Thus, we conclude that large
fraction of the AGASA 8 events above $10^{20}$ eV might originate in the
topdown scenarios, or that the cosmic ray flux measured by the HiRes experiment
might be better. We also discuss the origin of UHECRs below $10^{20.0}$ eV
through comparisons between the number density of astrophysical source
candidates and our result ($\sim 10^{-6}$ Mpc$^{-3}$).
