We have analyzed how anisotropic emission of radiation affects the observed sample of ultraluminous X-ray sources (ULXs) by performing simulations of the evolution of stellar populations, employing recent developments in stellar and binary physics, and by utilizing a geometrical beaming model motivated by theory and observation. Whilst ULXs harboring black hole accretors (BH ULXs) are typically emitting isotropically, the majority of ULXs with neutron star accretors (NS ULXs) are found to be beamed. These findings confirm previous assertions that a significant fraction of ULXs are hidden from view due to a substantial misalignment of the emission beam and the line-of-sight. We find the total number of NS ULXs in regions with constant star formation, solar metallicity, and ages above ~1 Gyr to be higher than the BH ULXs, although observationally both populations are comparable. For lower metallicities BH ULX dominate both the total and observed ULX populations. As far as burst star-formation is concerned, young ULX populations are dominated by BH ULXs, but this changes as the population ages and, post star-formation, NS ULXs dominate both the observed and total population of ULXs. We also compare our simulation output to a previous analytical prediction for the relative ratio of BH to NS ULXs in idealized flux-limited observations and find broad agreement for all but the lowest metallicities. In so doing we find that in such surveys the observed ULX population should be heavily dominated by black-hole systems rather than by systems containing neutron stars.
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