  Dense systems of magnetic nanoparticles may exhibit dipolar collective
behavior. However, two fundamental questions remain unsolved: i) whether the
transition temperature may be affected by the particle anisotropy or it is
essentially determined by the intensity of the interparticle dipolar
interactions, and ii) what is the minimum ratio of dipole-dipole interaction
($E_\text{dd}$) to nanoparticle anisotropy ($K_{\text{ef}}V$, anisotropy
$\times$ volume) energies necessary to crossover from individual to collective
behavior. A series of particle assemblies with similarly intense dipolar
interactions but widely varying anisotropy is studied. The $K_\text{ef}$ is
tuned through different degrees of cobalt-doping in maghemite nanoparticles,
resulting in a variation of nearly an order of magnitude. All the bare particle
compacts display collective behavior, except the one made with the highest
anisotropy particles, which presents ``marginal'' features. Thus, a threshold
of $K_{\text{ef}} V/E_{\text{dd}} \approx 130$ to suppress collective behavior
is derived, in good agreement with Monte Carlo simulations. This translates
into a crossover value of $\approx 1.7$ for the easily accessible parameter
$T_\text{MAX}$(interacting)$/T_\text{MAX}$(non-interacting) (ratio of the peak
temperatures of the zero-field-cooled magnetization curves of interacting and
dilute particle systems), which is successfully tested against the literature
to predict the individual-like$/$collective behavior of any given interacting
particle assembly comprising relatively uniform particles.
