  The last two decades have seen a surge in kinetic and macroscopic models
derived to investigate the multi-scale aspects of self-organised biological
aggregations. Because the individual-level details incorporated into the
kinetic models (e.g., individual speeds and turning rates) make them somewhat
difficult to investigate, one is interested in transforming these models into
simpler macroscopic models, by using various scaling techniques that are
imposed by the biological assumptions of the models. Here, we consider three
scaling approaches (parabolic, hydrodynamic and grazing collision limits) that
can be used to reduce a class of non-local 1D and 2D models for biological
aggregations to simpler models existent in the literature. Next, we investigate
how some of the spatio-temporal patterns exhibited by the original kinetic
models are preserved via these scalings. To this end, we focus on the parabolic
scaling for non-local 1D models and apply asymptotic preserving numerical
methods, which allow us to analyse changes in the patterns as the scaling
coefficient $\epsilon$ is varied from $\epsilon=1$ (for 1D transport models) to
$\epsilon=0$ (for 1D parabolic models). We show that some patterns (describing
stationary aggregations) are preserved in the limit $\epsilon\to 0$, while
other patterns (describing moving aggregations) are lost in this limit. To
understand the loss of these patterns, we construct bifurcation diagrams.
