  Self-organisation of individuals within large collectives occurs throughout
biology. Mathematical models can help elucidate the individual-level mechanisms
behind these dynamics, but analytical tractability often comes at the cost of
biological intuition. Discrete models provide straightforward interpretations
by tracking each individual yet can be computationally expensive.
Alternatively, continuous models supply a large-scale perspective by
representing the "effective" dynamics of infinite agents, but their results are
often difficult to translate into experimentally relevant insights. We address
this challenge by quantitatively linking spatio-temporal dynamics of continuous
models and individual-based data in settings with biologically realistic,
time-varying cell numbers. Specifically, we introduce and fit scaling
parameters in continuous models to account for discrepancies that can arise
from low cell numbers and localised interactions. We illustrate our approach on
an example motivated by zebrafish-skin pattern formation, in which we create a
continuous framework describing the movement and proliferation of a single cell
population by upscaling rules from a discrete model. Our resulting continuous
models accurately depict ensemble average agent-based solutions when migration
or proliferation act alone. Interestingly, the same parameters are not optimal
when both processes act simultaneously, highlighting a rich difference in how
combining migration and proliferation affects discrete and continuous dynamics.
