  Reaction--diffusion mechanism are a robust paradigm that can be used to
represent many biological and physical phenomena over multiple spatial scales.
Applications include intracellular dynamics, the migration of cells and the
patterns formed by vegetation in semi-arid landscapes. Moreover, domain growth
is an important process for embryonic growth and wound healing. There are many
numerical modelling frameworks capable of simulating such systems on growing
domains, however each of these may be well suited to different spatial scales
and particle numbers. Recently, spatially extended hybrid methods on static
domains have been produced in order to bridge the gap between these different
modelling paradigms in order to represent multiscale phenomena. However, such
methods have not been developed with domain growth in mind. In this paper, we
develop three hybrid methods on growing domains, extending three of the
prominent static domain hybrid methods. We also provide detailed algorithms to
allow others to employ them. We demonstrate that the methods are able to
accurately model three representative reaction-diffusion systems accurately and
without bias.
