Halle & Olderman in the 1970s created a model of 23 types of architectural models to which all tree species are believed to conform. They started with the idea that the shoot apical meristem/s (“SAM” – the primary growing tip) is/are the ‘treemakers’.ref The behaviour of the SAM over time determines the form of the tree. They identified four types of meristems (active growing shoots) which led to different forms – those with a single meristem (like a palm), those with modular construction which follow a precisely repeating pattern, trees with trunk/branch differentiation and those in which the meristem changes direction to produce both trunk and branch.ref These depended on factors like whether the SAM is reproductive or vegetative, whether it grows vertically or horizontally, whether growth of the SAM is continuous or rhythmic (ie. has a period of dormancy or a growth pause) and the chronology of growth of each meristem.ref
Below is an updated version which includes some models added later (and one which was removed as nobody found a real tree which conformed to the theoretical model).
Each architectural model has a unique combination of growth, branching, axis differentiation and position of sexual structures.ref Not all of these are relevant to bonsai – as you can see Holttum & Corner don’t branch and Tomlinson & Bell branch underground. Many of these models are relevant for palms, cycads and tropical trees which aren’t commonly used for bonsai.
Two of the architectural models represent many of the trees used in bonsai at least in the Northern Hemisphereref – Massart’s and Rauh’s model – their main difference is in the branching angle with Massart’s at an angle to the stem and Rauh’s growing upwards. In both models the trunk is monopodial – it keeps extending upwards and is dominant.
Massart’s model represents Abies, Picea, Sequoia, Metasequoia, Cedrus, Taxodium, Taxus, Cephalotaxus, Ginkgo & Ilex aquifolium. More forms and discussion of Massart’s model are represented in this post.
Rauh’s model covers the Cupressaceae family (cypress, juniper & redwood), some Araucariaceae, the Pinaceae family including most Pinus species, the Podocarpaceae family, as well as angiosperms such as oak, maple and ash. This is shown in more detail in this post.
If you’re looking to understand the architectural model for your particular tree, you might consult this book – it mainly focuses on tropical trees but gives some pointers on working it out.
Some other models include Attim’s model for Eucalyptus, this is similar to Rauh’s model but follows a continuous growth pattern – in these trees as one leaf expands outside the bud it is replaced by a new bud initiated at the shoot apex.
Troll’s model is applicable for hemlock, acacia, beech, where “axes are all plagiotropic (ie. horizontal), the architecture being build by their continual superposition; main-line axes contribute part trunk, part branch, the proximal part becoming erected, most often secondarily after leaf fall” – it is believed that reaction wood is involved in determining this architecture (the type of wood created to stabilise a branch against gravity – compression wood developed under the branch in the case of gymnosperms, and tension wood developed above the branch in the case of angiosperms). Hemlock is a gymnosperm with this model.
Finally, trees can move from one model to another when they move from their juvenile vegetative phase to their reproductive phase. For example Apple has been found to conform to Rauh’s model when juvenile but Scarrone’s when reproductive:ref