To determine the growth of a tree we use some simple principles that allow us to conclude lengths of new tree segments, number of new buds, senescence of sapwood and foliage, diameter growth of the tree etc.
2.1 Length of a New Tree Segment
The length of a tree segment is determined basically by branching and the local light conditions in the tree crown. Branch order effect shortens the length of a tree segment compared to the other tree segments in similar light conditions but in more favourable (closer the main stem) position in a tree. This mimics e.g., the effect of slowing down the fluid and nutrient flow in the branches of the tree.
Relative shadiness shortens the tree segment according to its local light climate. For example at the top of a Scots pine the light climate is ideal and gradually get worse within the crown due to the self shading.
2.2 New Buds
Number of new buds at the tip of the branches is simply determined with the help of the foliage mass of the mother tree segment (i.e., the tree segment behind the leading bud). The more foliage the mother tree segment has the more vital is the branch and more buds can be produced. For example a Scots pine has usually 4-6 new buds in the main stem and 2-4 in branches.
2.3 Diameter Growth
The most important single hypothesis in determing the diameter growth is that of sapwood equivalence. This means that the tree segment below a junction (A0 in the figure) of several tree segments must produce equal amount of sapwood than the tree segments just above (A1,A2 and A3 in the figure) in terms of area . This is called the pipe model principle.
2.4 Sapwood Senescence
Sapwood is a major "maintenance" cost for a tree. If the sapwood is no longer needed for transportation of water and nutrients it can be killed. The living sapwood turns to dead heartwood.
In the model we have basically two hypothesis to determine sapwood senescence. For the first, according two the pipe model (in 2.3) we assume that the effect of sapwood senescence is propagated downwords in a tree. That is, the tree segment below in a junction must match the heartwood area coming from above the junction. Secondly, the local senescence of sapwood in a tree segment is controlled by the death of foliage. Sapwood is needed to support foliage and when the foliage dies in a tree segment the sapwood area proportional to the mass of death foliage can be killed.
2.5 Gradual Bending of Branches
Finally, the architecture of a tree is affected by gradual bending of branches. In LIGNUM we don't have a model (physiological or based on strength calculations) for such phenomena, but a simple algorithm can implement branch bending shown in figure. This is suitable for example for young Scots pine trees.