On the Ecology of Mountainous Forests in a Changing Climate: A ...

62 Chapter 3
In most forest gap models Eq. 3.9 is used to predict optimum diameter growth (Shugart
1984, Botkin 1993). However, the formulation of Eq. 3.8 conceals the assumptions
about the “cost associated with tree size”, i.e. respiration. It can be hypothesized that
maintenance respiration should be proportional e.g. to stem volume or stem surface
(Kinerson 1975); reconstructing from Eq. 3.8 an equation where the formulation of
respiration is explicit (see Moore 1989), we obtain
∆V c
∆t
= kR · gL c – kS · V c · D c (3.10)
Thus, in the conventional growth equation maintenance respiration is assumed to be proportional
to a power higher than tree volume, which is not realistic. In view of this limitation,
Moore (1989) developed an equation for tree diameter increment from a simple
carbon budget of the tree: Considering biomass (volume) increment and assuming that (a)
gross photosynthesis is proportional to leaf area gL c and (b) respiration is proportional to
stem volume V c , we can write
∆V c
∆t
= kR · gL c – kS · V c (3.11)
Next we assume the following allometric relationships:
(c) gL c = k 1·D c
2 (Whittaker & Marks 1975) (3.12)
(d) gH c = 137 + kB 2,s·D c + kB 3,s·D c
2 (Ker & Smith 1955) (3.13)
(e) V c = k 2·D c2·gH c (the volume of a cone) (3.14)
Using these assumptions, the following equation for diameter increment is obtained (for
the details of the derivation, see Moore 1989):
∆D c
∆t
=
kG s ⋅ D c ⋅ 1 - gH c
kHm s
2
274 + 3⋅kB 2,s ⋅D c + 4⋅kB 3,s ⋅D c · ƒ(e) c (3.15)
where ƒ(e) c is a multiplier used to reduce maximum growth according to the environmental
constraints described below. This equation has a form similar to the conventional
equation (Eq. 3.9), but its assumptions conform more to biological expectations. Thus it
is used to predict the diameter increment in FORCLIM-P (Fig. 3.6).