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

50 Chapter 3
be exaggerated. Moreover, generally too small growth increments will be obtained, especially
if many factors are considered. For example, if each of four growth factors is 0.5,
then 0.5 4 = 0.0625, i.e. the actual growth rate is only 6% of maximum growth. A different
approach was used e.g. in the FORECE model (Kienast 1987); it consists of applying
what has been called “Liebig's Law of the Minimum” (cf. Pomeroy & Alberts 1988):
Only the smallest of all the growth factors is used to reduce maximum growth. In this
approach it is assumed that the growth factors are independent of each other, and that no
compensation is possible. The advantage is that unrealistically low growth rates are
avoided, but this approach is satisfactory only if few factors are present: The more factors
are considered the more probable it is that some of them can compensate for others. Thus
a synthesis of the two approaches will be developed in the FORCLIM model, which tries
to combine the desirable features of each approach.
TREE MORTALITY
Age-dependent mortality rates of trees can be obtained from tree life tables (e.g.
Harcombe 1987) and often have a characteristic U-shape: The mortality rate of young
trees is high, indicating strong competition for light and considerable self-thinning, followed
by a lower, constant mortality rate of the vigorous adult trees, and a higher mortality
rate of old trees (Goff & West 1975, Harcombe 1987). The latter may be a consequence
of their lower vigour and their size; these factors make them more susceptible to
disease, windthrow, and lightning.
These features of tree mortality rates can be modelled by combining a constant and a
stress-induced mortality rate (Fig. 3.2): The former reflects processes that are not
modelled explicitly in FORCLIM, such as attacks by fungi or insects and the death of
small trees by falling boles. This mortality rate is augmented when a tree grows very
slowly: Due to shading, small trees often reach a small fraction of the possible maximum
growth rate only. On the other hand, large trees often show negligible absolute growth
rates. Thus, the stress-induced mortality is assumed to occur if diameter growth has been
less than a certain absolute increment or a certain fraction of the maximum increment for
several years (SGr, Fig. 3.2; Kienast 1987, Solomon & Bartlein 1993). The variable
SGr contains a memory for past environmental conditions; therefore it is a state variable
in the model (Fig. 3.2). It should also be noted that the stress-induced mortality provides
a link between tree growth and tree mortality.