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

Analysis of existing forest gap models 23
cific biomass variables it is less than 200 years. It should also be noted that the largest
significant lag of tree numbers is always smaller than the largest significant lag of the corresponding
biomass.
In conclusion, the Davos and Bern simulations represent two examples of the various
patterns possible under the gap-phase dynamics hypothesis: A species-poor, slowly
growing forest whose pattern is dominated by one self-replacing species on the one hand,
and a species-rich, fast growing forest with a diverse array of species replacement and
competition on the other hand. In this sense, the FORECE model can be viewed as a valid
computer based description of the gap dynamics hypothesis (Watt 1947, Shugart 1984).
The length of a gap dynamics cycle in the simulated unmanaged forests, i.e. ≈200 and
≈150 years at Davos and Bern, respectively, is higher than the rotation length in managed
forests of the area (e.g. Dengler et al. 1990). However, the idea that extremely old trees
are abundant in “virgin” forests is supported neither by the present simulation study nor
by field data (e.g. Leibundgut 1993). We may conclude that two samples taken from the
same forest patch in the model can be considered to be independent from each other if the
lag between them is at least 200 years.
2.2.2 Statistical sampling of the stochastic process
For many applications of gap models, the behaviour of a single patch is of little interest
because the major emphasis is on the dynamics of a larger area of forested land. Thus,
the results from several patches may be averaged to obtain the dynamics on larger scales.
Immediately there raises a question: How many patches do we have to simulate if we
want their average to be reliable? How fast does this average converge towards the expected
value? Are 5 patches sufficient, does it take 50, or even 500 (cf. Tab. 2.1)?
MATERIAL & METHODS
Species biomass and the numbers of trees originating from multiple simulation runs are
rarely normally distributed at a given point in time (Fig. 2.8). Therefore, simple measures
of convergence like the coefficient of variation (Zar 1984) do not provide robust estimates
of model convergence. For highly skewed distributions, a more robust statistical
measure is the interval between the 10% and the 90% percentile (p 10 , p 90 ) for the range