On the Ecology of Mountainous Forests in a Changing Climate: A ...
On the Ecology of Mountainous Forests in a Changing Climate: A ...
On the Ecology of Mountainous Forests in a Changing Climate: A ...
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Analysis <strong>of</strong> exist<strong>in</strong>g forest gap models 23<br />
cific biomass variables it is less than 200 years. It should also be noted that <strong>the</strong> largest<br />
significant lag <strong>of</strong> tree numbers is always smaller than <strong>the</strong> largest significant lag <strong>of</strong> <strong>the</strong> correspond<strong>in</strong>g<br />
biomass.<br />
In conclusion, <strong>the</strong> Davos and Bern simulations represent two examples <strong>of</strong> <strong>the</strong> various<br />
patterns possible under <strong>the</strong> gap-phase dynamics hypo<strong>the</strong>sis: A species-poor, slowly<br />
grow<strong>in</strong>g forest whose pattern is dom<strong>in</strong>ated by one self-replac<strong>in</strong>g species on <strong>the</strong> one hand,<br />
and a species-rich, fast grow<strong>in</strong>g forest with a diverse array <strong>of</strong> species replacement and<br />
competition on <strong>the</strong> o<strong>the</strong>r hand. In this sense, <strong>the</strong> FORECE model can be viewed as a valid<br />
computer based description <strong>of</strong> <strong>the</strong> gap dynamics hypo<strong>the</strong>sis (Watt 1947, Shugart 1984).<br />
The length <strong>of</strong> a gap dynamics cycle <strong>in</strong> <strong>the</strong> simulated unmanaged forests, i.e. ≈200 and<br />
≈150 years at Davos and Bern, respectively, is higher than <strong>the</strong> rotation length <strong>in</strong> managed<br />
forests <strong>of</strong> <strong>the</strong> area (e.g. Dengler et al. 1990). However, <strong>the</strong> idea that extremely old trees<br />
are abundant <strong>in</strong> “virg<strong>in</strong>” forests is supported nei<strong>the</strong>r by <strong>the</strong> present simulation study nor<br />
by field data (e.g. Leibundgut 1993). We may conclude that two samples taken from <strong>the</strong><br />
same forest patch <strong>in</strong> <strong>the</strong> model can be considered to be <strong>in</strong>dependent from each o<strong>the</strong>r if <strong>the</strong><br />
lag between <strong>the</strong>m is at least 200 years.<br />
2.2.2 Statistical sampl<strong>in</strong>g <strong>of</strong> <strong>the</strong> stochastic process<br />
For many applications <strong>of</strong> gap models, <strong>the</strong> behaviour <strong>of</strong> a s<strong>in</strong>gle patch is <strong>of</strong> little <strong>in</strong>terest<br />
because <strong>the</strong> major emphasis is on <strong>the</strong> dynamics <strong>of</strong> a larger area <strong>of</strong> forested land. Thus,<br />
<strong>the</strong> results from several patches may be averaged to obta<strong>in</strong> <strong>the</strong> dynamics on larger scales.<br />
Immediately <strong>the</strong>re raises a question: How many patches do we have to simulate if we<br />
want <strong>the</strong>ir average to be reliable? How fast does this average converge towards <strong>the</strong> expected<br />
value? Are 5 patches sufficient, does it take 50, or even 500 (cf. Tab. 2.1)?<br />
MATERIAL & METHODS<br />
Species biomass and <strong>the</strong> numbers <strong>of</strong> trees orig<strong>in</strong>at<strong>in</strong>g from multiple simulation runs are<br />
rarely normally distributed at a given po<strong>in</strong>t <strong>in</strong> time (Fig. 2.8). Therefore, simple measures<br />
<strong>of</strong> convergence like <strong>the</strong> coefficient <strong>of</strong> variation (Zar 1984) do not provide robust estimates<br />
<strong>of</strong> model convergence. For highly skewed distributions, a more robust statistical<br />
measure is <strong>the</strong> <strong>in</strong>terval between <strong>the</strong> 10% and <strong>the</strong> 90% percentile (p 10 , p 90 ) for <strong>the</strong> range