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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60 Chapter 3<br />
gBFlag s =<br />
0 U(0,1) < gBrP s = (kBrow s –1) · kBrPr<br />
30<br />
1 else<br />
(3.4)<br />
where U(0,1) is a random number with uniform distribution <strong>in</strong> <strong>the</strong> range [0…1], kBrow s<br />
is <strong>the</strong> species-specific brows<strong>in</strong>g tolerance, and kBrPr is brows<strong>in</strong>g pressure on a nom<strong>in</strong>al<br />
scale between 0 (no brows<strong>in</strong>g) and 10 (heavy brows<strong>in</strong>g). The sapl<strong>in</strong>g mortality (gBrP s )<br />
thus <strong>in</strong>creases l<strong>in</strong>early with <strong>in</strong>creas<strong>in</strong>g brows<strong>in</strong>g <strong>in</strong>tensity, and <strong>the</strong> maximum mortality<br />
ranges from 0 to 66.7% depend<strong>in</strong>g on <strong>the</strong> parameter kBrow s (Fig. 3.5 right). The<br />
current quantification <strong>of</strong> this mortality is entirely speculative because a quantitative basis<br />
could not be found <strong>in</strong> <strong>the</strong> literature (e.g. Näscher 1979, Eiberle & Nigg 1986, Liss 1988,<br />
Albrecht 1989). However, latest research (Rechste<strong>in</strong>er 1993, Kräuchi 1994) may allow<br />
for a more reliable formulation <strong>of</strong> this environmental filter controll<strong>in</strong>g sapl<strong>in</strong>g establishment.<br />
Moreover, <strong>the</strong> brows<strong>in</strong>g pressure parameter kBrPr could be replaced by an <strong>in</strong>put<br />
variable uBrPr, thus provid<strong>in</strong>g <strong>the</strong> l<strong>in</strong>k to models <strong>of</strong> game population dynamics (e.g.<br />
Schröder 1976, Buchli 1979).<br />
Degree-days<br />
Sapl<strong>in</strong>g establishment is assumed to be impossible when <strong>the</strong> annual sum <strong>of</strong> degree-days<br />
does not conform to <strong>the</strong> degree-day requirements <strong>of</strong> <strong>the</strong> tree species, which are def<strong>in</strong>ed by<br />
<strong>the</strong> parameters kDDM<strong>in</strong> s and kDDMax s (Shugart 1984):<br />
gDFlag s =<br />
1 kDDM<strong>in</strong> s < uDD < kDDMax s<br />
0 else<br />
(3.5)<br />
Immigration<br />
The last factor that modifies sapl<strong>in</strong>g establishment rates is <strong>in</strong>troduced to simulate simple<br />
immigration scenarios <strong>of</strong> <strong>the</strong> tree species:<br />
gIFlag s =<br />
1 kImmYr s > t<br />
0 else<br />
(3.6)<br />
where kImmYr s is a parameter denot<strong>in</strong>g <strong>the</strong> first simulation year where <strong>the</strong> species may<br />
establish, and t is <strong>the</strong> current simulation time. The choice <strong>of</strong> kImmYr s depends on <strong>the</strong><br />
hypo<strong>the</strong>sis to be tested, such as a specific immigration scenario or <strong>the</strong> complete exclusion<br />
<strong>of</strong> a given species from a simulation experiment.