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

16 Chapter 2
Tab. 2.1: Comparison of various forest gap models with respect to the state vector update, the typical
number of simulations performed, the patch size used, and the corresponding size of the equilibrium
landscape (equals the number of simulations times patch size). E stands for Establishment, G for Growth
and M for Mortality. A consistent sequence of calculation would be M – G – E.
Model name
Number of
simulations
Patch size
[m2]
Equilibrium
landscape
size [ha]
State vector
update
Reference
JABOWA 100 100 1 E – M – G Botkin et al. (1972a,b)
FORET 100 833 8.3 M – E – G Shugart & West (1977)
LINKAGES 20 833 1.7 E – G – M Pastor & Post (1985)
FORENA 10 833 0.8 M – E – G Solomon (1986)
FORECE 50 833 4.2 E – G – M Kienast (1987)
FORSKA 5 1000 0.5 E – G – M Leemans & Prentice (1989)
EXE 10 833 0.8 E – G – M Martin (1992)
A different solution to the updating problem can be achieved when each state variable x i
of the mathematical model is represented by two variables in the simulation model, e.g.
“x i ” and “x i New”. Like this, the update equations of the variables may be calculated in
any sequence if they all use the “x i ” variables only and assign their updated values to the
“x i New” variables. At the end of the time step, the update of the state vector is performed
by assigning all the “x i New” variables to the respective “x i ” variables (cf. Fischlin et al.
1990).
To test the sensitivity of the FORECE model to a change in the update mechanism, the
original model written in FORTRAN (Kienast 1987) was translated to the programming
language Modula-2 (Wirth 1985, Wirth et al. 1992). The programming library Dialog-
Machine (Fischlin 1986) and the simulation software ModelWorks (Fischlin et al. 1990)
within the RAMSES environment on Apple Macintosh computers (Fischlin 1991) were
used to implement this model version, which is called FORECE V1.0. Then a correct updating
mechanism (Fig. 2.1 right) was implemented in Modula-2 as well, leading to version
1.1 of the FORECE model.
The differences between FORECE version 1.0 and 1.1 were examined in detail by means
of extensive simulation studies along an altitudinal gradient in the European Alps (results
not shown). The implementation of a consistent update mechanism of the state variables
in FORECE did not lead to significant changes of the simulated species composition, although
the correct updating is fundamentally different from a systems theoretical viewpoint.
This seems to confirm Shugart's (1984) finding that no single part of a forest gap
model is very sensitive to its exact formulation. However, the influence of the changed