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

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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
Analysis of existing forest gap models 17 update mechanism on the frequency distribution of tree numbers is not negligible, and this may be important in studies that compare and validate gap models (e.g. Leemans 1992). In conclusion, forest gap models can be viewed as a mixture of discrete time and discrete event models, which for practical reasons are implemented as discrete time models (Sequential Machines, Zeigler 1976). However, many gap models do not conform to the formalism of a sequential machine in the way they handle the update of state variables and should be revised in this respect. 2.2 Statistical analysis 2.2.1 Characteristics of model behaviour on a single forest patch The basic unit of the gap dynamics hypothesis in forests is a small area of land in the order of 100 to 1'000 m 2 (0.01-0.1 ha; cf. Tab. 2.1). Various terms have been proposed to denote such a unit (Botkin et al. 1972a,b, Pickett & White 1985, Kienast 1987): The term “plot” is ambiguous since it may also denote a graphical representation of data. A “gap” would be close to the term “gap dynamics”, yet this is confusing since such a “gap” could also carry a mature stand. The term “patch” is unambiguous and clear; therefore I will refer to the basic unit of the gap dynamics hypothesis as a patch, corresponding to the title of the book by Pickett & White (1985). Before setting out for a detailed analysis of forest gap models, it may be useful to have a look at the simulation results produced on one single patch of 1 / 12 ha in the FORECE model, exemplifying both the nature of gap dynamics and some of their basic statistical properties. MATERIAL & METHODS The FORECE model V1.1 was used to simulate forest dynamics at two sites on one patch each: The site Davos is typical of forests in the subalpine zone, which are composed of a few coniferous species. These forests have comparably low biomass, and tree growth generally is slow. The site Bern is representative of the mixed deciduous forests on the
Page 1: Diss. ETH No. 10638 On the Ecology
Page 4 and 5: ii Table of contents A BSTRACT.....
Page 6 and 7: iv APPENDIX .......................
Page 8 and 9: vi Harald BUGMANN, 1994: On the eco
Page 10 and 11: viii Harald BUGMANN, 1994: Aspekte
Page 13 and 14: 1 1 . Introduction 1.1 Climatic cha
Page 15 and 16: Introduction 3 1.2 Methods for the
Page 17 and 18: Introduction 5 in a changing climat
Page 19 and 20: Introduction 7 Their integrative ca
Page 21 and 22: Introduction 9 (1984) provides a mo
Page 23 and 24: Introduction 11 The main advantage
Page 25 and 26: 13 2 . Analysis of existing forest
Page 27: Analysis of existing forest gap mod
Page 31 and 32: Analysis of existing forest gap mod
Page 39 and 40: The forest model FORCLIM 45 carbon
Page 41 and 42: The forest model FORCLIM 47 TREE GR
Page 43 and 44: The forest model FORCLIM 49 gBFlag
Page 45 and 46: The forest model FORCLIM 51 Disturb
Page 47 and 48: The forest model FORCLIM 53 decay o
Page 49 and 50: The forest model FORCLIM 55 the est
Page 51 and 52: The forest model FORCLIM 57 3.3 Mod
Page 53 and 54: The forest model FORCLIM 59 Light a
Page 55 and 56: The forest model FORCLIM 61 Overall
Page 57 and 58: The forest model FORCLIM 63 D (cm)
Page 59 and 60: The forest model FORCLIM 65 a) b) c
Page 61 and 62: The forest model FORCLIM 67 Growth
Page 63 and 64: The forest model FORCLIM 69 Stress-
Page 65 and 66: The forest model FORCLIM 71 Tab. 3.
Page 67 and 68: The forest model FORCLIM 73 3.3.2 F
Page 69 and 70: The forest model FORCLIM 75 where k
Page 71 and 72: The forest model FORCLIM 77 NITROGE
Page 73 and 74: The forest model FORCLIM 79 peratur
Page 75 and 76: The forest model FORCLIM 81 of degr
Page 77 and 78: The forest model FORCLIM 83 microcl
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The forest model FORCLIM 85 Tab. 3.
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The forest model FORCLIM 87 3.4.3 F
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The forest model FORCLIM 89 All the
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The forest model FORCLIM 91 The mas
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The forest model FORCLIM 93 FORCLIM
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Behaviour of FORCLIM along a transe
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Parameter sensitivity & model valid
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153 6 . Model applications Climatic
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Model applications 155 The simulate
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Model applications 157 6.2 Possible
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Model applications 159 simulation s
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Model applications 161 Simulation e
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Model applications 163 At the site
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Model applications 165 Bever Biomas
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Model applications 167 tainty inher
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Model applications 169 scenario cho
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Discussion 171 Finally, the analysi
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Discussion 173 bitrarily chosen par
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Discussion 175 comparably small imp
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Discussion 177 end of the 21st cent
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Conclusions 179 Ecological factors
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Conclusions 181 species composition
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References 183 Begon, M., Harper, J
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References 185 Burger, H., 1951. Ho
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References 187 Faber, P.J., 1991. A
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References 189 Huntley, B. & Birks,
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References 191 Leemans, R. & Prenti
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References 193 Olson, J.S., 1963. E
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References 195 Rudloff, W., 1981. W
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References 197 Smith, T.M., Leemans
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References 199 Whittaker, R.H., 195
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Appendix 201 II. Derivation of para
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Appendix 203 Tab. A-4: Tree species
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Appendix 205 Tab. A-7: Values for m
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Appendix 207 The minimum winter tem
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Appendix 209 Tab. A-11: Shade toler
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Appendix 211 Tab. A-14: Climatic pa
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Appendix 213 IV. Source code of the
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Appendix 215 FROM SimBase IMPORT De
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Appendix 217 END; (* IF *) prevDay
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Appendix 219 PROCEDURE InitializeFW
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Appendix 221 InstallSeparator( fMen
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Appendix 223 FROM FCPFileIO IMPORT
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Appendix 225 modelSp^.p.kHm := sens
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Appendix 227 DeclMV( meanLitt[leafS
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Appendix 229 Swiss Federal Institut
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Appendix 231 (*********************
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Appendix 233 BEGIN WITH sp^ DO d :=
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Appendix 235 Definition module FCPB
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Appendix 237 Purpose Simulation mod
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Appendix 239 END Immobilization; PR
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Appendix 241 CONST lem = 3; VAR ef:
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Appendix 243 Purpose Provides the b
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Appendix 245 Example of a text file
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Appendix 247 Tab. A-15: Lower end o
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Appendix 249 Tab. A-17: Percentage
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Appendix 251 Tab. A-19: Significant
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Appendix 253 VI. Derivation of para
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Appendix 255 Tab. A-21: Species-spe
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Appendix 257 Tab. A-22 (continued)
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