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

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114 Chapter 4 600 Airolo (E/P) Biomass (t/ha) 500 400 300 200 100 Ulmus scabra Quercus robur Quercus petraea Populus nigra Fagus silvatica Betula pendula Acer pseudoplatanus Acer platanoides Picea excelsa Larix decidua Abies alba 0 0 400 Year 800 1200 Fig. 4.13: Average species composition from 200 forest patches simulated by the combined FORCLIM-E/P model, assuming a nutrient-rich soil at the site Airolo. 4.4 A new method for estimating the equilibrium species composition In many studies using forest gap models, it is more important to evaluate the steady state species composition than to know the transient behaviour of the model starting from the highly unrealistic initial condition of a bare patch. Under these circumstances, it would be desirable to have a method for estimating the steady state species composition that avoids the need to simulate the transient behaviour on many patches. A way to achieve this is the following: Instead of simulating many patches (say, 200) over a comparably short time (say, 1200 years), one can simulate just one patch over a much longer time span. Discarding the first centuries of transient behaviour, the average species composition over time will be the same as the average species composition across many patches, because the stochastic process underlying forest gap models appears to be stationary. The species composition of two points in time of one patch is autocorrelated (section 2.2); hence the distance between the samples (∆t) should be chosen so that autocorrelation becomes negligible. On the other hand, the number of samples (n) should be sufficiently large. If the required ∆t and n fulfil the inequality ∆t·n < 200·1200, then this estimation procedure is more efficient than the conventional method of simulating many patches.
Behaviour of FORCLIM along a transect in the European Alps 115 There are two fundamental questions to be addressed within this context: 1) How close to the “true” equilibrium state are the estimates as a function of n and ∆t? In addition to theoretical reasoning, simulation experiments can yield quantitative information on the precision of such estimates. 2) How similar to each other are two estimates of the same steady state, using a given n and ∆t? This question is especially important if two model variants are to be compared, e.g. for assessing the effect of climatic change on species composition. Moreover, is it possible to develop a threshold for significant differences between steady states for a given n and ∆t? 4.4.1 Material & methods To answer the above two questions, two sets of simulation experiments were conducted with the FORCLIM-E/P model. From the analysis in section 2.2.1, it can be hypothesized that temporal autocorrelation is important at lags up to more than 100 years, and the data from section 2.2.2 suggest that the sample size should be larger than 100. Thus, to answer question 1, a factorial design was used with n = 50, 100, 200, 400, 1000, and ∆t = 100, 150 years. This yielded a total of 10 experimental setups. For each setup, 20 simulation runs were performed, and a steady state was estimated from each run. The first 1000 years of each simulation were discarded (transient behaviour, cf. chapter 4). The “true” equilibrium was assumed to be the average of the 20 steady states estimated with n = 1000 and ∆t = 150, thus corresponding to 20'000 points. The percentage similarity coefficient (PS) introduced in Eq. 2.3 was used for comparing the steady states, and simulations were conducted for the site Bern (cf. Appendix III). From these results, the combination of n = 200 and ∆t = 150 years was chosen for further study, i.e. to answer question 2. It may be hypothesized that it is easier – both in a forest gap model and in reality – to estimate the composition of a species-poor forest with one dominating species than that of a diverse forest with many co-dominating species. Moreover, the abundance of a species that is always present on a patch but has low biomass is easier to estimate than that of a species with episodic occurrence, but that attains large biomass when it is present. Thus, the PS between independent estimates of the same steady state at a given site should depend on the number of species and their roles at that site (cf. Shugart 1984). To test this hypothesis, 400 steady states were estimated at
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Diss. ETH No. 10638 On the Ecology
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ii Table of contents A BSTRACT.....
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iv APPENDIX .......................
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vi Harald BUGMANN, 1994: On the eco
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viii Harald BUGMANN, 1994: Aspekte
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1 1 . Introduction 1.1 Climatic cha
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Introduction 3 1.2 Methods for the
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Introduction 5 in a changing climat
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Introduction 7 Their integrative ca
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Introduction 9 (1984) provides a mo
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Introduction 11 The main advantage
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13 2 . Analysis of existing forest
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Analysis of existing forest gap mod
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The forest model FORCLIM 45 carbon
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The forest model FORCLIM 47 TREE GR
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The forest model FORCLIM 49 gBFlag
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The forest model FORCLIM 51 Disturb
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The forest model FORCLIM 53 decay o
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The forest model FORCLIM 55 the est
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The forest model FORCLIM 57 3.3 Mod
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The forest model FORCLIM 59 Light a
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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
Page 79 and 80: The forest model FORCLIM 85 Tab. 3.
Page 81 and 82: The forest model FORCLIM 87 3.4.3 F
Page 83 and 84: The forest model FORCLIM 89 All the
Page 85 and 86: The forest model FORCLIM 91 The mas
Page 87 and 88: The forest model FORCLIM 93 FORCLIM
Page 89 and 90: Behaviour of FORCLIM along a transe
Page 107: Behaviour of FORCLIM along a transe
Page 115 and 116: Parameter sensitivity & model valid
Page 147 and 148: 153 6 . Model applications Climatic
Page 149 and 150: Model applications 155 The simulate
Page 151 and 152: Model applications 157 6.2 Possible
Page 153 and 154: Model applications 159 simulation s
Page 155 and 156: Model applications 161 Simulation e
Page 157 and 158: 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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