draft - university of toronto t-space · pdf filedraft minimum age for clear-cutting native...

Draft

Minimum age for clear-cutting native species with energetic

potential in the Brazilian semi-arid

Journal Canadian Journal of Forest Research

Manuscript ID cjfr-2016-0392R3

Manuscript Type Note

Date Submitted by the Author 02-Dec-2016

Complete List of Authors Santana Otacilio Universidade Federal de Pernambuco Biophysics and Radiobiology

Keyword growth rings firewood Semi-Arid rotation age bioenergy

httpsmc06manuscriptcentralcomcjfr-pubs

Canadian Journal of Forest Research

Draft

1

Minimum age for clear-cutting native species with energetic potential in the Brazilian 1

semi-arid region 2

3

Otacilio Antunes Santana1 4

Av Prof Moraes Rego ndeg 1235 Departamento de Biofiacutesica e Radiobiologia (DBR) 5

Mestrado Profissional em Rede Nacional para o Ensino das Ciecircncias Ambientais 6

(PROFCIAMB) Centro de Biociecircncias (CB) Universidade Federal de Pernambuco (UFPE) 7

Cidade Universitaria Recife Pernambuco Brazil 50670-901 8

otaciliosantanagmailcom 9

otaciliosantanaufpebr 10

+55 81 997371266 11

1Author for correspondence 12

13

14

15

16

17

18

19

20

21

22

23

24

25

of 24



Draft

2

Abstract 26

What is the minimum age for clear-cutting native species with energetic potential in the 27

Brazilian semi-arid region This was the central question of this study which aimed at 28

estimating the minimum cutting cycle for native woody species from an area covered by a 29

sustainable forest management plan Individuals (n = 240) of twelve species native to the 30

semi-arid region were measured and wood discs were taken from them to collect data relative 31

to i) volume by an industrial 3D scanner ii) density using a high-frequency densitometer 32

iii) age by a growth ring measuring device and iv) the lower heating value by an oxygen 33

bomb calorimeter and an elemental analyzer Data were fitted to mathematical models by 34

regression analysis to determine the relationship and significance between the variables 35

analyzed The estimated minimum age for the harvesting of native woody species was 47 36

years determined by the age at which there was stabilization of volume growth curves over 37

time and an increase in density and heating power (wood retraction) 38

39

Keywords growth rings firewood rotation age bioenergy 40

41

42

43

44

45

46

47

48

49

50

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3

1 Introduction 51

The mean annual increment (MAI) and the current annual increment (CAI) are parameters 52

that allow estimation of the optimal age of timber harvest under sustainable forest 53

management but their calculation is laborious (costly expensive and requires a large data set) 54

and time consuming in woody species of the Brazilian semi-arid region Although sustainable 55

forest management plans are in place for this region such difficulty results in ages for clear 56

cut cycles without a scientific basis to justify these possible cycles Unlike rapidly growing 57

species of Eucalyptus and Pinus that invest their biomass mainly in shoots native woody 58

species of the Brazilian semi-arid region have slow initial growth investing most of their 59

biomass initially in roots (high root to shoot ratio) this as a support structure to reduce water 60

loss and against herbivorous attack (from which organs find refuge in the soil) (Lima and 61

Rodal 2010 Costa et al 2014 Santana and Encinas 2016) In addition the individual 62

architecture of woody plants in the Brazilian semi-arid region is based on broad ramifications 63

of the trunk and branches which makes it difficult to estimate the independent variables 64

namely height and diameter used in volumetric calculations (Barros et al 2010) 65

In addition to shoot volume other variables are essential for estimating the energy 66

potential of wood The bulk density chemical composition (eg cellulose and lignin) 67

percentage of vessels and parenchyma moisture content and size of fibers are some 68

parameters that influence the heating value of wood However these parameters are 69

correlated and represented by the density of the wood which has a significant direct and 70

proportional relationship with the heating value of wood (Gebreegziabher et al 2013) The 71

age of the individual plant is another important factor because with advancing age and the 72

stabilization of growth in height woody individuals increase the carbon accumulation on their 73

trunks and branches thus increasing the value of the massvolume ratio of the timber Adult 74

wood is characterized by high density long tracheids thick cell walls high percentage of 75

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4

latewood low percentage of spiral grain low percentage of nodes high percentage of 76

cellulose low percentage of compression wood high transverse shrinkage smaller microfibril 77

angle and greater mechanical strength (Rowell 2012) 78

The optimal age for harvesting a planted forest stand for wood production is when the 79

current annual increment curve intersects the mean annual increment curve At that point the 80

rate of growth in wood volume begins to reduce over time and the economic profitability in 81

relation to forest investment also begins to fall (Prodan 1968) In semi-arid regions in 82

addition to a reduced rate of wood volume growth as trees age wood density often increases 83

over time as an ecophysiological strategy of native tree species to cope with moisture 84

limitations (Liu et al 2013 Klein et al 2014 Santana and Encinas 2016) This wood 85

retraction is evident in the aerial part of the plant and can enhance the rootshoot ratio even if 86

the leaf area index continues to develop over time (Santana and Encinas 2016) Before of the 87

wood retraction occurs a reduction of the rate of growth in wood volume and an increasing of 88

the rate of growth in wood density are observed (Paula 1993 Santana and Encinas 2016) 89

Thus in semi-arid regions the time at which wood volume growth levels off and when the 90

density and LHV curves change their inclination angle in relation to age could represent a 91

parameter defines the best time for harvesting wood destined for bioenergy uses (Liu et al 92

2013 Klein et al 2014) There is not an analytical or exact method for calculating this point 93

of levelling off or for detecting a critical change in the inclination angle of wood density and 94

LHV curves but these trends are supported by observations in the literature (Althoff et al 95

2016 Santana and Encinas 2016) 96

In 2013 91 of the Brazilian energy matrix was based on wood used as firewood and 97

charcoal which has increased the demand for this resource by approximately 5 per year 98

(Brasil 2013) In the semi-arid region of the state of Pernambuco the extracted wood is used 99

as an energy source of the Polo Gesseiro do Araripe (Araripina Microregion) which has 39 100

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5

gypsum mines and 869 industries to cement manufacture which fill 73 of their energy 101

requirements with wood but the small manufacturers use 100 wood to meet their energy 102

needs The production of a 10000 kg of plaster requires 05 st native wood which has an 103

annual demand of 55middot104 million kgyear (Silva 20082009) The sustainable production of 104

wood fuel would require a total area of 155000 hectares specifically for the plaster industry 105

with a cutting cycle ranging from 10 to 15 years But the Northeastern Plants Association 106

(APNE 2014) has the registration of 94 sustainable forest management plans in the state of 107

Pernambuco covering an area of 39748 hectares insufficient to meet the energy demands of 108

the Polo which grows 10 (Sindugesso 2011) to 25 per year in addition to a growing 109

ceramics industry (CPRH 2014) 110

The goal of this study was to estimate the minimum age for a clear cutting cycle of 111

native woody species from an area governed by a sustainable forest management plan in the 112

semi-arid region according to requirements for implementation and maintenance of Annual 113

Production Unit described by the Normative Instruction of the Brazil Ministry of the 114

Environment (number 1 of 06252009 ndash MMA 2009) 115

116

2 Materials and Methods 117

The wood analyzed came from a forest management farm (Figure 1A) in the state of 118

Pernambuco (8deg35rsquoS and 37deg59rsquoW) having a semi-arid climate with annual rainfall below 119

1000 mm (550 mm in 2015 APAC 2016) and mean annual temperature greater than 27degC 120

or a BSh climate according to the Koumlppen classification (Peel et al 2007) This farm is 121

located on the lsquoSertaneja Meridional e Raso da Catarinarsquo geomorphological depression The 122

soils have been classified into four classes Haplic Cambisol Salic Gleysol Yellow Oxisol 123

Haplic Planosol and the vegetation has been classified into Closed Arboreal Open Arboreal 124

and Shrub structural classes (Aguiar et al 2013) 125

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6

The vegetation analyzed came from the clearcutting of experimental plots in a 126

sustainably managed forest of the Semi-Arid Forest Management Network (MMA 2009) The 127

twelve predominant tree species have a cumulative importance value index of 96 measured 128

in 20 plots of 50 x 100 m (10 ha) with a 1271 stemsha density (diameter at breast height ge 1 129

cm) (Aguiar et al 2013) evaluated according to the Permanent Plot Measurements Protocol 130

of the Semi-Arid Forest Management Network and Rodal et al (1992) 131

The species and number of evaluated individuals of each species were Acacia 132

kallunkiae JWGrimes amp Barneby Fabaceae (n = 13) Acacia piauhiensis Benth Fabaceae 133

(n = 15) Anadenanthera colubrina (Vell) Brenan Var cebil (Griseb) Reis Fabaceae (n = 134

27) Aspidosperma pyrifolium Mart Apocynaceae (n = 35) Poincianella pyramidalis (Tul) 135

L P Queiroz Fabaceae (n = 12) Croton blanchetianus Baill Euphorbiaceae (n = 9) 136

Erythrina velutina Willd Papilionoideae (n = 17) Jatropha elliptica (Pohl) MullArg 137

Euphorbiaceae (n = 33) Maytenus rigida (Mart) Benth Celastraceae (n = 16) Mimosa 138

caesalpiniifolia Benth Fabaceae (n = 8) Myracrodruon urundeuva All Anacardiaceae (n = 139

29) and Peltophorum dubium (Spreng) Taub Fabaceae (n = 26) 140

Harvested trees were analyzed for volumetry (Figure 1B) densitometry (Figure 1C) 141

dating (Figure 1C) and calorimetry (Figure 1D) The volume of the wood (m3) was measured 142

by an industrial 3D scanner (3D scanner - SK-DK-FX - four Lens Foshan Shangke 143

Machinery Co Ltd Guangdong Province China) in which all parts (trunk + branches) were 144

reduced to 1 m length (Figure 1B) in a mobile studio in locus The density of the wood and 145

the age (growth rings) were measured from sectioned discs 2 cm thick by means of high-146

frequency densitometry (Schinker et al 2003) in LignoStationTM using LignoScop (Rinntech 147

Heidelberg Germany) (Figure 1C) to scan surfaces using cameras attached to the microscope 148

and LignoScan to scan the wood surface using high-frequency (1600 dpi) with 0001 mm 149

precision (Shchupakivskyy et al 2014) Standard procedures (Fritts 1976 Lisi et al 2008) 150

Page 6 of 24



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7

and COFECHA software (The University of Tennessee Knoxville Grissino-Mayer 2001) 151

were used for cross-dating and standardization The irregularity of inter-annual rain or of 152

another climate event could be revised by the crossdating analysis This analysis could 153

identify growth zone and false growth rings in an inter-annual period (Pagotto et al 2015) 154

The equipment performed 1200 factorial (1200) crossdating analyzes (240 studied 155

individuals with five replicates each) 156

The Higher Heating Value (HHV) of the wood was calculated by collecting data 157

measured with a calorimeter (C6000 global standards 210 IKAreg Staufen Germany) 158

(Guumlnther et al 2012) Samples were ground to a maximum size of 25 microm Lower Heating 159

Value (LHV) was determined by subtracting the heat of vaporization of the water vapor from 160

the higher heating value The water vapor was determined by variance of the hydrogen 161

content of the sample measured through the Element-Analyzer (Vario EL Elementar 162

Analysesystem GmbH Langenselbold Germany) (Figure 1D) These procedures followed the 163

standards DIN EN ISO 1716-2009 DIN 51900-1 2000 DIN 51900-3 2005 (Guumlnther et al 164

2012) and ABNTNBR 863384 165

The relationships between variables (Y = volume and X = density Y= volume and X 166

= age Y = lower heating value and X = density Y = density and X = age Y = lower heating 167

value and X = volume and Y = lower heating value and X = age) were performed by fitting 168

the data to a wide array of mathematical growth models (Table 1) using regression analysis to 169

calculate a coefficient of determination (R2) root-mean-square error (RMSE) significance 170

level (p) and the fit curve and the selection of the best fit model (based on maximizing R2 171

minimizing RMSE and minimizing p) for each case (Zar 1999) The regression analysis was 172

preceded by the DrsquoAgostino Normality test (DAgostino et al 1990) for each variable to 173

validate statistical premises The models were chosen as indicated by Kleinbaum et al (2013) 174

The possible multicollinearity among variables was calculated by the Farrar-Glauber test 175

Page 7 of 24



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8

(Farrar amp Glauber 1976) Adjustments graphics statistical deviation and coefficient of 176

variation were calculated using Statistica 12 (Statsoft Dell Tulsa USA) 177

178

3 Results 179

The mean age of the study population was 46 years (CV = 152 Figure 2A) ranging from 180

98 years (Peltophorum dubium) to 5 years (Croton blanchetianus) The mean volume was 181

012 m3 (CV = 119 Figure 2B) per individual tree with individuals ranging in size from 182

a minimum volume of 0003 m3 (Croton blanchetianus) to a maximum volume of 040 m3 183

(Acacia kallunkiae) The mean wood density was 08 g cm-3 (CV = 71 Figure 2C) 184

varying between 04 g cm-3 (Jatropha elliptica) and 105 g cm-3 (Acacia kallunkiae) The 185

mean lower heating value was 4863 kcal kg-1 (CV = 62 Figure 2D) ranging from 186

3783 kcal kg-1 (Acacia piauhiensis) to 5697 kcal kg-1 (Erythrina velutina) 187

Data reflecting the relationship between volume and density and between volume and 188

age were well fit to sigmoidal models (5 parameters) significantly (R2 gt 086 RMSE lt 005 189

p lt 0001 Figure 3A and 3B Table 2) In both relationships volume began to rise sharply 190

(curve growth gt 45deg slope relative to the dependent variable) to the point where it became 191

constant (curve growth lt 5deg slope in relation to the dependent variable) and then slowed 192

relative to growth of the independent variable (density or age) The relationship between the 193

lower heating value (LHV) and density was the most significant (R2 gt 097 RMSE lt 003 p 194

lt 0001) directly and significantly increasing with increasing density (Figure 3C Table 2) 195

Multicollinearity was not found in the models tested (p gt 0800) Considering the relationship 196

between density and LHV with the age of individuals data fitted to the exponential growth 197

model (double and with five parameters) in which from a given year 47 years for density 198

and 495 for LHV there is a levelling off of the curve (Figure 3D and 3F Table 2) with a 199

more marked increase in the values of these variables (curve growthgt 45 degslope relative to the 200

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9

dependent variable) than previously (growth curve asymp 30 deg slope relative to the dependent 201

variable) As for the relationship between LHV and volume data fitted to the Chapman model 202

(four parameters) (Figure 3E Table 2) indicating that in the higher volume growth phase the 203

increase in LHV value is less pronounced (curve growth lt 15deg slope in relation to the 204

dependent variable) than when the volume growth begins to stabilize (growth curve gt 45deg 205

slope in relation to the dependent variable) 206

The minimum age for clear cutting cycle in an area of Sustainable Forest Management 207

Plan in the semi-arid region with the destination of wood with energy purposes suggested by 208

the variables analyzed was from 468 (47) years (Figure 3B) This is the average tree age at 209

which there is a stabilization of the volume growth (curve growth lt 5deg slope in relation to the 210

dependent variable) and pronounced growth of the LHV (from 495 years Figure 3F) and 211

density (from 47 years Figure 3D) 212

213

4 Discussion 214

One limitation of this study lies in the impracticality of working with a larger sample size 215

given the time required for cutting and loading for transportation (about 24 hours) making it 216

difficult to scan other woody individuals in the semi-arid region However 240 individuals 217

were measured with five replicates of each measurement or analysis improving the reliability 218

and accuracy of data collected 219

Our findings corroborate what has already been reported for the area (Aguiar et al 220

2013) which before the Sustainable Forest Management Plan had reduced logging (gt 20 221

individuals ha year) The values of volume density and LHV varied within the 95 222

confidence intervals reported in the literature for the mean values of the species analyzed 223

volume (from biomass) from 0001 m3 (Santana and Souto 2006) to 050 m3 (Silva and 224

Sampaio 2008) density from 03 g cm-3 (Lima and Rodal 2010) to 12 g cm-3 (Paula 1993) 225

Page 9 of 24



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10

and LHV from 3800 kcal kg-1 (Medeiros Neto et al 2012) to 5800 kcal kg-1 (Quirino et al 226

2004) 227

The rapid growth in the volume of tree species over the years and a subsequent 228

stabilization of this growth is commonly observed in the literature not only for fast growing 229

plantation species (Encinas et al 2011) but also for native species (Felker 1986 Lima 1986 230

Vico et al 2015 Santana and Encinas 2016) This stabilization is considered as the saturation 231

period of the plant individual both by limited environmental resources by competition with 232

others in their environment but also by individual senescence marked by the genetics of the 233

species (Hunt 1982 Felker 1986 Soares et al 2011) The onset of the saturation senescence 234

or slow growth process as shown in Figure 3B from 47 years is marked in forestry science 235

by the beginning of the cutting cycle for vegetation intended for production of firewood and 236

charcoal (Rode et al 2014 Althoff et al 2016) When the volume tends to stabilize other 237

variables such as density (Figure 3 D) and heating value (Figure 3F) which have a high 238

correlation (R2 gt 097) continue to grow in value While a saturation of those values was not 239

observed in this work it is however emphasized in the literature (Hunt 1982 Felker 1986) 240

This reduction of the rate of growth of the wood volume and an increasing of the rate of 241

growth of the wood density and lower heating value (LHV) infer in the begin of wood 242

retraction Thus from the age of 47 the harvesting is strongly indicated 243

In other dry forests on Earth the cutting cycle of wood is ranges from 63 to 97 years 244

much longer than the 47 years derived here The causes for these longer rotation periods are 245

i) in India to avoid urban occupation (Agarwal et al 2016) ii) in Australia and Africa to 246

conserve the habitat for large mammals (Bhadouria et al 2016) iii) in West Africa to reduce 247

wildfire susceptibility and microclimate changes (Scheitera and Savadogo 2016) iv) in 248

Cameroon and Panama to preserve forest stands that are used in popular religious and sacred 249

rituals (Kemeuze et al 2016 Seijo et al 2016) v) in Costa Rica India Papua New Guinea 250

Page 10 of 24



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11

and Southern Africa to produce medicinal bioproducts (Schmiedel et al 2016) vi) in 251

Morocco and Argentina to perpetuate ethnobotanical and other cultural uses of natural 252

resources (Martiacutenez 2015 Blanco and Carriegravere 2016) and vii) in China to maintain the 253

groundwater flow near to surface by hydraulic lift from trees (Xiao and Huang 2016) In all 254

cases like in this work biodiversity preservation and firewood sustainability also were 255

objectives of forest management (Althoff et al 2016 Santana 2016) 256

257

5 Conclusion 258

The estimate of the minimum age for cutting cycle of native woody species in the evaluated 259

area in Brazilrsquos semi-arid region was 47 years determined by the age at which there was 260

stabilization of volume growth over time and an increase in density and heating power (wood 261

retraction) 262

263

Acknowledgements 264

The author is grateful to Pro-Reitoria de Pesquisa e Pos-Graduacao of the Universidade 265

Federal de Pernambuco (PROPESQUFPE) for the financial and logistical support and to 266

Research Group lsquoEducometriarsquo (UFPECNPq) by discussion and survey support The author 267

is very grateful to the reviewers for their careful and meticulous reading of the paper 268

269

References 270

Agarwal S Nagendra H and Ghate R 2016 The Influence of Forest Management 271

Regimes on Deforestation in a Central Indian Dry Deciduous Forest Landscape Land 5 27-272

43 doi 103390land5030027 273

Aguiar M M B Santana O A Inaacutecio E dos S B Amorim L B de and Almeida-274

Cortez J S 2013 Tree resilience after clear-cutting in sustainable forest management of 275

Page 11 of 24



Draft

12

semi-arids areas In 2nd United Nations Convention to Combat Desertification Scientific 276

Conference Edited by Walter J Ammann UN Bonn p 157-158 Available from 277

lthttpsgooglmf9uYUgt [accessed 12 January 2016] 278

Althoff T D Menezes R S C Carvalho A L Pinto A S Santiago G A C F Ometto 279

J P H B Randow C and Sampaio E V D S B 2016 Climate change impacts on the 280

sustainability of the firewood harvest and vegetation and soil carbon stocks in a tropical dry 281

forest in Santa Teresinha Municipality Northeast Brazil Forest Ecology and Management 282

360 367-375 doi 101016jforeco201510001 283

APAC ndash Agecircncia Pernambucana de Aacuteguas e Clima 2016 Monitoramento Pluviometrico 284

[online] Available from lt httpwwwapacpegovbrgt [accessed 11 November 2016] 285

APNE ndash Associaccedilatildeo de Plantas do Nordeste 2014 Centro Nordestino de Informaccedilotildees sobre 286

Plantas Planos de Manejo Sustentaacuteveis da Caatinga [online] Available from 287

lthttpwwwcniporgbrgt [accessed 12 January 2014] 288

Associaccedilatildeo Brasileira de Normas Teacutecnicas ndash ABNT 1984 NBR 8633 Carvatildeo vegetal ndash 289

determinaccedilatildeo do poder caloriacutefico ABNT Rio de Janeiro 12p 290

Barros B C Silva J A A Ferreira R L C and Rebouccedilas A C M N 2010 Volumetria 291

e sobrevivecircncia de espeacutecies nativas e exoacuteticas no Poacutelo Gesseiro do Araripe-PE Ciecircncia 292

Florestal 20 641-647 doi 105902198050982422 293

Bhadouria R Singh R Srivastava P and Raghubanshi A S 2016 Understanding the 294

ecology of tree-seedling growth in dry tropical environment a management perspective 295

Energy Ecology and Environment 1 296ndash309 doi 101007s40974-016-0038-3 296

Blanco J and Carriegravere S M 2016 Sharing local ecological knowledge as a human 297

adaptation strategy to arid environments Evidence from an ethnobotany survey in Morocco 298

Journal of Arid Environments 127 30-43 doi 101016jjaridenv201510021 299

Page 12 of 24



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13

Brasil Empresa de Pesquisa Energeacutetica 2013 Balanccedilo Energeacutetico Nacional 2013 ndash Ano base 300

2012 Relatoacuterio Siacutentese EPE Rio de Janeiro 55p 301

CPRH ndash Agecircncia Ambiental do Meio Ambiente de Pernambuco 2014 Madeira Ilegal ndash 302

Buscas [online] Available from lthttpwwwcprhpegovbrResultadosasppage=2amptexto= 303

MADEIRA20ILEGALgt [accessed 01 June 2014] 304

Costa T L Sampaio E V S B Sales M F Accioly L J O Althoff T D Pareyn F 305

G C Albuquerque E R G M and Menezes R S C 2014 Root and shoot biomasses in 306

the tropical dry forest of semi-arid Northeast Brazil Plant and Soil 378 113-123 doi 307

101007s11104-013-2009-1 308

DAgostino R B Belanger A and Dagostino Jr R B 1990 A suggestion for using 309

powerful and informative tests of normality American Statistician 44 316-321 doi 310

1023072684359 311

Encinas J I Santana O A and Imantildea C R 2011 Volumetric and Economic optimal 312

rotations for firewood production of Eucalyptus urophylla in Ipamery State of Goias 313

Floresta 41 905-912 doi 105380rfv41i425353 314

Farrar D and Glauber R 1976 Multicollinearity in Regression Analysis the Problem 315

Revisited Review of Economics and Statistics 49 92-107 doi 1023071937887 316

Felker P 1986 Establishment and productivity of tree plantings in semiarid regions Elsevier 317

Amsterdam 444 p 318

Fritts H C 1976 Tree Rings and Climate Academic Press London 566p 319

Grissino-Mayer H D 2001 Evaluating crossdating accuracy a manual and tutorial for the 320

computer program COFECHA Tree-Ring Research 57 205ndash221 321

Gebreegziabher T Oyedun A O and Hui C W 2013 Optimum biomass drying for 322

combustion ndash A modeling approach Energy 53 67-73 doi 101016jenergy201303004 323

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14

Guumlnther B Gebauer K Barkowski R Rosenthal M and Bues C T 2012 Calorific value 324

of selected wood species and wood products European Journal of Wood and Wood Products 325

70 755ndash757 doi 101007s00107-012-0613-z 326

Hunt R 1982 Plant growth curves The functional approach to plant growth analysis 327

Edward Arnold Ltd London 248 p 328

Kemeuze V A Sonwa D J Nkongmeneck B A and Mapongmetsem P M 2016 329

Sacred groves and biodiversity conservation in semi-arid area of Cameroon Case study of 330

Diamare plain In Quels botanistes pour le 21e siegravecle Meacutetiers enjeux et opportuniteacutes Edited 331

by N R Rakotoarisoa S Blackmore and B Riera UNESCO Paris pp 171-183 Available 332

from lthttpsgooglf0cxCAgt [accessed 12 March 2016] 333

Klein T Hoch G Yakir D and Koumlrner C 2014 Drought stress growth and nonstructural 334

carbohydrate dynamics of pine trees in a semi-arid forest Tree Physiology 71 1-12 doi 335

101093treephystpu071 336

Kleinbaum D Kupper L Nizam A and Rosenberg E 2013 Applied regression analysis 337

and other multivariable methods Cengage Learning Michigan 928p 338

Lima P C F 1986 Tree productivity in the semiarid zone of Brazil Forest ecology and 339

Management 16 5-13 doi 1010160378-1127(86)90003-4 340

Lima A L A and Rodal M J N 2010 Phenology and wood density of plants growing in 341

the semi-arid region of northeastern Brazil Journal of Arid Environments 74 1363-1373 342

doi 101016jjaridenv201005009 343

Lisi C S Tomazello Filho M Botosso P C Roig F A Maria V B R Ferreira-Fedele 344

L and Voigt A R A 2008 Tree-ring formation radial increment periodicity and 345

phenology of tree species from a seazonal semi-deciduous forest in southeast Brazil IAWA 346

Journal 29 189-207 doi 10116322941932-90000179 347

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15

Liu H Park W A Allen C D Guo D Wu X Anenkhonov O A Liang E 348

Sandanov DV Yin Y Qi Z and Badmaeva N K 2013 Rapid warming accelerates tree 349

growth decline in semi-arid forests of Inner Asia Global Change Biology 19 2500-2510 350

doi 101111gcb12217 351

Martiacutenez G J 2015 Cultural patterns of firewood use as a tool for conservation A study of 352

multiple perceptions in a semiarid region of Cordoba Central Argentina Journal of Arid 353

Environments 121 84-99 doi 101016jjaridenv201505004 354

Medeiros Neto P N Oliveira E Calegari L Almeida A M C Pimenta A S and 355

Carneiro A C O 2012 Caracteriacutesticas Fiacutesio-Quiacutemicas e energeacuteticas de duas espeacutecies de 356

ocorrecircncia no Semiaacuterido Brasileiro Ciecircncia Florestal 22 579-588 doi 357

105902198050986624 358

Ministeacuterio do Meio Ambiente ndash MMA 2009 Dispotildee sobre procedimentos teacutecnicos para 359

elaboraccedilatildeo apresentaccedilatildeo execuccedilatildeo e avaliaccedilatildeo teacutecnica de Planos de Manejo Florestal 360

Sustentaacutevel-PMFS da Caatinga e suas formaccedilotildees sucessoras e daacute outras providecircncias 361

Instruccedilatildeo Normativa Ndeg 1 de 25 de junho de 2009 Diaacuterio Oficial da Uniatildeo ndash Sec 1 120 93 362

Pagotto M A Roig F A Ribeiro A de S and Lisi C S 2015 Influence of regional 363

rainfall and Atlantic sea surface temperature on tree-ring growth of Poincianella pyramidalis 364

semiarid forest from Brazil Dendrochronologia 35 14-23 doi 365

101016jdendro201505007 366

Paula J E 1993 Madeiras da Caatinga uacuteteis para produccedilatildeo de energia Pesquisa 367

Agropecuaacuteria Brasileira 28 153-165 368

Peel M C Finlayson B L and McMahon T A 2007 Updated world map of the Koumlppen-369

Geiger climate classification Hydrology and Earth System Sciences 11 1633ndash1644 doi 370

105194hess-11-1633-2007 371

Page 15 of 24



Draft

16

Quirino W F Vale A T Andrade A P A Abreu V L S and Azevedo A C S 2004 372

Poder Caloriacutefico da Madeira e de Resiacuteduos Lignolceluloacutesicos Biomassa amp Energia 1 173-373

182 374

Prodan M 1968 Forest Biometrics Pergamon Oxford doi 101016B978-0-08-012441-375

450001-8 376

Rede de Manejo Florestal da Caatinga 2005 Protocolo de mediccedilotildees de parcelas permanentes 377

Comitecirc Teacutecnico Cientiacutefico Associaccedilatildeo Plantas do Nordeste Recife 21 p 378

Rodal M J N Sampaio E V S B and Figueiredo M A 1992 Manual sobre meacutetodos de 379

estudo floriacutestico e fitossocioloacutegico - ecossistema Caatinga Sociedade Botacircnica do Brasil 380

Brasiacutelia 24 p 381

Rode R Leite G L Silva M L Ribeiro C A A S and Binoti D H B 2014 The 382

economics and optimal management regimes of eucalyptus plantations A case study of 383

forestry outgrower schemes in Brazil Forest Policy and Economics 44 26-33 doi 384

101016jforpol201405001 385

Rowell R M 2012 Handbook of wood chemistry and wood composites CRC press Boca 386

Raton 703 p 387

Santana J A S and Souto J S 2006 Diversidade e estrutura fitossocioloacutegica da Caatinga 388

na Estaccedilatildeo Ecoloacutegica do Seridoacute-RN Revista de Biologia e Ciecircncias da Terra 6 232-242 389

Santana O A 2016 Resistecircncia social na Caatinga aacuterida a narrativa de quem ficou no 390

colapso ambiental Desenvolvimento e Meio Ambiente 38 419-438 doi 391

httpdxdoiorg105380dmav38i043574 392

Santana O A and Encinas J I 2016 Dendrophysiological plant strategies of Poincianella 393

pyramidalis (Tul) LP Queiroz after wood herbivory in semiarid region of Paraiacuteba - Brazil 394

Acta Scientiarum Biological Sciences 38 179-186 doi 104025actascibiolsciv38i229089 395

Page 16 of 24



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17

Schneider P R 1998 Anaacutelise de regressatildeo aplicada agrave engenharia florestal UFSMCEPEF 396

Santa Maria 236 p 397

Schinker M G Hansen N Spiecker H 2003 High-frequency densitometry mdash a new 398

method for the rapid evaluation of wood density variations IAWA Journal 24 231ndash239 doi 399

10116322941932-90001592 400

Shchupakivskyy R Clauder L Linke N and Pfriem A 2014 Application of high-401

frequency densitometry to detect changes in early- and latewood density of oak (Quercus 402

robur L) due to thermal modification European Journal of Wood and Wood Products 72 5-403

10 doi 101007s00107-013-0744-x 404

Scheitera S and Savadogo P 2016 Ecosystem management can mitigate vegetation shifts 405

induced by climate change in West Africa Ecological Modelling 332 19ndash27 doi 406

101016jecolmodel201603022 407

Schmiedel U Araya Y Bortolotto M I Boeckenhoff L Hallwachs W Janzen D 408

Kolipaka S S Novotny V Palm M Parfondry M Smanis A and Toko P 2016 409

Contributions of paraecologists and parataxonomists to research conservation and social 410

development Conservation Biology 30 506ndash519 doi 101111cobi12661 411

Seijo M M Huerta R P Torneacute J M Torneacute C M and Vidal E A 2016 Madera 412

Carbonizada en contextos funeraacuterios de la jefatura de Riacuteo Grande Panamaacute Antracologiacutea en el 413

sitio de el Cantildeo Chungaraacute 48 277-294 doi 104067S0717-73562016005000013 414

Silva G C and Sampaio E V S B 2008 Biomassas de partes aeacutereas em plantas de 415

caatinga Revista Aacutervore 32 567-575 doi 101590S0100-67622008000300017 416

Sindusgesso 2001 Newsletter [online] Available from lthttpwwwsindusgessoorgbrgt 417

[accessed 13 June 2014] 418

Page 17 of 24



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18

Silva J A A 20082009 Potencialidades de florestas energeacuteticas de Eucalyptus no Poacutelo 419

Gesseiro do Araripe-Pernambuco Anais da Academia Pernambucana de Ciecircncia 420

Agronocircmica 5-6 301-319 421

Soares C P B Paula Neto F and Souza A L 2011 Dendrometria e inventaacuterio florestal 422

Editora UFV Viccedilosa 272p 423

Vico G Thompson S E Manzoni S Molini A Albertson J D Almeida‐Cortez J S 424

Fay P A Feng X Guswa A J Liu H Wilson T G and Porporato A 2015 Climatic 425

ecophysiological and phenological controls on plant ecohydrological strategies in seasonally 426

dry ecosystems Ecohydrology 8 660-681 doi 101002eco1533 427

Xiao Q and Huang M 2016 Fine root distributions of shelterbelt trees and their water 428

sources in an oasis of arid northwestern China Journal of Arid Environments 130 30-39 429

doi 101016jjaridenv201603004 430

Zar J 1999 Biostatistical analysis Prentice Hall New Jersey 431

Page 18 of 24



Draft

Figure 1 Map showing the origin of the tree individuals studied (A) and methodological steps volumetry (B) densitometry and dating (C) and calorimetry (D)

714x851mm (72 x 72 DPI)

Page 19 of 24



Draft

Figure 2 Age (A) volume (B) density (C) and lower heating value (LHV) (D) of twelve native species analyzed in the semi-arid region

1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft

Figure 3 Relationship between the analyzed variables volume lower heating value (LHV) density and age of the 240 woody individuals measured

1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1

Table 1 Mathematical models used for data fit

Model Equation

Polynomial (linear) i 0 1 i iY Xβ β ε= + sdot +

Polynomial (Quadratic) 2

i 0 1 i 2 i iY X Xβ β β ε= + sdot + sdot +

Polynomial (Cubic) 2 3

i 0 1 i 2 i 3 i iY X X Xβ β β β ε= + sdot + sdot + sdot +

Sigmoidal (3 parameters) 1 2

3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+

Sigmoidal (4 parameters) i 2

3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+

Sigmoidal (5 parameters) 4

i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +

Logistic (3 parameters) 3

1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+

Weibull (4 parameters)

41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +

Gompertz (3 parameters) Xi 2

3e

i 1 iY e

ββ

β ε minus minus= +


3e

i 0 1 iY e

ββ

β β ε minus minus= + +

Hill (3 parameters) 2

2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+

Chapman (3 parameters) ( ) 32 iX

i 1 iY 1 eβββ εminus= minus +


i 0 1 iY 1 eβββ β εminus= + minus +

Exponential Growth (Simple 1 parameter) 1 iX

i iY eβ εsdot= +

Exponential Growth (Simple 2 parameters) 2 iX

i 1 iY eββ εsdot= sdot +


i 0 1 iY eββ β εsdot= + sdot +

Exponential Growth (Double 1 parameter) 2 i 4 iX X

i 1 3 iY e eβ ββ β εsdot sdot= sdot + sdot +


i 0 1 3 iY e eβ ββ β β εsdot sdot= + sdot + sdot +

Yi = observed value of the dependent variable Xi = observed value of the independent variable βi = regression equation

parameters εi = fit error

Page 23 of 24



Draft

3

Table 2 Significant fit of data to models for six analyzed relationships volume vs density (A) volume vs age (B) lower

heating value vs density (C) density vs age (D) lower heating value vs volume (E) and lower heating value vs age (F)

Model Function R2 RMSE p

A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial

(linear) i iY 3736 1738 X= + sdot 097 0026 lt 0001

D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X

iY 0193 0248 e 0210 esdot sdot= minus + sdot + sdot 091 0034 lt 0001

E

Chapman (4

parameters) ( )i 6438

6297 X

iY 0004 0001 1 eminus sdot= + minus 090 0048 lt 0001

F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

1

Minimum age for clear-cutting native species with energetic potential in the Brazilian 1

semi-arid region 2

3

Otacilio Antunes Santana1 4

Av Prof Moraes Rego ndeg 1235 Departamento de Biofiacutesica e Radiobiologia (DBR) 5

Mestrado Profissional em Rede Nacional para o Ensino das Ciecircncias Ambientais 6

(PROFCIAMB) Centro de Biociecircncias (CB) Universidade Federal de Pernambuco (UFPE) 7

Cidade Universitaria Recife Pernambuco Brazil 50670-901 8

otaciliosantanagmailcom 9

otaciliosantanaufpebr 10

+55 81 997371266 11

1Author for correspondence 12

13

14

15

16

17

18

19

20

21

22

23

24

25

Page 1 of 24



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2

Abstract 26













39


41

42

43

44

45

46

47

48

49

50

of 24



Draft

3

1 Introduction 51

























Page 3 of 24



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4


























Page 4 of 24



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5
















116










Page 5 of 24



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6


























Page 6 of 24



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7















2012) and ABNTNBR 863384 165











Page 7 of 24



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8



178

3 Results 179






















Page 8 of 24



Draft

9













213

4 Discussion 214












Page 9 of 24



Draft

10


2004) 227
























Page 10 of 24



Draft

11







257

5 Conclusion 258




retraction) 262

263






269

References 270



43 doi 103390land5030027 273



Page 11 of 24



Draft

12








360 367-375 doi 101016jforeco201510001 283










Florestal 20 641-647 doi 105902198050982422 293







Page 12 of 24



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13









101007s11104-013-2009-1 308



1023072684359 311







Amsterdam 444 p 318






Page 13 of 24



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14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

Page 14 of 24



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15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



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16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

2

Abstract 26













39


41

42

43

44

45

46

47

48

49

50

Page 2 of 24



Draft

3

1 Introduction 51

























of 24



Draft

4


























Page 4 of 24



Draft

5
















116










Page 5 of 24



Draft

6


























Page 6 of 24



Draft

7















2012) and ABNTNBR 863384 165











Page 7 of 24



Draft

8



178

3 Results 179






















Page 8 of 24



Draft

9













213

4 Discussion 214












Page 9 of 24



Draft

10


2004) 227
























Page 10 of 24



Draft

11







257

5 Conclusion 258




retraction) 262

263






269

References 270



43 doi 103390land5030027 273



Page 11 of 24



Draft

12








360 367-375 doi 101016jforeco201510001 283










Florestal 20 641-647 doi 105902198050982422 293







Page 12 of 24



Draft

13









101007s11104-013-2009-1 308



1023072684359 311







Amsterdam 444 p 318






Page 13 of 24



Draft

14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

Page 14 of 24



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15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

3

1 Introduction 51

























Page 3 of 24



Draft

4


























of 24



Draft

5
















116










Page 5 of 24



Draft

6


























Page 6 of 24



Draft

7















2012) and ABNTNBR 863384 165











Page 7 of 24



Draft

8



178

3 Results 179






















Page 8 of 24



Draft

9













213

4 Discussion 214












Page 9 of 24



Draft

10


2004) 227
























Page 10 of 24



Draft

11







257

5 Conclusion 258




retraction) 262

263






269

References 270



43 doi 103390land5030027 273



Page 11 of 24



Draft

12








360 367-375 doi 101016jforeco201510001 283










Florestal 20 641-647 doi 105902198050982422 293







Page 12 of 24



Draft

13









101007s11104-013-2009-1 308



1023072684359 311







Amsterdam 444 p 318






Page 13 of 24



Draft

14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

Page 14 of 24



Draft

15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

4


























Page 4 of 24



Draft

5
















116










of 24



Draft

6


























Page 6 of 24



Draft

7















2012) and ABNTNBR 863384 165











Page 7 of 24



Draft

8



178

3 Results 179






















Page 8 of 24



Draft

9













213

4 Discussion 214












Page 9 of 24



Draft

10


2004) 227
























Page 10 of 24



Draft

11







257

5 Conclusion 258




retraction) 262

263






269

References 270



43 doi 103390land5030027 273



Page 11 of 24



Draft

12








360 367-375 doi 101016jforeco201510001 283










Florestal 20 641-647 doi 105902198050982422 293







Page 12 of 24



Draft

13









101007s11104-013-2009-1 308



1023072684359 311







Amsterdam 444 p 318






Page 13 of 24



Draft

14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

Page 14 of 24



Draft

15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

5
















116










Page 5 of 24



Draft

6


























of 24



Draft

7















2012) and ABNTNBR 863384 165











Page 7 of 24



Draft

8



178

3 Results 179






















Page 8 of 24



Draft

9













213

4 Discussion 214












Page 9 of 24



Draft

10


2004) 227
























Page 10 of 24



Draft

11







257

5 Conclusion 258




retraction) 262

263






269

References 270



43 doi 103390land5030027 273



Page 11 of 24



Draft

12








360 367-375 doi 101016jforeco201510001 283










Florestal 20 641-647 doi 105902198050982422 293







Page 12 of 24



Draft

13









101007s11104-013-2009-1 308



1023072684359 311







Amsterdam 444 p 318






Page 13 of 24



Draft

14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

Page 14 of 24



Draft

15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

6


























Page 6 of 24



Draft

7















2012) and ABNTNBR 863384 165











of 24



Draft

8



178

3 Results 179






















Page 8 of 24



Draft

9













213

4 Discussion 214












Page 9 of 24



Draft

10


2004) 227
























Page 10 of 24



Draft

11







257

5 Conclusion 258




retraction) 262

263






269

References 270



43 doi 103390land5030027 273



Page 11 of 24



Draft

12








360 367-375 doi 101016jforeco201510001 283










Florestal 20 641-647 doi 105902198050982422 293







Page 12 of 24



Draft

13









101007s11104-013-2009-1 308



1023072684359 311







Amsterdam 444 p 318






Page 13 of 24



Draft

14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

Page 14 of 24



Draft

15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

7















2012) and ABNTNBR 863384 165











Page 7 of 24



Draft

8



178

3 Results 179






















of 24



Draft

9













213

4 Discussion 214












Page 9 of 24



Draft

10


2004) 227
























Page 10 of 24



Draft

11







257

5 Conclusion 258




retraction) 262

263






269

References 270



43 doi 103390land5030027 273



Page 11 of 24



Draft

12








360 367-375 doi 101016jforeco201510001 283










Florestal 20 641-647 doi 105902198050982422 293







Page 12 of 24



Draft

13









101007s11104-013-2009-1 308



1023072684359 311







Amsterdam 444 p 318






Page 13 of 24



Draft

14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

Page 14 of 24



Draft

15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

8



178

3 Results 179






















Page 8 of 24



Draft

9













213

4 Discussion 214












of 24



Draft

10


2004) 227
























Page 10 of 24



Draft

11







257

5 Conclusion 258




retraction) 262

263






269

References 270



43 doi 103390land5030027 273



Page 11 of 24



Draft

12








360 367-375 doi 101016jforeco201510001 283










Florestal 20 641-647 doi 105902198050982422 293







Page 12 of 24



Draft

13









101007s11104-013-2009-1 308



1023072684359 311







Amsterdam 444 p 318






Page 13 of 24



Draft

14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

Page 14 of 24



Draft

15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

9













213

4 Discussion 214












Page 9 of 24



Draft

10


2004) 227
























of 24



Draft

11







257

5 Conclusion 258




retraction) 262

263






269

References 270



43 doi 103390land5030027 273



Page 11 of 24



Draft

12








360 367-375 doi 101016jforeco201510001 283










Florestal 20 641-647 doi 105902198050982422 293







Page 12 of 24



Draft

13









101007s11104-013-2009-1 308



1023072684359 311







Amsterdam 444 p 318






Page 13 of 24



Draft

14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

Page 14 of 24



Draft

15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

10


2004) 227
























Page 10 of 24



Draft

11







257

5 Conclusion 258




retraction) 262

263






269

References 270



43 doi 103390land5030027 273



of 24



Draft

12








360 367-375 doi 101016jforeco201510001 283










Florestal 20 641-647 doi 105902198050982422 293







Page 12 of 24



Draft

13









101007s11104-013-2009-1 308



1023072684359 311







Amsterdam 444 p 318






Page 13 of 24



Draft

14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

Page 14 of 24



Draft

15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

11







257

5 Conclusion 258




retraction) 262

263






269

References 270



43 doi 103390land5030027 273



Page 11 of 24



Draft

12








360 367-375 doi 101016jforeco201510001 283










Florestal 20 641-647 doi 105902198050982422 293







of 24



Draft

13









101007s11104-013-2009-1 308



1023072684359 311







Amsterdam 444 p 318






Page 13 of 24



Draft

14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

Page 14 of 24



Draft

15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

12








360 367-375 doi 101016jforeco201510001 283










Florestal 20 641-647 doi 105902198050982422 293







Page 12 of 24



Draft

13









101007s11104-013-2009-1 308



1023072684359 311







Amsterdam 444 p 318






of 24



Draft

14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

Page 14 of 24



Draft

15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

13









101007s11104-013-2009-1 308



1023072684359 311







Amsterdam 444 p 318






Page 13 of 24



Draft

14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

of 24



Draft

15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

14



70 755ndash757 doi 101007s00107-012-0613-z 326














Management 16 5-13 doi 1010160378-1127(86)90003-4 340



doi 101016jjaridenv201005009 343




Journal 29 189-207 doi 10116322941932-90000179 347

Page 14 of 24



Draft

15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

15




doi 101111gcb12217 351







105902198050986624 358








101016jdendro201505007 366





105194hess-11-1633-2007 371

Page 15 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

16



182 374


450001-8 376









101016jforpol201405001 385


Raton 703 p 387









Page 16 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

17





10116322941932-90001592 400




10 doi 101007s00107-013-0744-x 404



101016jecolmodel201603022 407












Page 17 of 24



Draft

18












doi 101016jjaridenv201603004 430


of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

18












doi 101016jjaridenv201603004 430


Page 18 of 24



Draft


714x851mm (72 x 72 DPI)

of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft


714x851mm (72 x 72 DPI)

Page 19 of 24



Draft


1103x1446mm (72 x 72 DPI)

of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft


1103x1446mm (72 x 72 DPI)

Page 20 of 24



Draft


1431x1577mm (72 x 72 DPI)

of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft


1431x1577mm (72 x 72 DPI)

Page 21 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

1


Model Equation







3

1i iX

Y

1 e

ββ

βε

minusminus

= +

+


3

1i 0 iX

Y

1 e

ββ

ββ ε

minusminus

= + +

+


i 2

3

1i 0 i

X

Y

1 e

ββ

β

ββ ε

minusminus

= + + +


1i i

i

2

YX

1

β

βε

β

= +

+


1i 0 i

i

2

YX

1

β

ββ ε

β

= + +

+


41

4i 2 3

5

X ln2

i 1 iY 1 e

β

ββ ββ

β ε

minus + minus

= minus +


41

4i 2 3

5

X ln2

i 0 1 iY 1 e

β

ββ ββ

β β ε

minus + minus

= + minus +


3e

i 1 iY e

ββ



3e

i 0 1 iY e

ββ



2 2

1 ii i

3 i

XY

X

β

β β

βε

β= +

+

Page 22 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



Draft

2


2 2

1 ii 0 i

3 i

XY

X

β

β β

ββ ε

β= + +

+






i iY eβ εsdot= +











Page 23 of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

of 24



Draft

3




A Sigmoidal (5

parameters)

i

i 0005X 0423

0001

0509Y 012

1 e

minus minus

= minus + +

086 0044 lt 0001

B

Sigmoidal (5

parameters)

i

i 3799X 23861

4287

0031Y 0007

1 e

minus minus

= + +

089 0037 lt 0001

C

Polynomial


D

Exponential

Growth (Double 5

parameters)

i i0001 X 0019 X


E

Chapman (4


6297 X


F

Exponential

Growth (Double 5

parameters)

i i0001 X 0044 X


Source Author

Page 24 of 24



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