Mathematical models in agriculture: quantitative methods for the plant, animal and ecological science
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Wallingford [u.a.]
CABI Publ.
2007
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 906 S. graph. Darst. |
| ISBN: | 085199010X |
Internformat
MARC
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| 100 | 1 | |a Thornley, John H. M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical models in agriculture |b quantitative methods for the plant, animal and ecological science |c J. H. M. Thornley and J. France |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Wallingford [u.a.] |b CABI Publ. |c 2007 | |
| 300 | |a XVII, 906 S. |b graph. Darst. | ||
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| 650 | 4 | |a Agriculture - Modèles mathématiques | |
| 650 | 4 | |a Landwirtschaft | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Agriculture |x Mathematical models | |
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| 700 | 1 | |a France, J. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804134566234947584 |
|---|---|
| adam_text | Titel: Mathematical models in agriculture
Autor: Thornley, John H. M.
Jahr: 2007
Contents
Preface xv
PART I TECHNIQUES
1 Role of Mathematical Models I
Summary 1
1.1 Agriculture and Science 1
1.2 What is a Mathematical Model? 3
1.3 Hierarchy in Biology 6
1.4 Types of Models 7
1.5 Evaluation and Validation of Models 10
1.6 Possible Modelling Objectives 11
1.7 Models for Research and Models for Application 13
1.8 Models: Documentation, Presentation and Reviewing 14
1.9 Units 17
Exercises 18
2 Dynamic Deterministic Models 19
Summary 19
2.1 Variables 19
2.1.1 State variables 20
2.1.2 Rate variables 20
2.1.3 Driving variables 21
2.1.4 Other variables 21
2.2 Parameters and Constants 22
2.3 Differential Equations 23
2.3.1 Explicit time dependence 24
2.3.2 Memory and delay 25
vi Contents
2.4 Numerical Integration 26
2.4.1 Euler s method - a first-order method 28
2.4.2 Trapezoidal method - a second-order method 30
2.4.3 Runge-Kutta method - a fourth-order fixed step
method 31
2.4.4 Oscillations caused by too large an integration step 32
2.4.5 Stiff equations 3 3
2.5 Models and Data: to Fit or Not to Fit 36
2.5.1 Predictions and measurements 37
2.5.2 Residual lack of fit 38
2.5.3 Confidence limits for fitted parameters 39
2.5.4 Sensitivity analysis 41
2.6 Multiple Steady States 41
2.6.1 Switches 42
2.6.2 Catastrophe 47
2.6.3 Oscillations 49
2.6.4 Chaos 50
Exercises 54
3 Mathematical Programming 57
Summary 57
3.1 Introduction 57
3.2 Mathematical Formulation 58
3.2.1 Example 59
3.3 Graphical Solution 62
3.4 Computer Solution 65
3.5 Worked Example 71
3.5.1 Formulation 72
3.5.2 Solution 74
3.6 Special Topics 76
3.6.1 Parametric programming 76
3.6.2 Separable programming 77
3.6.3 Integer programming 83
3.6.4 Goal programming 84
3.6.5 Dynamic programming 85
Exercises 88
4 Basic Biological Processes 91
Summary 91
4.1 Chemical Kinetics 91
4.1.1 First-order reactions 93
4.1.2 Second-order reactions 96
4.1.3 Stochastic approach to chemical kinetics 98
4.2 Catalysis 102
4.2.1 Arrhenius equation 103
4.2.2 Phenomenological temperature function 105
Contents vii
4.3 Biochemical Kinetics 107
4.3.1 Michaelis-Menten kinetics 107
4.3.2 Sigmoidal kinetics 109
4.3.3 Transport plus Michaelis—Menten kinetics 110
4.3.4 Bisubstrate Michaelis—Menten equation 113
4.3.5 Inhibition 114
4.3.6 Activation 116
4.3.7 Futile cycles 116
4.4 Transport 118
4.4.1 Diffusion — Fick s law 118
4.4.2 Convection 120
4.4.3 General equation for transport and chemical
reaction 120
4.4.4 Examples 122
4.4.5 Lumped representation of transport 126
4.4.6 Difference equation representation 128
4.5 Local and Non-local Variables 129
Exercises 131
5 Growth Functions 136
Summary 136
5.1 Introduction 136
5.2 Exponential Growth 139
5.3 Monomolecular Equation 140
5.4 Logistic Equation 143
5.5 Gompertz Equation 145
5.6 Chanter Equation 148
5.7 Exponential Quadratic Equation 150
5.8 Von Bertalanffy Equation 152
5.9 Richards Equation 155
5.10 Schumacher Equation 157
5.11 Morgan Equation 160
5.12 Other Growth Equations 163
Exercises 169
6 Simple Dynamic Growth Models 172
Summary 172
6.1 Introduction 172
6.2 Autocatalytic Growth with Sigmoidal Substrate Limitation 173
6.3 Delayed Growth 174
6.4 Compensatory Growth 178
6.4.1 Model scheme 178
6.4.2 Simulations 182
6.5 Square-root-time Growth Equation 184
6.6 Open Logistic Growth 186
6.7 Logistic Equation Modified for Substrate Supply and
Product Inhibition 188
VIII
Contents
6.8 Gompertz with Delayed Development 190
6.9 Expo-linear-asymptotic Growth 192
6.9.1 Hyperbolic formulation 193
6.9.2 Negative-exponential formulation 196
6.10 Allometry and Scaling 196
6.10.1 Application of simple geometrical factors 198
6.10.2 A branching model for allometric scaling 199
6.10.3 Scaling in relation to maturity 202
6.11 Biological Oscillators 204
6.11.1 Gene-metabolism oscillator 204
6.11.2 Alternative-pathways oscillator 206
6.11.3 Grazed-pasture oscillator 208
Exercises 210
7 Simple Ecological Models 213
Summary 213
7.1 Introduction 213
7.2 Difference Equations and Differential Equations 214
7.3 Age-structured Models of Population Growth 215
7.3.1 Discrete-age discrete-time model 216
7.3.2 Discrete-age continuous-time scheme 219
7.3.3 Continuous-age continuous-time model 221
7.4 Morph-structured Growth Model 223
7.5 Morph- and Age-structured Growth Model 226
7.6 Lotka-Volterra Type Model 227
7.7 Disease/Epidemic Models 229
7.7.1 Five-compartment disease model 229
7.7.2 Spatial aspects 230
Exercises 233
8 Environment and Weather 235
Summary 235
8.1 Introduction 235
8.2 Time 236
8.3 Solar Angles and Day Length 237
8.3.1 Day length switching 241
8.4 Representing Weather in Models 243
8.4.1 Need for diurnal data in models 243
8.4.2 Matching measured diurnal data to the model 244
8.4.3 Generating diurnal data from daily data 245
8.4.4 Generating daily data from monthly data
deterministically 251
8.4.5 Generating daily data from monthly data
stochastically 253
8.4.6 Deterministic sinusoidal seasonal variation 262
8.5 Bright Sunshine Hours and Daily Radiation Receipt 263
Contents ix
8.6 Angular Distribution of Radiation 264
8.6.1 Direct solar radiation 265
8.6.2 Diffuse radiation from a clear sky 265
8.6.3 Overcast skies 265
8.7 Wind 267
8.7.1 Diurnal variation 269
8.7.2 Seasonal variation 270
8.8 Climate Change 270
Exercises 272
PART II CROPS
9 Plant and Crop Processes 275
Summary 275
9.1 Introduction 275
9.2 Light Interception 277
9.2.1 Crops with closed canopies 278
9.2.2 Single plant 282
9.2.3 Discontinuous canopies 284
9.2.4 Mixtures 287
9.3 Photosynthesis 288
9.3.1 Overview of photosynthesis 289
9.3.2 Leaf photosynthesis 290
9.3.3 Canopy photosynthesis 295
9.3.4 Integrable closed-canopy models 296
9.3.5 Single-plant photosynthesis 301
9.3.6 Photosynthesis of discontinuous canopies 303
9.3.7 Mixtures 305
9.4 Nitrogen Uptake; Nitrogen Fixation 305
9.4.1 Nitrogen uptake 306
9.4.2 Nitrogen fixation 309
9.5 Growth and Respiration 310
9.5.1 Growth 311
9.5.2 Maintenance 312
9.5.3 Pathway analysis 313
9.5.4 Futile cycles 324
9.6 Allocation 326
9.6.1 Empiricism 327
9.6.2 Teleonomy 327
9.6.3 Mechanism 333
9.7 Development 341
9.7.1 Temperature sums 343
9.7.2 Generalized developmental rates 345
9.7.3 Compartmental models of development 346
9.7.4 Survey of recent contributions 348
9.8 Water 349
9.8.1 Water potential 350
Contents
9.8.2 Soil water 353
9.8.3 Root and shoot water 357
9.8.4 Transpiration 362
9.8.5 Soil surface evaporation 373
9.8.6 Rainfall interception by canopy and evaporation 374
9.9 Leaf Stomatal Resistance 375
9.9.1 Basic definitions 376
9.9.2 Responses of stomata to environment and plant
variables 378
Exercises 381
10 Crop Models 385
Summary 385
10.1 Introduction 385
10.2 Crop Model Structure 387
10.3 Simple Generic Daily Crop Model 388
10.3.1 Environment 390
10.3.2 Temperature functions 392
10.3.3 Plant submodel 393
10.3.4 Litter and soil submodel 401
10.3.5 Hydrology 403
10.3.6 Simulations 408
10.4 Supply-Demand Models 413
10.4.1 Supply and demand in relation to carbon and
nitrogen 415
10.4.2 Supply-demand model of lettuce growth with
osmotic regulation 416
10.4.3 Supply-demand models: do they have a role? 425
10.5 Plant Competition 426
10.5.1 Two plants compete for a single substrate 427
10.5.2 Interaction of two plants simulated 429
10.5.3 Crops, weeds and mixtures 431
10.5.4 Self-thinning: the three-halves rule 436
10.5.5 Intercropping and agroforestry 439
10.5.6 Genetically modified crops 441
10.6 Allelopathy and Phytotoxicity 444
10.6.1 Stimulus and inhibition 445
10.6.2 Dynamics of an allelochemical and its effect 445
Exercises 447
11 Crop Husbandry 450
Summary 450
11.1 Introduction 450
11.2 A Grass Drying Enterprise 451
11.3 Allocating Land to Arable Crops 454
11.4 Harvesting Plans for Brussels Sprouts 457
11.5 Planting Wheat 460
Contents xi
11.6 Grazing 462
11.6.1 Systems of rotational grazing 462
11.6.2 Continuous and rotational grazing 464
11.7 Grassland and Fertilizer Usage 466
11.8 Silage 469
11.8.1 Anaerobic phase of ensiling 469
Exercises 477
12 Plant Diseases and Pests 481
Summary 481
12.1 Introduction 481
12.2 Estimation of Yield Loss 483
12.3 Disease Prediction 484
12.3.1 Potato late blight 484
12.3.2 Sugar beet yellows virus 487
12.4 Mechanistic Disease Simulation 488
12.4.1 Sugar beet fungal root infection 488
12.4.2 Potato late blight 494
12.5 Pests 504
12.5.1 Plant, pests and parasites 504
12.5.2 Plants and aphids 508
Exercises 518
PART III ANIMALS
13 Animal Processes 522
Summary 522
13.1 Introduction 522
13.2 Tissue and Whole-body Protein Synthesis 523
13.3 Production of Volatile Fatty Acids in the Rumen 525
13.4 Viability of the Fungal Population in the Rumen 529
13.5 Leucine Kinetics in the Udder 534
13.6 Degradation of Feed in the Rumen 539
13.6.1 In sacco system 539
13.6.2 In vitro system 543
13.7 Passage of Digesta through the Gastro-intestinal Tract 547
Exercises 553
14 Animal Organs 560
Summary 560
14.1 Introduction 560
14.2 The Mammary Gland 560
14.2.1 Hormone, H 562
14.2.2 Division of undifferentiated cells, Cu 563
14.2.3 Production and loss of secretory cells, Cs 563
14.2.4 Secretion and removal of milk, M 565
14.2.5 Averaged amount of milk in animal, M 566
14.2.6 Substrate, S 567
xii Contents
14.2.7 Mathematical summary 567
14.2.8 Application 568
14.2.9 More detailed mammary models 570
14.3 The Rumen 570
14.3.1 Model description 570
14.3.2 Model application 573
14.3.3 Model developments 5 74
14.4 Other Organs 575
14.5 Blood 575
14.5.1 Dual indicator method for estimating blood flow 577
14.5.2 Blood flow and uptake of nutrients by the udder 579
Exercises 583
15 Whole-animal Models 593
Summary 593
15.1 Introduction 593
15.2 The Veal Calf 593
15.2.1 Digestion 594
15.2.2 Protein metabolism 595
15.2.3 Energy metabolism 596
15.2.4 Body ash and auxiliary variables 596
15.2.5 Model application 597
15.3 The Lactating Dairy Cow 599
15.3.1 Rumen module 600
15.3.2 Body metabolism module 602
15.3.3 Model application 603
15.3.4 Other dairy cow models 604
15.4 The Pig 605
15.4.1 Auspig 605
15.4.2 Lactating sow model 607
Exercises 610
16 Animal Products 620
Summary 620
16.1 Introduction 620
16.2 Milk Yield by the Dairy Cow 620
16.2.1 Gaines equation 621
16.2.2 Wood equation 622
16.2.3 Dijkstra equation 627
16.2.4 Other lactation equations 630
16.3 Efficiency of Energy Utilization for Milk Production 632
16.4 Meat Produced by the Growing Animal 635
16.4.1 Blaxter equation 636
16.4.2 Allometry and body composition 640
16.5 Efficiency of Energy Utilization for Growth 641
16.5.1 Intake and liveweight gain 642
16.5.2 Feed consumption and liveweight 644
Contents
16.6 Egg Production by the Laying Hen 645
16.6.1 McMillan equation 646
16.6.2 Other egg production equations 649
16.7 Amino Acid Requirements of Laying Hens 650
16.7.1 Hurwitz equation 650
16.7.2 Reading model 651
16.8 Calcium and Phosphorus Flows in Laying Hens 654
16.8.1 Model formulation 655
16.8.2 Operation 661
16.8.3 Results 661
16.9 Wool Growth 663
16.9.1 Physiology of wool growth 664
16.9.2 Research models of wool growth 664
16.9.3 Simplified models of wool growth for decision
support 670
Exercises 672
17 Animal Husbandry 677
Summary 677
17.1 Introduction 677
17.2 Ration Formulation 677
17.3 Allocating Pregnant Ewes to Feeding Groups 682
17.4 Effects of Feeding Level on Milk Production and
Live-weight 685
17.5 Pattern of Calving 688
17.6 Replacement 690
Exercises 691
18 Animal Diseases 694
Summary 694
18.1 Introduction 694
18.2 Bovine Spongiform Encephalopathy 695
18.2.1 Deterministic five-pool BSE model 695
18.2.2 Age-stratified BSE model 698
18.3 Rabbit Haemorrhagic Disease 703
18.4 Foot and Mouth Disease 706
18.4.1 Single-farm disease dynamics 708
18.4.2 Spatial disease spread 711
18.4.3 Secondary infections 712
Exercises 715
Solutions to Exercises 717
Mathematical Glossary 803
Bessel Functions 803
Binomial and Poisson Distributions 805
Coordinate Axes Systems 808
xiv Contents
Determinants, see Matrices and Determinants
Differentiation 810
Dirac Delta Function 812
Duality 813
Eigenvalues 814
Error Function 815
Fourier Series 816
F-test 818
Gamma Function and Gamma Distribution 818
Geometric Series 822
Hôpital s Rule 822
Hyperbolas: Rectangular and Non-rectangular 823
Integration by Parts 825
Linear Differential Equations 825
Matrices and Determinants 827
Newton-Raphson Method 830
Normal and Log-normal Distribution Functions 831
Numerical Differentiation 835
Partial Fractions 835
Poisson Distribution, see Binomial and Poisson Distributions
Quadratic Forms 836
Taylor Series 837
t-distribution 838
Vectors 839
Appendix: Constants and Conversions 841
Bibliography: Further Reading and References 843
Index 887
|
| adam_txt |
Titel: Mathematical models in agriculture
Autor: Thornley, John H. M.
Jahr: 2007
Contents
Preface xv
PART I TECHNIQUES
1 Role of Mathematical Models I
Summary 1
1.1 Agriculture and Science 1
1.2 What is a Mathematical Model? 3
1.3 Hierarchy in Biology 6
1.4 Types of Models 7
1.5 Evaluation and Validation of Models 10
1.6 Possible Modelling Objectives 11
1.7 Models for Research and Models for Application 13
1.8 Models: Documentation, Presentation and Reviewing 14
1.9 Units 17
Exercises 18
2 Dynamic Deterministic Models 19
Summary 19
2.1 Variables 19
2.1.1 State variables 20
2.1.2 Rate variables 20
2.1.3 Driving variables 21
2.1.4 Other variables 21
2.2 Parameters and Constants 22
2.3 Differential Equations 23
2.3.1 Explicit time dependence 24
2.3.2 Memory and delay 25
vi Contents
2.4 Numerical Integration 26
2.4.1 Euler's method - a first-order method 28
2.4.2 Trapezoidal method - a second-order method 30
2.4.3 Runge-Kutta method - a fourth-order fixed step
method 31
2.4.4 Oscillations caused by too large an integration step 32
2.4.5 Stiff equations 3 3
2.5 Models and Data: to Fit or Not to Fit 36
2.5.1 Predictions and measurements 37
2.5.2 Residual lack of fit 38
2.5.3 Confidence limits for fitted parameters 39
2.5.4 Sensitivity analysis 41
2.6 Multiple Steady States 41
2.6.1 Switches 42
2.6.2 Catastrophe 47
2.6.3 Oscillations 49
2.6.4 Chaos 50
Exercises 54
3 Mathematical Programming 57
Summary 57
3.1 Introduction 57
3.2 Mathematical Formulation 58
3.2.1 Example 59
3.3 Graphical Solution 62
3.4 Computer Solution 65
3.5 Worked Example 71
3.5.1 Formulation 72
3.5.2 Solution 74
3.6 Special Topics 76
3.6.1 Parametric programming 76
3.6.2 Separable programming 77
3.6.3 Integer programming 83
3.6.4 Goal programming 84
3.6.5 Dynamic programming 85
Exercises 88
4 Basic Biological Processes 91
Summary 91
4.1 Chemical Kinetics 91
4.1.1 First-order reactions 93
4.1.2 Second-order reactions 96
4.1.3 Stochastic approach to chemical kinetics 98
4.2 Catalysis 102
4.2.1 Arrhenius equation 103
4.2.2 Phenomenological temperature function 105
Contents vii
4.3 Biochemical Kinetics 107
4.3.1 Michaelis-Menten kinetics 107
4.3.2 Sigmoidal kinetics 109
4.3.3 Transport plus Michaelis—Menten kinetics 110
4.3.4 Bisubstrate Michaelis—Menten equation 113
4.3.5 Inhibition 114
4.3.6 Activation 116
4.3.7 Futile cycles 116
4.4 Transport 118
4.4.1 Diffusion — Fick's law 118
4.4.2 Convection 120
4.4.3 General equation for transport and chemical
reaction 120
4.4.4 Examples 122
4.4.5 Lumped representation of transport 126
4.4.6 Difference equation representation 128
4.5 Local and Non-local Variables 129
Exercises 131
5 Growth Functions 136
Summary 136
5.1 Introduction 136
5.2 Exponential Growth 139
5.3 Monomolecular Equation 140
5.4 Logistic Equation 143
5.5 Gompertz Equation 145
5.6 Chanter Equation 148
5.7 Exponential Quadratic Equation 150
5.8 Von Bertalanffy Equation 152
5.9 Richards Equation 155
5.10 Schumacher Equation 157
5.11 Morgan Equation 160
5.12 Other Growth Equations 163
Exercises 169
6 Simple Dynamic Growth Models 172
Summary 172
6.1 Introduction 172
6.2 Autocatalytic Growth with Sigmoidal Substrate Limitation 173
6.3 Delayed Growth 174
6.4 Compensatory Growth 178
6.4.1 Model scheme 178
6.4.2 Simulations 182
6.5 Square-root-time Growth Equation 184
6.6 'Open' Logistic Growth 186
6.7 Logistic Equation Modified for Substrate Supply and
Product Inhibition 188
VIII
Contents
6.8 Gompertz with Delayed Development 190
6.9 Expo-linear-asymptotic Growth 192
6.9.1 Hyperbolic formulation 193
6.9.2 Negative-exponential formulation 196
6.10 Allometry and Scaling 196
6.10.1 Application of simple geometrical factors 198
6.10.2 A branching model for allometric scaling 199
6.10.3 Scaling in relation to maturity 202
6.11 Biological Oscillators 204
6.11.1 Gene-metabolism oscillator 204
6.11.2 Alternative-pathways oscillator 206
6.11.3 Grazed-pasture oscillator 208
Exercises 210
7 Simple Ecological Models 213
Summary 213
7.1 Introduction 213
7.2 Difference Equations and Differential Equations 214
7.3 Age-structured Models of Population Growth 215
7.3.1 Discrete-age discrete-time model 216
7.3.2 Discrete-age continuous-time scheme 219
7.3.3 Continuous-age continuous-time model 221
7.4 Morph-structured Growth Model 223
7.5 Morph- and Age-structured Growth Model 226
7.6 Lotka-Volterra Type Model 227
7.7 Disease/Epidemic Models 229
7.7.1 Five-compartment disease model 229
7.7.2 Spatial aspects 230
Exercises 233
8 Environment and Weather 235
Summary 235
8.1 Introduction 235
8.2 Time 236
8.3 Solar Angles and Day Length 237
8.3.1 Day length switching 241
8.4 Representing Weather in Models 243
8.4.1 Need for diurnal data in models 243
8.4.2 Matching measured diurnal data to the model 244
8.4.3 Generating diurnal data from daily data 245
8.4.4 Generating daily data from monthly data
deterministically 251
8.4.5 Generating daily data from monthly data
stochastically 253
8.4.6 Deterministic sinusoidal seasonal variation 262
8.5 Bright Sunshine Hours and Daily Radiation Receipt 263
Contents ix
8.6 Angular Distribution of Radiation 264
8.6.1 Direct solar radiation 265
8.6.2 Diffuse radiation from a clear sky 265
8.6.3 Overcast skies 265
8.7 Wind 267
8.7.1 Diurnal variation 269
8.7.2 Seasonal variation 270
8.8 Climate Change 270
Exercises 272
PART II CROPS
9 Plant and Crop Processes 275
Summary 275
9.1 Introduction 275
9.2 Light Interception 277
9.2.1 Crops with closed canopies 278
9.2.2 Single plant 282
9.2.3 Discontinuous canopies 284
9.2.4 Mixtures 287
9.3 Photosynthesis 288
9.3.1 Overview of photosynthesis 289
9.3.2 Leaf photosynthesis 290
9.3.3 Canopy photosynthesis 295
9.3.4 Integrable closed-canopy models 296
9.3.5 Single-plant photosynthesis 301
9.3.6 Photosynthesis of discontinuous canopies 303
9.3.7 Mixtures 305
9.4 Nitrogen Uptake; Nitrogen Fixation 305
9.4.1 Nitrogen uptake 306
9.4.2 Nitrogen fixation 309
9.5 Growth and Respiration 310
9.5.1 Growth 311
9.5.2 Maintenance 312
9.5.3 Pathway analysis 313
9.5.4 Futile cycles 324
9.6 Allocation 326
9.6.1 Empiricism 327
9.6.2 Teleonomy 327
9.6.3 Mechanism 333
9.7 Development 341
9.7.1 Temperature sums 343
9.7.2 Generalized developmental rates 345
9.7.3 Compartmental models of development 346
9.7.4 Survey of recent contributions 348
9.8 Water 349
9.8.1 Water potential 350
Contents
9.8.2 Soil water 353
9.8.3 Root and shoot water 357
9.8.4 Transpiration 362
9.8.5 Soil surface evaporation 373
9.8.6 Rainfall interception by canopy and evaporation 374
9.9 Leaf Stomatal Resistance 375
9.9.1 Basic definitions 376
9.9.2 Responses of stomata to environment and plant
variables 378
Exercises 381
10 Crop Models 385
Summary 385
10.1 Introduction 385
10.2 Crop Model Structure 387
10.3 Simple Generic Daily Crop Model 388
10.3.1 Environment 390
10.3.2 Temperature functions 392
10.3.3 Plant submodel 393
10.3.4 Litter and soil submodel 401
10.3.5 Hydrology 403
10.3.6 Simulations 408
10.4 Supply-Demand Models 413
10.4.1 Supply and demand in relation to carbon and
nitrogen 415
10.4.2 Supply-demand model of lettuce growth with
osmotic regulation 416
10.4.3 Supply-demand models: do they have a role? 425
10.5 Plant Competition 426
10.5.1 Two plants compete for a single substrate 427
10.5.2 Interaction of two plants simulated 429
10.5.3 Crops, weeds and mixtures 431
10.5.4 Self-thinning: the three-halves rule 436
10.5.5 Intercropping and agroforestry 439
10.5.6 Genetically modified crops 441
10.6 Allelopathy and Phytotoxicity 444
10.6.1 Stimulus and inhibition 445
10.6.2 Dynamics of an allelochemical and its effect 445
Exercises 447
11 Crop Husbandry 450
Summary 450
11.1 Introduction 450
11.2 A Grass Drying Enterprise 451
11.3 Allocating Land to Arable Crops 454
11.4 Harvesting Plans for Brussels Sprouts 457
11.5 Planting Wheat 460
Contents xi
11.6 Grazing 462
11.6.1 Systems of rotational grazing 462
11.6.2 Continuous and rotational grazing 464
11.7 Grassland and Fertilizer Usage 466
11.8 Silage 469
11.8.1 Anaerobic phase of ensiling 469
Exercises 477
12 Plant Diseases and Pests 481
Summary 481
12.1 Introduction 481
12.2 Estimation of Yield Loss 483
12.3 Disease Prediction 484
12.3.1 Potato late blight 484
12.3.2 Sugar beet yellows virus 487
12.4 Mechanistic Disease Simulation 488
12.4.1 Sugar beet fungal root infection 488
12.4.2 Potato late blight 494
12.5 Pests 504
12.5.1 Plant, pests and parasites 504
12.5.2 Plants and aphids 508
Exercises 518
PART III ANIMALS
13 Animal Processes 522
Summary 522
13.1 Introduction 522
13.2 Tissue and Whole-body Protein Synthesis 523
13.3 Production of Volatile Fatty Acids in the Rumen 525
13.4 Viability of the Fungal Population in the Rumen 529
13.5 Leucine Kinetics in the Udder 534
13.6 Degradation of Feed in the Rumen 539
13.6.1 In sacco system 539
13.6.2 In vitro system 543
13.7 Passage of Digesta through the Gastro-intestinal Tract 547
Exercises 553
14 Animal Organs 560
Summary 560
14.1 Introduction 560
14.2 The Mammary Gland 560
14.2.1 Hormone, H 562
14.2.2 Division of undifferentiated cells, Cu 563
14.2.3 Production and loss of secretory cells, Cs 563
14.2.4 Secretion and removal of milk, M 565
14.2.5 Averaged amount of milk in animal, M 566
14.2.6 Substrate, S 567
xii Contents
14.2.7 Mathematical summary 567
14.2.8 Application 568
14.2.9 More detailed mammary models 570
14.3 The Rumen 570
14.3.1 Model description 570
14.3.2 Model application 573
14.3.3 Model developments 5 74
14.4 Other Organs 575
14.5 Blood 575
14.5.1 Dual indicator method for estimating blood flow 577
14.5.2 Blood flow and uptake of nutrients by the udder 579
Exercises 583
15 Whole-animal Models 593
Summary 593
15.1 Introduction 593
15.2 The Veal Calf 593
15.2.1 Digestion 594
15.2.2 Protein metabolism 595
15.2.3 Energy metabolism 596
15.2.4 Body ash and auxiliary variables 596
15.2.5 Model application 597
15.3 The Lactating Dairy Cow 599
15.3.1 Rumen module 600
15.3.2 Body metabolism module 602
15.3.3 Model application 603
15.3.4 Other dairy cow models 604
15.4 The Pig 605
15.4.1 Auspig 605
15.4.2 Lactating sow model 607
Exercises 610
16 Animal Products 620
Summary 620
16.1 Introduction 620
16.2 Milk Yield by the Dairy Cow 620
16.2.1 Gaines equation 621
16.2.2 Wood equation 622
16.2.3 Dijkstra equation 627
16.2.4 Other lactation equations 630
16.3 Efficiency of Energy Utilization for Milk Production 632
16.4 Meat Produced by the Growing Animal 635
16.4.1 Blaxter equation 636
16.4.2 Allometry and body composition 640
16.5 Efficiency of Energy Utilization for Growth 641
16.5.1 Intake and liveweight gain 642
16.5.2 Feed consumption and liveweight 644
Contents
16.6 Egg Production by the Laying Hen 645
16.6.1 McMillan equation 646
16.6.2 Other egg production equations 649
16.7 Amino Acid Requirements of Laying Hens 650
16.7.1 Hurwitz equation 650
16.7.2 Reading model 651
16.8 Calcium and Phosphorus Flows in Laying Hens 654
16.8.1 Model formulation 655
16.8.2 Operation 661
16.8.3 Results 661
16.9 Wool Growth 663
16.9.1 Physiology of wool growth 664
16.9.2 Research models of wool growth 664
16.9.3 Simplified models of wool growth for decision
support 670
Exercises 672
17 Animal Husbandry 677
Summary 677
17.1 Introduction 677
17.2 Ration Formulation 677
17.3 Allocating Pregnant Ewes to Feeding Groups 682
17.4 Effects of Feeding Level on Milk Production and
Live-weight 685
17.5 Pattern of Calving 688
17.6 Replacement 690
Exercises 691
18 Animal Diseases 694
Summary 694
18.1 Introduction 694
18.2 Bovine Spongiform Encephalopathy 695
18.2.1 Deterministic five-pool BSE model 695
18.2.2 Age-stratified BSE model 698
18.3 Rabbit Haemorrhagic Disease 703
18.4 Foot and Mouth Disease 706
18.4.1 Single-farm disease dynamics 708
18.4.2 Spatial disease spread 711
18.4.3 Secondary infections 712
Exercises 715
Solutions to Exercises 717
Mathematical Glossary 803
Bessel Functions 803
Binomial and Poisson Distributions 805
Coordinate Axes Systems 808
xiv Contents
Determinants, see Matrices and Determinants
Differentiation 810
Dirac Delta Function 812
Duality 813
Eigenvalues 814
Error Function 815
Fourier Series 816
F-test 818
Gamma Function and Gamma Distribution 818
Geometric Series 822
Hôpital's Rule 822
Hyperbolas: Rectangular and Non-rectangular 823
Integration by Parts 825
Linear Differential Equations 825
Matrices and Determinants 827
Newton-Raphson Method 830
Normal and Log-normal Distribution Functions 831
Numerical Differentiation 835
Partial Fractions 835
Poisson Distribution, see Binomial and Poisson Distributions
Quadratic Forms 836
Taylor Series 837
t-distribution 838
Vectors 839
Appendix: Constants and Conversions 841
Bibliography: Further Reading and References 843
Index 887 |
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| author | Thornley, John H. M. France, J. |
| author_facet | Thornley, John H. M. France, J. |
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| discipline | Agrarwissenschaft Agrar-/Forst-/Ernährungs-/Haushaltswissenschaft / Gartenbau Wirtschaftswissenschaften |
| discipline_str_mv | Agrarwissenschaft Agrar-/Forst-/Ernährungs-/Haushaltswissenschaft / Gartenbau Wirtschaftswissenschaften |
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| id | DE-604.BV020851991 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:20:11Z |
| indexdate | 2024-07-09T20:26:39Z |
| institution | BVB |
| isbn | 085199010X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014173686 |
| oclc_num | 56614314 |
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| owner_facet | DE-M49 DE-BY-TUM |
| physical | XVII, 906 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | CABI Publ. |
| record_format | marc |
| spelling | Thornley, John H. M. Verfasser aut Mathematical models in agriculture quantitative methods for the plant, animal and ecological science J. H. M. Thornley and J. France 2. ed. Wallingford [u.a.] CABI Publ. 2007 XVII, 906 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Agriculture - Modèles mathématiques Landwirtschaft Mathematisches Modell Agriculture Mathematical models Landwirtschaft (DE-588)4034402-2 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 s Landwirtschaft (DE-588)4034402-2 s DE-604 France, J. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014173686&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Thornley, John H. M. France, J. Mathematical models in agriculture quantitative methods for the plant, animal and ecological science Agriculture - Modèles mathématiques Landwirtschaft Mathematisches Modell Agriculture Mathematical models Landwirtschaft (DE-588)4034402-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4034402-2 (DE-588)4114528-8 |
| title | Mathematical models in agriculture quantitative methods for the plant, animal and ecological science |
| title_auth | Mathematical models in agriculture quantitative methods for the plant, animal and ecological science |
| title_exact_search | Mathematical models in agriculture quantitative methods for the plant, animal and ecological science |
| title_exact_search_txtP | Mathematical models in agriculture quantitative methods for the plant, animal and ecological science |
| title_full | Mathematical models in agriculture quantitative methods for the plant, animal and ecological science J. H. M. Thornley and J. France |
| title_fullStr | Mathematical models in agriculture quantitative methods for the plant, animal and ecological science J. H. M. Thornley and J. France |
| title_full_unstemmed | Mathematical models in agriculture quantitative methods for the plant, animal and ecological science J. H. M. Thornley and J. France |
| title_short | Mathematical models in agriculture |
| title_sort | mathematical models in agriculture quantitative methods for the plant animal and ecological science |
| title_sub | quantitative methods for the plant, animal and ecological science |
| topic | Agriculture - Modèles mathématiques Landwirtschaft Mathematisches Modell Agriculture Mathematical models Landwirtschaft (DE-588)4034402-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Agriculture - Modèles mathématiques Landwirtschaft Mathematisches Modell Agriculture Mathematical models |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014173686&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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