Matrix population models: construction, analysis, and interpretation
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Sunderland, Mass.
Sinauer Associates
2001
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. [669]-710) |
| Physical Description: | XXII, 722 S. |
| ISBN: | 0878930965 9780878931217 |
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| 245 | 1 | 0 | |a Matrix population models |b construction, analysis, and interpretation |c Hal Caswell |
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| 650 | 4 | |a Matrices - Informatique | |
| 650 | 7 | |a Modulaire matrices |2 gtt | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Matrices |x Data processing | |
| 650 | 4 | |a Population biology |x Computer simulation | |
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Record in the Search Index
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| adam_text | Matrix
Population
Models
CONSTRUCTION, ANALYSIS, AND INTERPRETATION
J
Second Edition f
HAL C!ASWELL
Biology Department
Woods Hole Oceanographic Institution
Sinauer Associate, In amp; «Euhlisher s
Sunderland, M j
•t
4_ * *?*£**•
Contents
Preface xvii
Preface to the First Edition xxi
1 Introduction ) 1
1 1 The life cycle: Linking the individual and
the population 1
1 2 Demography 2
1 3 Overview of the book 3
131 Examples 4
132 MATLAB programs 5
1 4 Construction, analysis, and interpretation 5
1 5 Mathematical prerequisites 5
1 6 Notation 6
2 Age-Classified Matrix Models 8
2 1 The Leslie matrix 8
2 2 Projection: the simplest form of analysis 11
221A set of questions 18
2 3 The Leslie matrix and the life table 20
231 Survival 21
232 Reproduction 22
2 4 Constructing age-classified matrices 22
241 Birth-flow populations 23
242 Birth-pulse populations 25
2 5 Assumptions: Projection vs forecasting 29
2 6 History 31
3 Stage-Classified Life Cycles 35
3 1 State variables 35
311 Zadeh s theory of state 36
312 State variables in population models 37
viii CONTENTS
3 2 Age as a state variable: When does it fail? 38
321 Size-dependent vital rates and plastic growth 39
322 Multiple modes of reproduction 40
323 Population subdivision and multistate demography 41
3 3 Statistical evaluation of state variables 41
331 Continuous response, continuous or discrete state 41
332 Discrete state, discrete response 43
333 Continuous state, discrete response 54
3 4 Overview 55
Stage-Classified Matrix Models 56
4 1 The life cycle graph 56
4 2 The matrix model 59
4 3 Metapopulation and multistate models 62
431 Modelling dispersal 65
432 Integrodifference equation models 71
433 Other examples 72
4 4 Solution of the projection equatio n 72
441 Derivation 1 74
442 Derivation 2 75
443 Effects of the eigenvalues 76
4 5 Ergodicity 79
451 The Perron-Frobenius theorem 79
452 Population growth rate: The strong ergodic theorem 84
453 Imprimitive matrices 87
454 Reducible matrices 88
4 6 Reproductive value 92
4 7 Transient dynamics and convergence 94
471 The damping ratio and convergence 95
472 The period of oscillation 100
473 Measuring the distance to the stable stage distribution 101
474 Population momentum 104
4 8 Computation of eigenvalues and eigenvectors 106
481 Eigenvalues and eigenvectors in MATLAB 107
482 The power method 108
4 9 Assumptions revisited 109
Events in the Life Cycle 110
51A=T+F 110
511 The life cycle as a Markov chain I l l
512 The analysis of absorbing chains 112
5 2 Lifetime event probabilities 115
5 3 Age-specific traits 116
CONTENTS ix
531 Age-specific survival 118
532 Age-specific fertility 120
533 Age at first reproduction 124
534 Net reproductive rate 126
535 Generation time 128
536 Age-within-stage distributions 130
6 Parameter Estimation 133
6 1 Identified individuals 134
611 Observed transition frequencies 134
612 Mark-recapture methods 136
6 2 Inverse methods for time series 142
621 Regression methods 142
622 Wood s quadratic programming method 144
623A maximum likelihood approach 152
624 Stage-frequency methods 154
6 3 Stable stage-distribution methods 154
631 Age-classified models 154
632 Size-classified models 157
633 Death assemblages 157
6 4 Stage-duration distributions 159
641 The geometric distribution 160
642 Fixed stage durations 160
643 Variable stage durations 162
644 Iterative calculation 164
645 Negative binomial stage durations 164
646 Duration distributions compared 165
6 5 Multiregional or age-size models 166
6 6 Size categories: The Vandermeer-Moloney algorithms 169
6 7 Fertilities in stage-classified models 171
671 Birth-flow populations 171
672 Birth-pulse populations : 172
673 Anonymous reproduction 173
6 8 Overview 174
7 Analysis of the Life Cycle Graph 176
7 1 The 2-transform 177
711 ^-transform solution of difference equations 177
712 The z-transformed life cycle graph 178
7 2 Reduction of the life cycle graph 178
721 Multistep transitions 181
7 3 The characteristic equation 181
731 Derivation 184
CONTENTS
7 4 The stable stage distribution 185
741 Derivation 187
7 5 Reproductive value 187
751A second interpretation of reproductive value 189
752A note on eigenvectors of reducible matrices 190
7 6 Partial life cycle analysis 190
7 7 Annual organisms 192
Structured Population Models 194
8 1 Partial differential equation models 194
811 Lotka s renewal equation 196
812 Discretizing Lotka s equation: Don t bother 197
813 Diffusion models 198
814 PDE models and matrix models 198
815 The escalator boxcar train 199
8 2 Delay-differential equation models 201
8 3 Integrodifference equation models i 202
8 4 i-state configuration models 202
8 5 Choosing a model 204
Sensitivity Analysis 206
9 1 Eigenvalue sensitivity 208
911 Perturbations of matrix elements 208
912 Sensitivity and age 211
913 Sensitivities in stage- and size-classified models 213
914 What about those zeros? 215
915 Sensitivity to multistep transitions 217
916 Total derivatives and multiple perturbations 218
917 Sensitivity to changes in development rate 220
918 Predictions from sensitivities 224
919 An overall eigenvalue sensitivity index 224
9 1 10 A third interpretation of reproductive value 225
9 2 Elasticity analysis 226
921 Elasticity and age 227
922 Elasticities as contributions to A 229
923 Elasticities of A to lower-level parameters 232
924 Comparative analysis of elasticity patterns 233
925 Predictions from elasticities 240
926 Sensitivity or elasticity? 243
9 3 Sensitivity analysis of transient dynamics 244
931 Sensitivity of the damping ratio 244
932 Sensitivity of the period 247
9 4 Sensitivities of eigenvectors 247
CONTENTS xi
941 Sensitivities of scaled eigenvectors 250
9 5 Generalized inverses in sensitivity analysis 251
9 6 Sensitivity analysis of Markov chains 251
9 7 Second Derivatives of Eigenvalues 254
971 Perturbation analysis of elasticities 256
10 Life Table Response Experiments 258
10 1 Fixed designs 260
10 1 1 One-way designs 260
10 1 2 Factorial designs 263
10 2 Random designs and variance decomposition 269
10 3 Regression designs 273
10 4 Extensions 274
10 4 1 Higher-order terms 274
10 4 2 Other demographic statistics 275
10 4 3 Other demographic models 275
10 4 4 More mechanisms 276
10 4 5 Statistics 277
10 5 Prospective and retrospective analyses 277
11 Evolutionary Demography 279
11 1 Fitness 280
11 1 1 Population genetics 281
11 1 2 Quantitative genetics 282
11 1 3 Invasion and ESS analysis 291
11 2 Sensitivity, elasticity, and selection 295
11 3 Lifetime reproductive success and
individual fitness 295
11 4 Fitness and reproductive value 297
12 Statistical Inference 299
12 1 Confidence intervals and uncertainty 300
12 1 1 Series approximations 300
12 1 2 Bootstrap standard errors 304
12 1 3 Bootstrap confidence intervals 306
12 1 4 Complex data structures 309
12 1 5 More on the bootstrap 315
12 1 6 Monte Carlo uncertainty analysis 319
12 1 7 The precision of estimates of A 322
12 2 Loglinear analysis of transition matrices 326
12 2 1 One factor 327
12 2 2 Two factors 330
12 2 3 Model selection and AIC 332
xii CONTENTS
12 2 4 Presentation of loglinear analyses 334
12 3 Randomization tests 335
12 3 1 The randomization test procedure 337
12 3 2 Types of data 338
12 3 3 Examples of randomization tests 338
12 3 4 Advantages of randomization tests 343
12 3 5 Implementation 345
13 Periodic Environments 346
13 1 Periodic matrix products 347
13 1 1 Notation 348
13 1 2 Eigenvalues and eigenvectors 349
13 1 3 Matrices don t commute, and why that matters 354
13 1 4 Sensitivity analysis of periodic matrix models 356
13 2 Annual organisms 361
13 2 1 Periodic matrix models for annuals 362
13 3 Other approaches to periodic environments 368
13 3 1 Classification by season of birth 368
13 3 2 Discrete Fourier analysis 368
13 4 Deterministic, aperiodic environments 369
13 4 1 Weak ergodicity 369
14 Environmental Stochasticity 377
14 1 Formulation of stochastic models 377
14 1 1 Models for the environment 378
14 1 2 Linking the environment and the vital rates 381
14 1 3 Projecting the population 382
14 2 Stochastic ergodic theorems 382
14 2 1 Stage distributions 382
14 2 2 Stochastic reproductive value 384
14 2 3 Sufficient conditions for stochastic ergodicity 384
14 2 4 An overview of ergodic results 386
14 3 Stochastic population growth 387
14 3 1 The Lewontin-Cohen model 387
14 3 2 Beyond iid processes 392
14 3 3 Ergodic properties of random matrix products 393
14 3 4 Growth of the mean 394
14 3 5 Which growth rate is relevant? 395
14 3 6 Calculating the stochastic growth rate 396
14 3 7 Calculation of the variance a1 399
14 3 8 Scalar and matrix models compared 400
14 4 Sensitivity and elasticity analyses 401
14 4 1 From numerical simulations 402
CONTENTS xiii
14 4 2 From Tuljapurkar s approximation 407
14 4 3 Sensitivity of log As to variability 408
14 5 Examples of stochastic models 409
14 5 1 Striped bass: Variability in recruitment 409
14 5 2 Clams: Parametric distributions of recruitment 410
14 5 3 Stochastic models from sequence of matrices 415
14 5 4 Markov chain models for the environment 419
14 5 5 Random selection of matrix elements 430
14 5 6 Applications of Tuljapurkar s approximation 435
14 5 7 Some suggestions 435
14 6 Evolution in stochastic environments 436
14 6 1 Fitness and ESS in stochastic environments 436
14 6 2 An example: Delayed reproduction 437
14 6 3 Life history studies 440
14 7 Sensitivity: Stochastic and deterministic
models 443
14 8 Extinction in stochastic environments 443
14 81A model for quasi-extinction 444
14 8 2 Sensitivity analysis 447
14 9 Short-term stochastic forecasts 449
15 Demographic Stochasticity 452
15 1 Stochastic simulations 453
15 1 1 Assumptions, essential and otherwise 456
15 1 2 Simulating individuals 456
15 13A computationally efficient alternative 458
15 1 4 Bad luck, or something worse? 462
15 1 5 Time-varying and density-dependent models 464
15 2 The Galton-Watson branching process 464
15 2 1 Probability generating functions 466
15 2 2 Population projection 467
15 2 3 Projection of moments : 470
15 2 4 Limit theorems and asymptotic dynamics 471
15 2 5 Extinction 472
15 2 6 Quasi-stationary distributions 475
15 2 7 Extinction, effective population size, and elasticity 475
15 3 Multitype branching processes 478
15 3 1 From matrix models to branching processes 479
15 3 2 Mean and covariance of offspring production 483
15 4 Analysis of multitype branching processes 486
15 4 1 Population projection 486
15 4 2 Projection of moments 486
15 4 3 Limit theorems and asymptotic dynamics 491
xiv CONTENTS
15 4 4 Extinction probability 493
15 4 5 Extinction probability and reproductive value 497
15 4 6 Elasticities of extinction probability and of A 497
15 4 7 Subcritical multitype branching processes 499
15 5 Branching processes in random environments 501
15 6 Assumptions revisited 502
16 Density-Dependent Models 504
16 1 Model construction 505
16 1 1 Types of density dependence 505
16 1 2 Examples 508
16 2 Asymptotic dynamics and invariant sets 513
16 2 1 Finding equilibria 518
16 3 Stability and instability 519
16 4 Local stability of equilibria 519
16 4 1 The Jury criteria 522
16 5 Bifurcation diagrams 525
16 6 Bifurcations of equilibria: A field guide 526
16 6 1 +1 bifurcations 528
16 62-1 bifurcations: The flip bifurcation 533
16 6 3 Complex conjugate pairs: The Hopf bifurcation 533
16 6 4 Supercritical and subcritical bifurcations 537
16 7 Chaos 538
16 7 1 Lyapunov exponents and
quantitative unpredictability 542
16 7 2 Routes to chaos 543
16 7 3 Chaotic power spectra 546
16 8 Transient dynamics 548
16 8 1 Reactivity and resilience of stable equilibria 548
16 8 2 Unstable equilibria 550
16 8 3 Strange repellers and chaotic transients 551
16 8 4 Effects of random perturbations 551
16 9 Multiple attractors and
qualitative unpredictability 552
IG lOTribolium: Models and experiments 553
16 UPerturbation analysis and evolution 557
16 11 1 Sensitivity analysis of equilibria 559
16 11 2Invasion and evolution 560
16 12Stochasticity and density dependence 565
CONTENTS xv
17 Two-Sex Models 568
17 1 Sexual dimorphism in the vital rates 568
17 2 Dominance, sex ratio, and
the marriage squeeze 570
17 3 Two-sex models 571
17 31A simple two-sex model 572
17 3 2 The birth and fertility functions 574
17 3 3 Frequency and density dependence 576
17 3 4 The equilibrium population structure 576
17 3 5 Stability of population structure 578
17 3 6 Nussbaum s global stability theorem 581
17 4 Competition for mates 581
17 4 1 Numerical results: Competition and instability 583
17 5 The birth matrix-mating rule model 585
17 6 More detailed models of mating 587
17 7 Frequency and density dependence combined -588
17 8 Extinction and the sex ratio 589
i
18 Conservation and Management 591
18 1 Conservation 592
18 1 1 Assessment 592
18 1 2 Diagnosis 601
18 1 3 Prescription 604
18 1 4 Prognosis 619
18 1 5 Conservation conclusions 629
18 2 Pest control 629
18 2 1 Reducing population size 630
18 2 2 Extermination 631
18 2 3 Halting invasion 632
18 2 4 Some examples of pest control 634
18 3 Harvesting 640
18 3 1 Optimal harvesting - 642
18 4 Overview 644
19 Concluding Remarks 646
19 1 The most important task 646
19 2 Testing models 648
19 3 A complete demographic analysis 649
19 4 Directions for research 651
xvi CONTENTS
A The Basics of Matrix Algebra 653
A I Motivation 653
A 2 Definitions 654
A 3 Operations 655
A31 Addition 655
A32 Scalar multiplication 655
A33 The transpose and the adjoint 655
A34 The trace 656
A35 Scalar product 656
A36 Matrix multiplication 656
A37 The Kronecker and Hadamard products 658
A 4 Matrix inversion 659
A41 The identity matrix 659
A42 Inversion and the solution of algebraic equations 659
A43A useful fact about homogeneous systems 660
A 5 Determinants 660
A51 Properties of determinants 662
A 6 Eigenvalues and eigenvectors 662
A61 Eigenvectors 662
A62 Left eigenvectors 663
A63 The characteristic equation 663
A64 Finding the eigenvectors 664
A65 Complications 665
A66 Linear independence of eigenvectors 665
A67 Left and right eigenvectors 666
A68 Computation of eigenvalues and eigenvectors 666
A 7 Similarity 666
A71 Properties of similar matrices 667
A 8 Norms of vectors and matrices 667
A 9 Suggested reading 668
Bibliography 669
Copyright Permissions 711
Index 713
|
| any_adam_object | 1 |
| author | Caswell, Hal |
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| dewey-full | 577.8/8/0113 |
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| discipline | Biologie Wirtschaftswissenschaften Geographie |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV014624049 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:04:33Z |
| institution | BVB |
| isbn | 0878930965 9780878931217 |
| language | English |
| lccn | 00058836 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009939976 |
| oclc_num | 612054951 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 DE-945 DE-11 DE-20 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-945 DE-11 DE-20 |
| physical | XXII, 722 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Sinauer Associates |
| record_format | marc |
| spelling | Caswell, Hal Verfasser aut Matrix population models construction, analysis, and interpretation Hal Caswell 2. ed. Sunderland, Mass. Sinauer Associates 2001 XXII, 722 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. [669]-710) Biologie des populations - Simulation par ordinateur Demografie gtt Matrices - Informatique Modulaire matrices gtt Datenverarbeitung Matrices Data processing Population biology Computer simulation Populationsbiologie (DE-588)4046800-8 gnd rswk-swf Computersimulation (DE-588)4148259-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Matrixverfahren (DE-588)4169123-4 gnd rswk-swf Populationsdynamik (DE-588)4046803-3 gnd rswk-swf Sozialanthropologie (DE-588)4129436-1 gnd rswk-swf Populationsdynamik (DE-588)4046803-3 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Populationsbiologie (DE-588)4046800-8 s Matrixverfahren (DE-588)4169123-4 s Computersimulation (DE-588)4148259-1 s 1\p DE-604 Sozialanthropologie (DE-588)4129436-1 s 2\p DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009939976&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Caswell, Hal Matrix population models construction, analysis, and interpretation Biologie des populations - Simulation par ordinateur Demografie gtt Matrices - Informatique Modulaire matrices gtt Datenverarbeitung Matrices Data processing Population biology Computer simulation Populationsbiologie (DE-588)4046800-8 gnd Computersimulation (DE-588)4148259-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Matrixverfahren (DE-588)4169123-4 gnd Populationsdynamik (DE-588)4046803-3 gnd Sozialanthropologie (DE-588)4129436-1 gnd |
| subject_GND | (DE-588)4046800-8 (DE-588)4148259-1 (DE-588)4114528-8 (DE-588)4169123-4 (DE-588)4046803-3 (DE-588)4129436-1 |
| title | Matrix population models construction, analysis, and interpretation |
| title_auth | Matrix population models construction, analysis, and interpretation |
| title_exact_search | Matrix population models construction, analysis, and interpretation |
| title_full | Matrix population models construction, analysis, and interpretation Hal Caswell |
| title_fullStr | Matrix population models construction, analysis, and interpretation Hal Caswell |
| title_full_unstemmed | Matrix population models construction, analysis, and interpretation Hal Caswell |
| title_short | Matrix population models |
| title_sort | matrix population models construction analysis and interpretation |
| title_sub | construction, analysis, and interpretation |
| topic | Biologie des populations - Simulation par ordinateur Demografie gtt Matrices - Informatique Modulaire matrices gtt Datenverarbeitung Matrices Data processing Population biology Computer simulation Populationsbiologie (DE-588)4046800-8 gnd Computersimulation (DE-588)4148259-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Matrixverfahren (DE-588)4169123-4 gnd Populationsdynamik (DE-588)4046803-3 gnd Sozialanthropologie (DE-588)4129436-1 gnd |
| topic_facet | Biologie des populations - Simulation par ordinateur Demografie Matrices - Informatique Modulaire matrices Datenverarbeitung Matrices Data processing Population biology Computer simulation Populationsbiologie Computersimulation Mathematisches Modell Matrixverfahren Populationsdynamik Sozialanthropologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009939976&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT caswellhal matrixpopulationmodelsconstructionanalysisandinterpretation |