Item Details

Matrix Population Models: Construction, Analysis, and Interpretation

Hal Caswell
Format
Book
Published
Sunderland, Mass. : Sinauer Associates, c2001.
Edition
2nd ed
Language
English
ISBN
0878930965
Contents
  • 1.1 Life cycle: Linking the individual and the population 1
  • 1.3.2 Matlab programs 5
  • 1.4 Construction, analysis, and interpretation 5
  • 1.5 Mathematical prerequisites 5
  • 2 Age-Classified Matrix Models 8
  • 2.1 Leslie matrix 8
  • 2.2 Projection: the simplest form of analysis 11
  • 2.2.1 A set of questions 18
  • 2.3 Leslie matrix and the life table 20
  • 2.3.1 Survival 21
  • 2.3.2 Reproduction 22
  • 2.4 Constructing age-classified matrices 22
  • 2.4.1 Birth-flow populations 23
  • 2.4.2 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
  • 3.1.1 Zadeh's theory of state 36
  • 3.1.2 State variables in population models 37
  • 3.2 Age as a state variable: When does it fail? 38
  • 3.2.1 Size-dependent vital rates and plastic growth 39
  • 3.2.2 Multiple modes of reproduction 40
  • 3.2.3 Population subdivision and multistate demography 41
  • 3.3 Statistical evaluation of state variables 41
  • 3.3.1 Continuous response, continuous or discrete state 41
  • 3.3.2 Discrete state, discrete response 43
  • 3.3.3 Continuous state, discrete response 54
  • 4 Stage-Classified Matrix Models 56
  • 4.1 Life cycle graph 56
  • 4.2 Matrix model 59
  • 4.3 Metapopulation and multistate models 62
  • 4.3.1 Modelling dispersal 65
  • 4.3.2 Integrodifference equation models 71
  • 4.4 Solution of the projection equation 72
  • 4.4.1 Derivation 1 74
  • 4.4.2 Derivation 2 75
  • 4.4.3 Effects of the eigenvalues 76
  • 4.5 Ergodicity 79
  • 4.5.1 Perron-Frobenius theorem 79
  • 4.5.2 Population growth rate: The strong ergodic theorem 84
  • 4.5.3 Imprimitive matrices 87
  • 4.5.4 Reducible matrices 88
  • 4.6 Reproductive value 92
  • 4.7 Transient dynamics and convergence 94
  • 4.7.1 Damping ratio and convergence 95
  • 4.7.2 Period of oscillation 100
  • 4.7.3 Measuring the distance to the stable stage distribution 101
  • 4.7.4 Population momentum 104
  • 4.8 Computation of eigenvalues and eigenvectors 106
  • 4.8.1 Eigenvalues and eigenvectors in Matlab 107
  • 4.8.2 Power method 108
  • 4.9 Assumptions revisited 109
  • 5 Events in the Life Cycle 110
  • 5.1 A = T + F 110
  • 5.1.1 Life cycle as a Markov chain 111
  • 5.1.2 Analysis of absorbing chains 112
  • 5.2 Lifetime event probabilities 115
  • 5.3 Age-specific traits 116
  • 5.3.1 Age-specific survival 118
  • 5.3.2 Age-specific fertility 120
  • 5.3.3 Age at first reproduction 124
  • 5.3.4 Net reproductive rate 126
  • 5.3.5 Generation time 128
  • 5.3.6 Age-within-stage distributions 130
  • 6 Parameter Estimation 133
  • 6.1 Identified individuals 134
  • 6.1.1 Observed transition frequencies 134
  • 6.1.2 Mark-recapture methods 136
  • 6.2 Inverse methods for time series 142
  • 6.2.1 Regression methods 142
  • 6.2.2 Wood's quadratic programming method 144
  • 6.2.3 A maximum likelihood approach 152
  • 6.2.4 Stage-frequency methods 154
  • 6.3 Stable stage-distribution methods 154
  • 6.3.1 Age-classified models 154
  • 6.3.2 Size-classified models 157
  • 6.3.3 Death assemblages 157
  • 6.4 Stage-duration distributions 159
  • 6.4.1 Geometric distribution 160
  • 6.4.2 Fixed stage durations 160
  • 6.4.3 Variable stage durations 162
  • 6.4.4 Iterative calculation 164
  • 6.4.5 Negative binomial stage durations 164
  • 6.4.6 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
  • 6.7.1 Birth-flow populations 171
  • 6.7.2 Birth-pulse populations 172
  • 6.7.3 Anonymous reproduction 173
  • 7 Analysis of the Life Cycle Graph 176
  • 7.1 Z-transform 177
  • 7.1.1 z-transform solution of difference equations 177
  • 7.1.2 Z-transformed life cycle graph 178
  • 7.2 Reduction of the life cycle graph 178
  • 7.2.1 Multistep transitions 181
  • 7.3 Characteristic equation 181
  • 7.3.1 Derivation 184
  • 7.4 Stable stage distribution 185
  • 7.4.1 Derivation 187
  • 7.5 Reproductive value 187
  • 7.5.1 A second interpretation of reproductive value 189
  • 7.5.2 A note on eigenvectors of reducible matrices 190
  • 7.6 Partial life cycle analysis 190
  • 7.7 Annual organisms 192
  • 8 Structured Population Models 194
  • 8.1 Partial differential equation models 194
  • 8.1.1 Lotka's renewal equation 196
  • 8.1.2 Discretizing Lotka's equation: Don't bother 197
  • 8.1.3 Diffusion models 198
  • 8.1.4 PDE models and matrix models 198
  • 8.1.5 Escalator boxcar train 199
  • 8.2 Delay-differential equation models 201
  • 8.3 Integrodifference equation models 202
  • 8.4 i-state configuration models 202
  • 8.5 Choosing a model 204
  • 9 Sensitivity Analysis 206
  • 9.1 Eigenvalue sensitivity 208
  • 9.1.1 Perturbations of matrix elements 208
  • 9.1.2 Sensitivity and age 211
  • 9.1.3 Sensitivities in stage- and size-classified models 213
  • 9.1.4 What about those zeros? 215
  • 9.1.5 Sensitivity to multistep transitions 217
  • 9.1.6 Total derivatives and multiple perturbations 218
  • 9.1.7 Sensitivity to changes in development rate 220
  • 9.1.8 Predictions from sensitivities 224
  • 9.1.9 An overall eigenvalue sensitivity index 224
  • 9.1.10 A third interpretation of reproductive value 225
  • 9.2 Elasticity analysis 226
  • 9.2.1 Elasticity and age 227
  • 9.2.2 Elasticities as contributions to [lambda] 229
  • 9.2.3 Elasticities of [lambda] to lower-level parameters 232
  • 9.2.4 Comparative analysis of elasticity patterns 233
  • 9.2.5 Predictions from elasticities 240
  • 9.2.6 Sensitivity or elasticity? 243
  • 9.3 Sensitivity analysis of transient dynamics 244
  • 9.3.1 Sensitivity of the damping ratio 244
  • 9.3.2 Sensitivity of the period 247
  • 9.4 Sensitivities of eigenvectors 247
  • 9.4.1 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
  • 9.7.1 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 Precision of estimates of [lambda] 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
  • 12.2.4 Presentation of loglinear analyses 334
  • 12.3 Randomization tests 335
  • 12.3.1 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
  • 13.1.2 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 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 [sigma superscript 2] 399
  • 14.3.8 Scalar and matrix models compared 400
  • 14.4 Sensitivity and elasticity analyses 401
  • 14.4.1 From numerical simulations 402
  • 14.4.2 From Tuljapurkar's approximation 407
  • 14.4.3 Sensitivity of log [lambda subscript s] 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
  • 14.8.1 A 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
  • 15.1.3 A 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 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
  • 15.4.4 Extinction probability 493
  • 15.4.5 Extinction probability and reproductive value 497
  • 15.4.6 Elasticities of extinction probability and of [lambda] 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
  • 16.2 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 Jury criteria 522
  • 16.5 Bifurcation diagrams 525
  • 16.6 Bifurcations of equilibria: A field guide 526
  • 16.6.1 +1 bifurcations 528
  • 16.6.2 -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
  • 16.10 Tribolium: Models and experiments 553
  • 16.11 Perturbation analysis and evolution 557
  • 16.11.1 Sensitivity analysis of equilibria 559
  • 16.11.2 Invasion and evolution 560
  • 16.12 Stochasticity and density dependence 565
  • 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
  • 17.3.1 A simple two-sex model 572
  • 17.3.2 Birth and fertility functions 574
  • 17.3.3 Frequency and density dependence 576
  • 17.3.4 Equilibrium population structure 576
  • 17.3.5 Stability of population structure 578
  • 17.3.6 Nussbaum's global stability theorem 581
  • 17.41 Competition for mates 581
  • 17.4.1 Numerical results: Competition and instability 583
  • 17.5 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
  • 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
  • 19.1 Most important task 646
  • 19.2 Testing models 648
  • 19.3 A complete demographic analysis 649
  • 19.4 Directions for research 651
  • A Basics of Matrix Algebra 653
  • A.1 Motivation 653
  • A.3 Operations 655
  • A.3.1 Addition 655
  • A.3.2 Scalar multiplication 655
  • A.3.3 Transpose and the adjoint 655
  • A.3.4 Trace 656
  • A.3.5 Scalar product 656
  • A.3.6 Matrix multiplication 656
  • A.3.7 Kronecker and Hadamard products 658
  • A.4 Matrix inversion 659
  • A.4.1 Identity matrix 659
  • A.4.2 Inversion and the solution of algebraic equations 659
  • A.4.3 A useful fact about homogeneous systems 660
  • A.5 Determinants 660
  • A.5.1 Properties of determinants 662
  • A.6 Eigenvalues and eigenvectors 662
  • A.6.1 Eigenvectors 662
  • A.6.2 Left eigenvectors 663
  • A.6.3 Characteristic equation 663
  • A.6.4 Finding the eigenvectors 664
  • A.6.5 Complications 665
  • A.6.6 Linear independence of eigenvectors 665
  • A.6.7 Left and right eigenvectors 666
  • A.6.8 Computation of eigenvalues and eigenvectors 666
  • A.7 Similarity 666
  • A.7.1 Properties of similar matrices 667
  • A.8 Norms of vectors and matrices 667.
Description
xxii, 722 p. : ill. ; 24 cm.
Notes
Includes bibliographical references (p. [669]-710) and index.
Technical Details
  • Access in Virgo Classic

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    a| xxii, 722 p. : b| ill. ; c| 24 cm.
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    g| 1.1 t| Life cycle: Linking the individual and the population g| 1 -- g| 1.3.2 t| Matlab programs g| 5 -- g| 1.4 t| Construction, analysis, and interpretation g| 5 -- g| 1.5 t| Mathematical prerequisites g| 5 -- g| 2 t| Age-Classified Matrix Models g| 8 -- g| 2.1 t| Leslie matrix g| 8 -- g| 2.2 t| Projection: the simplest form of analysis g| 11 -- g| 2.2.1 t| A set of questions g| 18 -- g| 2.3 t| Leslie matrix and the life table g| 20 -- g| 2.3.1 t| Survival g| 21 -- g| 2.3.2 t| Reproduction g| 22 -- g| 2.4 t| Constructing age-classified matrices g| 22 -- g| 2.4.1 t| Birth-flow populations g| 23 -- g| 2.4.2 t| Birth-pulse populations g| 25 -- g| 2.5 t| Assumptions: Projection vs. forecasting g| 29 -- g| 2.6 t| History g| 31 -- g| 3 t| Stage-Classified Life Cycles g| 35 -- g| 3.1 t| State variables g| 35 -- g| 3.1.1 t| Zadeh's theory of state g| 36 -- g| 3.1.2 t| State variables in population models g| 37 -- g| 3.2 t| Age as a state variable: When does it fail? g| 38 -- g| 3.2.1 t| Size-dependent vital rates and plastic growth g| 39 -- g| 3.2.2 t| Multiple modes of reproduction g| 40 -- g| 3.2.3 t| Population subdivision and multistate demography g| 41 -- g| 3.3 t| Statistical evaluation of state variables g| 41 -- g| 3.3.1 t| Continuous response, continuous or discrete state g| 41 -- g| 3.3.2 t| Discrete state, discrete response g| 43 -- g| 3.3.3 t| Continuous state, discrete response g| 54 -- g| 4 t| Stage-Classified Matrix Models g| 56 -- g| 4.1 t| Life cycle graph g| 56 -- g| 4.2 t| Matrix model g| 59 -- g| 4.3 t| Metapopulation and multistate models g| 62 -- g| 4.3.1 t| Modelling dispersal g| 65 -- g| 4.3.2 t| Integrodifference equation models g| 71 -- g| 4.4 t| Solution of the projection equation g| 72 -- g| 4.4.1 t| Derivation 1 g| 74 -- g| 4.4.2 t| Derivation 2 g| 75 -- g| 4.4.3 t| Effects of the eigenvalues g| 76 -- g| 4.5 t| Ergodicity g| 79 -- g| 4.5.1 t| Perron-Frobenius theorem g| 79 -- g| 4.5.2 t| Population growth rate: The strong ergodic theorem g| 84 -- g| 4.5.3 t| Imprimitive matrices g| 87 -- g| 4.5.4 t| Reducible matrices g| 88 -- g| 4.6 t| Reproductive value g| 92 -- g| 4.7 t| Transient dynamics and convergence g| 94 -- g| 4.7.1 t| Damping ratio and convergence g| 95 -- g| 4.7.2 t| Period of oscillation g| 100 -- g| 4.7.3 t| Measuring the distance to the stable stage distribution g| 101 -- g| 4.7.4 t| Population momentum g| 104 -- g| 4.8 t| Computation of eigenvalues and eigenvectors g| 106 -- g| 4.8.1 t| Eigenvalues and eigenvectors in Matlab g| 107 -- g| 4.8.2 t| Power method g| 108 -- g| 4.9 t| Assumptions revisited g| 109 -- g| 5 t| Events in the Life Cycle g| 110 -- g| 5.1 t| A = T + F g| 110 -- g| 5.1.1 t| Life cycle as a Markov chain g| 111 -- g| 5.1.2 t| Analysis of absorbing chains g| 112 -- g| 5.2 t| Lifetime event probabilities g| 115 -- g| 5.3 t| Age-specific traits g| 116 -- g| 5.3.1 t| Age-specific survival g| 118 -- g| 5.3.2 t| Age-specific fertility g| 120 -- g| 5.3.3 t| Age at first reproduction g| 124 -- g| 5.3.4 t| Net reproductive rate g| 126 -- g| 5.3.5 t| Generation time g| 128 -- g| 5.3.6 t| Age-within-stage distributions g| 130 -- g| 6 t| Parameter Estimation g| 133 -- g| 6.1 t| Identified individuals g| 134 -- g| 6.1.1 t| Observed transition frequencies g| 134 -- g| 6.1.2 t| Mark-recapture methods g| 136 -- g| 6.2 t| Inverse methods for time series g| 142 -- g| 6.2.1 t| Regression methods g| 142 -- g| 6.2.2 t| Wood's quadratic programming method g| 144 -- g| 6.2.3 t| A maximum likelihood approach g| 152 -- g| 6.2.4 t| Stage-frequency methods g| 154 -- g| 6.3 t| Stable stage-distribution methods g| 154 -- g| 6.3.1 t| Age-classified models g| 154 -- g| 6.3.2 t| Size-classified models g| 157 -- g| 6.3.3 t| Death assemblages g| 157 -- g| 6.4 t| Stage-duration distributions g| 159 -- g| 6.4.1 t| Geometric distribution g| 160 -- g| 6.4.2 t| Fixed stage durations g| 160 -- g| 6.4.3 t| Variable stage durations g| 162 -- g| 6.4.4 t| Iterative calculation g| 164 -- g| 6.4.5 t| Negative binomial stage durations g| 164 -- g| 6.4.6 t| Duration distributions compared g| 165 -- g| 6.5 t| Multiregional or age-size models g| 166 -- g| 6.6 t| Size categories: The Vandermeer-Moloney algorithms g| 169 -- g| 6.7 t| Fertilities in stage-classified models g| 171 -- g| 6.7.1 t| Birth-flow populations g| 171 -- g| 6.7.2 t| Birth-pulse populations g| 172 -- g| 6.7.3 t| Anonymous reproduction g| 173 -- g| 7 t| Analysis of the Life Cycle Graph g| 176 -- g| 7.1 t| Z-transform g| 177 -- g| 7.1.1 t| z-transform solution of difference equations g| 177 -- g| 7.1.2 t| Z-transformed life cycle graph g| 178 -- g| 7.2 t| Reduction of the life cycle graph g| 178 -- g| 7.2.1 t| Multistep transitions g| 181 -- g| 7.3 t| Characteristic equation g| 181 -- g| 7.3.1 t| Derivation g| 184 -- g| 7.4 t| Stable stage distribution g| 185 -- g| 7.4.1 t| Derivation g| 187 -- g| 7.5 t| Reproductive value g| 187 -- g| 7.5.1 t| A second interpretation of reproductive value g| 189 -- g| 7.5.2 t| A note on eigenvectors of reducible matrices g| 190 -- g| 7.6 t| Partial life cycle analysis g| 190 -- g| 7.7 t| Annual organisms g| 192 -- g| 8 t| Structured Population Models g| 194 -- g| 8.1 t| Partial differential equation models g| 194 -- g| 8.1.1 t| Lotka's renewal equation g| 196 -- g| 8.1.2 t| Discretizing Lotka's equation: Don't bother g| 197 -- g| 8.1.3 t| Diffusion models g| 198 -- g| 8.1.4 t| PDE models and matrix models g| 198 -- g| 8.1.5 t| Escalator boxcar train g| 199 -- g| 8.2 t| Delay-differential equation models g| 201 -- g| 8.3 t| Integrodifference equation models g| 202 -- g| 8.4 t| i-state configuration models g| 202 -- g| 8.5 t| Choosing a model g| 204 -- g| 9 t| Sensitivity Analysis g| 206 -- g| 9.1 t| Eigenvalue sensitivity g| 208 -- g| 9.1.1 t| Perturbations of matrix elements g| 208 -- g| 9.1.2 t| Sensitivity and age g| 211 -- g| 9.1.3 t| Sensitivities in stage- and size-classified models g| 213 -- g| 9.1.4 t| What about those zeros? g| 215 -- g| 9.1.5 t| Sensitivity to multistep transitions g| 217 -- g| 9.1.6 t| Total derivatives and multiple perturbations g| 218 -- g| 9.1.7 t| Sensitivity to changes in development rate g| 220 -- g| 9.1.8 t| Predictions from sensitivities g| 224 -- g| 9.1.9 t| An overall eigenvalue sensitivity index g| 224 -- g| 9.1.10 t| A third interpretation of reproductive value g| 225 -- g| 9.2 t| Elasticity analysis g| 226 -- g| 9.2.1 t| Elasticity and age g| 227 -- g| 9.2.2 t| Elasticities as contributions to [lambda] g| 229 -- g| 9.2.3 t| Elasticities of [lambda] to lower-level parameters g| 232 -- g| 9.2.4 t| Comparative analysis of elasticity patterns g| 233 -- g| 9.2.5 t| Predictions from elasticities g| 240 -- g| 9.2.6 t| Sensitivity or elasticity? g| 243 -- g| 9.3 t| Sensitivity analysis of transient dynamics g| 244 -- g| 9.3.1 t| Sensitivity of the damping ratio g| 244 -- g| 9.3.2 t| Sensitivity of the period g| 247 -- g| 9.4 t| Sensitivities of eigenvectors g| 247 -- g| 9.4.1 t| Sensitivities of scaled eigenvectors g| 250 -- g| 9.5 t| Generalized inverses in sensitivity analysis g| 251 -- g| 9.6 t| Sensitivity analysis of Markov chains g| 251 -- g| 9.7 t| Second Derivatives of Eigenvalues g| 254 -- g| 9.7.1 t| Perturbation analysis of elasticities g| 256 -- g| 10 t| Life Table Response Experiments g| 258 -- g| 10.1 t| Fixed designs g| 260 -- g| 10.1.1 t| One-way designs g| 260 -- g| 10.1.2 t| Factorial designs g| 263 -- g| 10.2 t| Random designs and variance decomposition g| 269 -- g| 10.3 t| Regression designs g| 273 -- g| 10.4 t| Extensions g| 274 -- g| 10.4.1 t| Higher-order terms g| 274 -- g| 10.4.2 t| Other demographic statistics g| 275 -- g| 10.4.3 t| Other demographic models g| 275 -- g| 10.4.4 t| More mechanisms g| 276 -- g| 10.4.5 t| Statistics g| 277 -- g| 10.5 t| Prospective and retrospective analyses g| 277 -- g| 11 t| Evolutionary Demography g| 279 -- g| 11.1 t| Fitness g| 280 -- g| 11.1.1 t| Population genetics g| 281 -- g| 11.1.2 t| Quantitative genetics g| 282 -- g| 11.1.3 t| Invasion and ESS analysis g| 291 -- g| 11.2 t| Sensitivity, elasticity, and selection g| 295 -- g| 11.3 t| Lifetime reproductive success and individual fitness g| 295 -- g| 11.4 t| Fitness and reproductive value g| 297 -- g| 12 t| Statistical Inference g| 299 -- g| 12.1 t| Confidence intervals and uncertainty g| 300 -- g| 12.1.1 t| Series approximations g| 300 -- g| 12.1.2 t| Bootstrap standard errors g| 304 -- g| 12.1.3 t| Bootstrap confidence intervals g| 306 -- g| 12.1.4 t| Complex data structures g| 309 -- g| 12.1.5 t| More on the bootstrap g| 315 -- g| 12.1.6 t| Monte Carlo uncertainty analysis g| 319 -- g| 12.1.7 t| Precision of estimates of [lambda] g| 322 -- g| 12.2 t| Loglinear analysis of transition matrices g| 326 -- g| 12.2.1 t| One factor g| 327 -- g| 12.2.2 t| Two factors g| 330 -- g| 12.2.3 t| Model selection and AIC g| 332 -- g| 12.2.4 t| Presentation of loglinear analyses g| 334 -- g| 12.3 t| Randomization tests g| 335 -- g| 12.3.1 t| Randomization test procedure g| 337 -- g| 12.3.2 t| Types of data g| 338 -- g| 12.3.3 t| Examples of randomization tests g| 338 -- g| 12.3.4- t| Advantages of randomization tests g| 343 -- g| 12.3.5 t| Implementation g| 345 -- g| 13 t| Periodic Environments g| 346 -- g| 13.1 t| Periodic matrix products g| 347 -- g| 13.1.2 t| Eigenvalues and eigenvectors g| 349 -- g| 13.1.3 t| Matrices don't commute, and why that matters g| 354 -- g| 13.1.4 t| Sensitivity analysis of periodic matrix models g| 356 -- g| 13.2 t| Annual organisms g| 361 -- g| 13.2.1 t| Periodic matrix models for annuals g| 362 -- g| 13.3 t| Other approaches to periodic environments g| 368 -- g| 13.3.1 t| Classification by season of birth g| 368 -- g| 13.3.2 t| Discrete Fourier analysis g| 368 -- g| 13.4 t| Deterministic, aperiodic environments g| 369 -- g| 13.4.1 t| Weak ergodicity g| 369 -- g| 14 t| Environmental Stochasticity g| 377 -- g| 14.1 t| Formulation of stochastic models g| 377 -- g| 14.1.1 t| Models for the environment g| 378 -- g| 14.1.2 t| Linking the environment and the vital rates g| 381 -- g| 14.1.3 t| Projecting the population g| 382 -- g| 14.2 t| Stochastic ergodic theorems g| 382 -- g| 14.2.1 t| Stage distributions g| 382 -- g| 14.2.2 t| Stochastic reproductive value g| 384 -- g| 14.2.3 t| Sufficient conditions for stochastic ergodicity g| 384 -- g| 14.2.4 t| An overview of ergodic results g| 386 -- g| 14.3 t| Stochastic population growth g| 387 -- g| 14.3.1 t| Lewontin-Cohen model g| 387 -- g| 14.3.2 t| Beyond iid processes g| 392 -- g| 14.3.3 t| Ergodic properties of random matrix products g| 393 -- g| 14.3.4 t| Growth of the mean g| 394 -- g| 14.3.5 t| Which growth rate is relevant? g| 395 -- g| 14.3.6 t| Calculating the stochastic growth rate g| 396 -- g| 14.3.7 t| Calculation of the variance [sigma superscript 2] g| 399 -- g| 14.3.8 t| Scalar and matrix models compared g| 400 -- g| 14.4 t| Sensitivity and elasticity analyses g| 401 -- g| 14.4.1 t| From numerical simulations g| 402 -- g| 14.4.2 t| From Tuljapurkar's approximation g| 407 -- g| 14.4.3 t| Sensitivity of log [lambda subscript s] to variability g| 408 -- g| 14.5 t| Examples of stochastic models g| 409 -- g| 14.5.1 t| Striped bass: Variability in recruitment g| 409 --
    505
    8
    0
    g| 14.5.2 t| Clams: Parametric distributions of recruitment g| 410 -- g| 14.5.3 t| Stochastic models from sequence of matrices g| 415 -- g| 14.5.4 t| Markov chain models for the environment g| 419 -- g| 14.5.5 t| Random selection of matrix elements g| 430 -- g| 14.5.6 t| Applications of Tuljapurkar's approximation g| 435 -- g| 14.5.7 t| Some suggestions g| 435 -- g| 14.6 t| Evolution in stochastic environments g| 436 -- g| 14.6.1 t| Fitness and ESS in stochastic environments g| 436 -- g| 14.6.2 t| An example: Delayed reproduction g| 437 -- g| 14.6.3 t| Life history studies g| 440 -- g| 14.7 t| Sensitivity: Stochastic and deterministic models g| 443 -- g| 14.8 t| Extinction in stochastic environments g| 443 -- g| 14.8.1 t| A model for quasi-extinction g| 444 -- g| 14.8.2 t| Sensitivity analysis g| 447 -- g| 14.9 t| Short-term stochastic forecasts g| 449 -- g| 15 t| Demographic Stochasticity g| 452 -- g| 15.1 t| Stochastic simulations g| 453 -- g| 15.1.1 t| Assumptions, essential and otherwise g| 456 -- g| 15.1.2 t| Simulating individuals g| 456 -- g| 15.1.3 t| A computationally efficient alternative g| 458 -- g| 15.1.4 t| Bad luck, or something worse? g| 462 -- g| 15.1.5 t| Time-varying and density-dependent models g| 464 -- g| 15.2 t| Galton-Watson branching process g| 464 -- g| 15.2.1 t| Probability generating functions g| 466 -- g| 15.2.2 t| Population projection g| 467 -- g| 15.2.3 t| Projection of moments g| 470 -- g| 15.2.4 t| Limit theorems and asymptotic dynamics g| 471 -- g| 15.2.5 t| Extinction g| 472 -- g| 15.2.6 t| Quasi-stationary distributions g| 475 -- g| 15.2.7 t| Extinction, effective population size, and elasticity g| 475 -- g| 15.3 t| Multitype branching processes g| 478 -- g| 15.3.1 t| From matrix models to branching processes g| 479 -- g| 15.3.2 t| Mean and covariance of offspring production g| 483 -- g| 15.4 t| Analysis of multitype branching processes g| 486 -- g| 15.4.1 t| Population projection g| 486 -- g| 15.4.2 t| Projection of moments g| 486 -- g| 15.4.3 t| Limit theorems and asymptotic dynamics g| 491 -- g| 15.4.4 t| Extinction probability g| 493 -- g| 15.4.5 t| Extinction probability and reproductive value g| 497 -- g| 15.4.6 t| Elasticities of extinction probability and of [lambda] g| 497 -- g| 15.4.7 t| Subcritical multitype branching processes g| 499 -- g| 15.5 t| Branching processes in random environments g| 501 -- g| 15.6 t| Assumptions revisited g| 502 -- g| 16 t| Density-Dependent Models g| 504 -- g| 16.1 t| Model construction g| 505 -- g| 16.1.1 t| Types of density dependence g| 505 -- g| 16.2 t| Asymptotic dynamics and invariant sets g| 513 -- g| 16.2.1 t| Finding equilibria g| 518 -- g| 16.3 t| Stability and instability g| 519 -- g| 16.4 t| Local stability of equilibria g| 519 -- g| 16.4.1 t| Jury criteria g| 522 -- g| 16.5 t| Bifurcation diagrams g| 525 -- g| 16.6 t| Bifurcations of equilibria: A field guide g| 526 -- g| 16.6.1 t| +1 bifurcations g| 528 -- g| 16.6.2 t| -1 bifurcations: The flip bifurcation g| 533 -- g| 16.6.3 t| Complex conjugate pairs: The Hopf bifurcation g| 533 -- g| 16.6.4 t| Supercritical and subcritical bifurcations g| 537 -- g| 16.7 t| Chaos g| 538 -- g| 16.7.1 t| Lyapunov exponents and quantitative unpredictability g| 542 -- g| 16.7.2 t| Routes to chaos g| 543 -- g| 16.7.3 t| Chaotic power spectra g| 546 -- g| 16.8 t| Transient dynamics g| 548 -- g| 16.8.1 t| Reactivity and resilience of stable equilibria g| 548 -- g| 16.8.2 t| Unstable equilibria g| 550 -- g| 16.8.3 t| Strange repellers and chaotic transients g| 551 -- g| 16.8.4 t| Effects of random perturbations g| 551 -- g| 16.9 t| Multiple attractors and qualitative unpredictability g| 552 -- g| 16.10 t| Tribolium: Models and experiments g| 553 -- g| 16.11 t| Perturbation analysis and evolution g| 557 -- g| 16.11.1 t| Sensitivity analysis of equilibria g| 559 -- g| 16.11.2 t| Invasion and evolution g| 560 -- g| 16.12 t| Stochasticity and density dependence g| 565 -- g| 17 t| Two-Sex Models g| 568 -- g| 17.1 t| Sexual dimorphism in the vital rates g| 568 -- g| 17.2 t| Dominance, sex ratio, and the marriage squeeze g| 570 -- g| 17.3 t| Two-sex models g| 571 -- g| 17.3.1 t| A simple two-sex model g| 572 -- g| 17.3.2 t| Birth and fertility functions g| 574 -- g| 17.3.3 t| Frequency and density dependence g| 576 -- g| 17.3.4 t| Equilibrium population structure g| 576 -- g| 17.3.5 t| Stability of population structure g| 578 -- g| 17.3.6 t| Nussbaum's global stability theorem g| 581 -- g| 17.41 t| Competition for mates g| 581 -- g| 17.4.1 t| Numerical results: Competition and instability g| 583 -- g| 17.5 t| Birth matrix-mating rule model g| 585 -- g| 17.6 t| More detailed models of mating g| 587 -- g| 17.7 t| Frequency and density dependence combined g| 588 -- g| 17.8 t| Extinction and the sex ratio g| 589 -- g| 18 t| Conservation and Management g| 591 -- g| 18.1 t| Conservation g| 592 -- g| 18.1.1 t| Assessment g| 592 -- g| 18.1.2 t| Diagnosis g| 601 -- g| 18.1.3 t| Prescription g| 604 -- g| 18.1.4 t| Prognosis g| 619 -- g| 18.1.5 t| Conservation conclusions g| 629 -- g| 18.2 t| Pest control g| 629 -- g| 18.2.1 t| Reducing population size g| 630 -- g| 18.2.2 t| Extermination g| 631 -- g| 18.2.3 t| Halting invasion g| 632 -- g| 18.2.4 t| Some examples of pest control g| 634 -- g| 18.3 t| Harvesting g| 640 -- g| 18.3.1 t| Optimal harvesting g| 642 -- g| 19.1 t| Most important task g| 646 -- g| 19.2 t| Testing models g| 648 -- g| 19.3 t| A complete demographic analysis g| 649 -- g| 19.4 t| Directions for research g| 651 -- g| A t| Basics of Matrix Algebra g| 653 -- g| A.1 t| Motivation g| 653 -- g| A.3 t| Operations g| 655 -- g| A.3.1 t| Addition g| 655 -- g| A.3.2 t| Scalar multiplication g| 655 -- g| A.3.3 t| Transpose and the adjoint g| 655 -- g| A.3.4 t| Trace g| 656 -- g| A.3.5 t| Scalar product g| 656 -- g| A.3.6 t| Matrix multiplication g| 656 -- g| A.3.7 t| Kronecker and Hadamard products g| 658 -- g| A.4 t| Matrix inversion g| 659 -- g| A.4.1 t| Identity matrix g| 659 -- g| A.4.2 t| Inversion and the solution of algebraic equations g| 659 -- g| A.4.3 t| A useful fact about homogeneous systems g| 660 -- g| A.5 t| Determinants g| 660 -- g| A.5.1 t| Properties of determinants g| 662 -- g| A.6 t| Eigenvalues and eigenvectors g| 662 -- g| A.6.1 t| Eigenvectors g| 662 -- g| A.6.2 t| Left eigenvectors g| 663 -- g| A.6.3 t| Characteristic equation g| 663 -- g| A.6.4 t| Finding the eigenvectors g| 664 -- g| A.6.5 t| Complications g| 665 -- g| A.6.6 t| Linear independence of eigenvectors g| 665 -- g| A.6.7 t| Left and right eigenvectors g| 666 -- g| A.6.8 t| Computation of eigenvalues and eigenvectors g| 666 -- g| A.7 t| Similarity g| 666 -- g| A.7.1 t| Properties of similar matrices g| 667 -- g| A.8 t| Norms of vectors and matrices g| 667.
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    a| Population biology x| Computer simulation.
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    a| QH352 .C375 2001 w| LC i| X004475182 k| CHECKEDOUT l| BY-REQUEST m| IVY t| BOOK

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