Structured-Population Models in Marine, Terrestrial, and Freshwater Systems

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Springer Science & Business Media, Jan 31, 1997 - Mathematics - 643 pages
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In the summer of 1993, twenty-six graduate and postdoctoral stu dents and fourteen lecturers converged on Cornell University for a summer school devoted to structured-population models. This school was one of a series to address concepts cutting across the traditional boundaries separating terrestrial, marine, and freshwa ter ecology. Earlier schools resulted in the books Patch Dynamics (S. A. Levin, T. M. Powell & J. H. Steele, eds., Springer-Verlag, Berlin, 1993) and Ecological Time Series (T. M. Powell & J. H. Steele, eds., Chapman and Hall, New York, 1995); a book on food webs is in preparation. Models of population structure (differences among individuals due to age, size, developmental stage, spatial location, or genotype) have an important place in studies of all three kinds of ecosystem. In choosing the participants and lecturers for the school, we se lected for diversity-biologists who knew some mathematics and mathematicians who knew some biology, field biologists sobered by encounters with messy data and theoreticians intoxicated by the elegance of the underlying mathematics, people concerned with long-term evolutionary problems and people concerned with the acute crises of conservation biology. For four weeks, these perspec tives swirled in discussions that started in the lecture hall and carried on into the sweltering Ithaca night. Diversity mayor may not increase stability, but it surely makes things interesting.
 

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Contents

Many Methods a Few Basic Concepts
3
What Do Structured Models Look Like?
4
Other Kinds of Structure
8
Why Include Population Structure?
9
Analysis of StructuredPopulation Models
10
Models and Modeling Some General Remarks
13
A Guide to the Rest of the Book
14
CHAPTER 2 Matrix Methods for Population Analysis
19
EggLarval Submodel
312
LifeStage Models
317
Concluding Remarks
325
CHAPTER 10 Evolutionary Dynamics of Structured Populations
329
Population Genetics and the Dynamics of StageStructured Populations
330
A Battle of the Sexes with Pair Formation
339
Appendix
351
CHAPTER 11 The Effect of Overlapping Generations and Population Structure on GeneFrequency Clines
355

Formulating Matrix Models
20
Analysis The Linear Case
26
Perturbation Analysis
32
DensityDependent Matrix Models
37
Conclusion
55
CHAPTER 3 Stochastic Matrix Models
59
Models of Randomness
60
Structure and Ergodicity
65
Stochastic Growth Rate
72
Other Aspects of Stochastic Dynamics
78
Invasion and ESS
80
Parting Words
81
Solutions
82
CHAPTER 4 DelayDifferential Equations for Structured Populations
89
A TwoStage Model of Population Growth in a Constant Environment
90
TwoStage Model with Density Dependence in the Adult Stage
95
Toward MoreGeneral StageStructured Models A TwoStage Model with EnvironmentDependent Juvenile Mortality
103
HostParasitoid Dynamics
108
Dynamically Varying Time Delays
111
MoreComplex Models
113
CHAPTER 5 A Gentle Introduction to Physiologically Structured Population Models
119
Modeling Individual Daphnia
122
Modeling the Individual and Its Environment
126
The SizeStructured Daphnia Population Model
138
The Model at the Population Level
143
Constant Environments Linear DensityIndependent Models
147
The Equilibrium of the Daphnia Model
158
Numerical Exploration of Dynamics
168
Stability Analysis of the Daphnia Equilibrium
177
Some Results and Implications for Daphnia
185
General Perspective
191
Appendix A
195
Appendix B
198
CHAPTER 6 Nonlinear Matrix Equations and Population Dynamics
205
Linear Matrix Models
206
Nonlinear Matrix Models
215
Some Examples
231
Concluding Remarks
240
Prospective and Retrospective Analyses
247
Demographic Analyses
249
Retrospective Analysis
251
An Example Calathea ovandensis
256
Discussion
265
CHAPTER 8 LifeHistory Evolution and Extinction
273
The Distribution of Populations
274
How Does the Stochastic Growth Rate Relate to Life History Evolution?
275
The Calculation of the Stochastic Growth Rate
276
LifeHistory Evolution
277
The Flavors of Reproductive Delay
282
The Geometry of Reproductive Delay
290
Population Extinction
294
Evolution Within and Between Populations
296
LifeHistory Evolution and Extinction
297
Future Directions
300
CHAPTER 9 Population Dynamics of Tribolium
303
LifeStage Interactions
304
Leslie Matrix Model
306
The Model
357
Discussion
367
CHAPTER 12 Dynamics of Populations with DensityDependent Recruitment and Age Structure
371
The Beginning
373
A Model of Populations with Age Structure and DensityDependent Recruitment
375
Examples of Applications
383
Discussion
401
CHAPTER 13 Models for Marine Ecosystems
409
TimeDependent Models
410
Spatially Dependent Models
420
Discussion and Summary
428
Implications for AbioticBiotic Coupling
433
Model Background
435
Model Analysis
437
Results
439
Discussion
442
Conclusions
448
CHAPTER 15 Stochastic Demography for Conservation Biology
451
Deterministic Demography
452
Stochastic Demography
453
Applications
460
Conclusion
465
CHAPTER 16 Sensitivity Analysis of StructuredPopulation Models for Management and Conservation
471
Modeling and Managing Elk Populations
473
Models and Control for Tick Populations
485
Elasticity under Environmental Variation
496
Conclusions
508
CHAPTER 17 Nonlinear Ergodic Theorems and Symmetric versus Asymmetric Competition
515
SingleSpecies Models
516
Interspecific Competition
520
Concluding Remarks
531
It Takes Two to Tango
533
Framework for Discrete TwoSex Mixing
535
Parameters for Preference Matrices
538
The TwoBody Problem in a Discrete Framework
541
TwoSex Mixing in AgeStructured Populations
546
Conclusions
550
CHAPTER 19 Inverse Problems and StructuredPopulation Dynamics
555
Models
556
Fitting Models to Data with Least Squares
559
Parametric Model Fitting
563
Regression Methods
567
Irritating Problems
569
Model Uncertainty and a Way of Tackling It
575
Choosing Model Complexity CrossValidation and Its Relatives
580
Conclusions
582
Dynamic Consequences of Stage Structure and Discrete Sampling
587
Nonlinearity and Modeling Strategies
588
Data Forcing Detail The Nicholsons Blowfly Experiment
590
Data Lacking Detail Discrete Maps of Continuous Time Processes
599
Conclusions
611
Competition A Diffusion Analysis
615
Multispecies Model
616
StageStructured Model
619
About the Authors
623
Index
631
Copyright

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About the author (1997)

Caswell is a Senior Scientist in the Biology Department of the Woods Hole Oceanographic Institution, where he holds the Robert W. Morse Chair for Excellence in Oceanography.

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