## Structured-Population Models in Marine, Terrestrial, and Freshwater SystemsShripad Tuljapurkar, Hal Caswell 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 |

631 | |

### Other editions - View all

Structured-Population Models in Marine, Terrestrial, and Freshwater Systems Shripad Tuljapurkar No preview available - 1996 |

Structured-Population Models in Marine, Terrestrial, and Freshwater Systems Shripad Tuljapurkar,Hal Caswell No preview available - 1997 |

### Common terms and phrases

adult survival age-structured analysis assumed assumption asymptotic behavior bifurcation Botsford boundary cannibalism Caswell changes chapter coefﬁcients cohort constant copepod Costantino covariance cycles Daphnia deﬁned deﬁnition delay demographic density-dependent dependence described Desharnais deterministic developmental distribution dominant eigenvalue Ecology effects eggs eigenvalue elasticity environment equation equilibrium estimates example fecundity females ﬁeld Figure ﬁnd ﬁrst ﬁt ﬂuctuations food density frequency function genetic genotype Gurney histories i-state increases inﬂuence interactions interval iteroparous Journal juvenile larvae Leslie matrix life-history linear males Mathematical Mathematical Biology matrix models Matrix Population Models nonlinear number of individuals Orzack parasitoid phytoplankton plankton population density population dynamics population growth rate population models positive equilibria predator projection matrix R. M. Nisbet random recruitment semelparous sensitivity simulations size-structured species speciﬁc stability stage stochastic growth rate structured model structured population structured-population models tion transition Tribolium trophic level Tuljapurkar ulation unstable variance variation vector vital rates zero zooplankton