Lecture Notes in Biomathematics

Transcription

1 Lecture Notes in Biomathematics Managing Editor: S. Levin 52 Population Biology Proceedings of the International Conference held at the University of Alberta, Edmonton, Canada, June 22-30,1982 Edited by H. I. Freedman and C. Strobeck Springer-Verlag Berlin Heidelberg New York Tokyo 1983

2 TABLE OF CONTENTS Preface List of Participants List of Contributors PART I POPULATION GENETICS 1 STROBECK, Curtis, Invited Guest Lecture: The Use of Coefficients of Identity to Study Random Drift 2 GREGORIUS, Hans-Rolf: Instability and Repulsivity of the Fixation States in Biallelic Selection Models 14 HOCHBERG, Kenneth J.: Microscopic Clustering of Population Processes 18 HOLT, Robert D.: Models for Peripheral Populations: The Role,- of Immigration HUNT, Fern: A Mathematical Analysis of the Chitty Hypothesis 33 MOODY, Michael E.: An Haploid Model for Genotype-Dependent Population Diffusion 41 ROSE, Michael R.: Further Models of Selection with 47 Antagonistic Pleiotropy WORZ-BUSEKROS, Angelika: Algebraic Methods in Genetics 54 PART II LIFE, HISTORY STRATEGIES 63 TEMPLETON, Alan R., Invited Guest Leetia-e: The Evolution of Life Histories Under Pleiotropic Constraints and "4 K-Selection CLARK, C.E.: On the r-k Tradeoff in Density Dependent Selection. '' GLASSER, John W. : A Test of Ideas About the Evolution of, Efficiencies and Strategies of Resource Use '* LEON, Jesus Alberto: Compensatory Strategies of Energy Investment in Uncertain Environments ~ > TAYLOR, P.D., and G.C. WILLIAMS: A Geometric Model for Optimal Life History 91 VINCENT, Thomas L., and Joel S. BROWN: Necessary Conditions for an Invasion 1 Proof Strategy '8 WHITTAKER, James V.: The Evolution of Stable Strategies 105 PART III POPULATION GROWTH KEYFITZ, Nathan, Invited Guest Lecture: Forecasting the Human Population AGUR, Zvia: Persistence in Uncertain Environments 125

3 XVI BLYTHE, S.P., R.M. NISBET and W.S.C. GURNEY: Formulating Population Models with Differential Aging BOJADZIEV, George: Population Modelling by Higher Order Differential Equations FINDLAY, C. Scott, Robert F. ROCKWELL, and Fred COOKE: Concerning the Time-Dependence of Population Vital Rates GINZBURG, Lev R., and Andrea PUGLIESE: Extinction Probabilities in Stochastic Age-Structured Models of Population Growth GURNEY, W.S.C, and R.M. NISBET: The Systematic Formulation of Delay-Differential Models of Age or Size Structured Populations- KRISHNAN, P., and N.M. LALU: Lotka Distribution for a Finite Mixture of Human Populations I LANGLAIS, Michel R.: A Problem in Nonlinear Age Dependent Population Diffusion PART IV COMPETITIVE SYSTEMS CHESSON, Peter L., Invited Guest Lecture: Coexistence of Competitors in a Stochastic Environment: The Storage Effect WALTMAN, Paul, Invited Guest Lecture: Models of Competition for a Single Resource BUTLER, G.J.: COSTE, Jean: Competitive Predator-Prey Systems and Coexistence Coexistence of Many Competing Species CUSHING, J.M., and M. SALEEM: Competition and Age-Structure GRANERO^PORATI, M.I., and A. PORATI: Selection of Molecular Species by Competition for a Common Source RASMUSSEN, Joseph B.: An Analysis of Competition Between The Larvae of a Deposit-Feeding and a Filter-Feeding Species of Chironomid (Diptera), Using a Mechanistic Model PART V PREDATOR-PREY SYSTEMS \ HASSELL, Michael P., Invited Guest Lecture: The Dynamics of Host-Parasitoid Interactions with Heterogeneity Host Density Dependence and Variable Sex Ratios DUTT, Ranabir: Some Applications of Coherent State Representation to Nonlinear Bio-Oscillators GARD, Thomas C: Mathematical Analysis of Some Resource-Prey- Predator Models: Application to a NPZ Microcosm Model GHOSH, P.K.: Resonance in Prey-Predator Systems HESTBECK, Jay B.: A Mathematical Model of Population Regulation in Cyclic Mammals LEUNG, Anthony W.: Monotone Schemes for Three Species Prey-Predator Reaction-Diffusion LEVINE, Daniel S.: Prey Models Some Age-Structure Effects in Predator- RAO, V.S.H., and H.I. FREEDMAN: A Model Predator-Prey System with Mutual Interference and Time Delay

4 XVII TAKEUCHI, Yasuhiro, and Norihiko ADACHI: Oscillations in -on Prey-Predator Volterra Models COMMUNITY ECOLOGY 327 LEVIN, Simon, Invited Guest Lecture: Coevplution BHARGAVA, S.C.: A Coexistence Model for N-Species Using Nearest Neighbour Interaction and the Role of Diffusion 335 CUSHING, J.M.: Periodic Lotka-Volterra Systems and Time Sharing of Ecological Niches 342 FREEDMAN, H.I., John F. ADDICOTT, and Bindhyachal RAI: Nonobligate and Obligate Models of Mutualism 349 HASTINGS, Harold M.: Stability of Community Interaction 355 Matrices PORATI, A., M.I. GRANERO-PORATI, and R. KRON-MORELLI: Biomass Flow, Structure and Stability of Model Ecological Systems 359 SILVERT, William: Is Dynamical Systems Theory the Best Way to Understand Ecosystem Stability?. 366 WALTER, G.G.: Stability in Compartmental Models PART VII RESOURCE MANAGEMENT 379 CLARK, Colin W., and Marc MANGEL, Invited Guest Lecture: Search Theory in Ecology and Resource Management BARCLAY, Hugh J.: Models of Pheromone Release for Pest Control in which Males Attract Females ' 389 BOTSFORD, Louis W.: Age- and Size-Specific Models in the Dungeness Crab Fishery HANSON, F.B., and C. TIER: Harvesting Under Small Demographic Uncertainty NUNNEY, Len: Resource Recovery Time: Just How Destabilizing Is It? PART VIII EPIDEMOLOGY AND IMMUNOLOGY ' 415 BECK, K., J.P. KEENER, and P. RICCIARDI: Influence of Infectious Disease on the Growth of a Population with Three Genotypes 416 MERRILL, Stephen: Interaction of Antitumor Cells: Competition and Interference ' 423 SHONKWILER, R., and Maynard THOMPSON: A Model for Infection 429 VAN DEN DRIESSCHE, P.: A Cyclic Epidemic Model with Temporary 433 Immunity and Vital Dynamics

5 XVII TAKEUCHI, Yasuhiro, and Norihiko ADACHI: Oscillations in -. Prey-Predator Volterra Models PART VI COMMUNITY ECOLOGY 327 LEVIN, Simon, Invited Guest Lecture: Coevolution " "328 BHARGAVA, S.C.: A Coexistence Model for N-Species Using Nearest Neighbour Interaction and the Role of Diffusion 335 CUSHING, J.M.: Periodic Lotka-Volterra Systems and Time Sharing of Ecological Niches FREEDMAN, H.I., John F. ADDICOTT, and Bindhyachal RAI: " Nonobligate and Obligate Models of Mutualism 349 HASTINGS, Harold M.: Stability of Community Interaction 355 Matrices PORATI, A., M.I. GRANERO-PORATI, and R. KRON-MORELLI: Biomass Flow, Structure and Stability of Model Ecological Systems 359 SILVERT, William: Is Dynamical Systems Theory the Best Way to Understand Ecosystem Stability? 366 WALTER, G.G.: Stability in Compartmental Models 372 "' PART VII RESOURCE MANAGEMENT 379 CLARK, Colin W., and Marc MANGEL, Invited Guest Lecture: Search Theory in Ecology and Resource Management 380 BARCLAY, Hugh J.: Models of Pheromone Release for Pest Control in which Males Attract Females 389 BOTSEORD, Louis W.: Age- and Size-Specific Models in the Dungeness Crab Fishery HANSON, F.B., and C. TIER: Harvesting Under Small Demographic Uncertainty NUNNEY, Len: Resource Recovery Time: Just How Destabilizing Is It? PART VIII EPIDEMOLOGY AND IMMUNOLOGY ' 415 BECK, K., J.P. KEENER, and P. RICCIARDI: Influence of Infectious Disease on the Growth of a Population with Three Genotypes 416 MERRILL, Stephen: Interaction of Antitumor Cells: Competition and Interference. 423 SHONKWILER, R., and Maynard THOMPSON: A Model for Infection 429 VAN DEN DRIESSCHE, P.: A Cyclic Epidemic Model with Temporary 433 Immunity and Vital Dynamics