## Population Biology: Proceedings of the International Conference held at the University of Alberta, Edmonton, Canada, June 22–30, 1982This volume contains the Proceedings of the International Conference in Population Biology held at The University of Alberta, Edmonton, Canada from June 22 to June 30, 1982. The Conference was sponsored by The University of Alberta and The Canadian Applied Mathematics Society, and overlapped with the summer meeting of CAMS. The main objectives of this Conference were: to bring mathematicians and biologists together so that they may interact for their mutual benefit; to bring those researchers interested in modelling in ecology and those interested in modelling in genetics together; to bring in keynote speakers in the delineated areas; to have sessions of contributed papers; and to present the opportunity for researchers to conduct workshops. With the exception of the last one, the objec tives were carried out. In order to lend some focus to the Conference, the following themes were adopted: models of species growth, predator-prey, competition, mutualism, food webs, dispersion, age structure, stability, evolution of ecological parameters, evolution of behaviour, life history strategies, group and social selection, and evolution of genetic systems. There were speakers (invited and/or contributed papers) in each of these areas. Talks were given on Tuesday, June 22 to Friday, June 25 and on Monday, June 28 to Wednesday, June 30. On each day there were several talks by the principal speakers as well as contributed sessions. Altogether, there were ninety one papers given, of which twelve were by the principal speakers. There were one hundred and twenty-three registered participants from twelve different countries. |

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### Contents

2 | |

Instability and Repulsivity of | 14 |

Models for Peripheral Populations The Role | 25 |

A Mathematical Analysis of the Chitty Hypothesis | 33 |

An Haploid Model for GenotypeDependent | 41 |

Further Models of Selection with | 47 |

Algebraic Methods in Genetics | 54 |

The Evolution | 64 |

Models of Competition | 199 |

Competitive PredatorPrey Systems and Coexistence | 210 |

Coexistence of Many Competing Species | 218 |

RAI Bindhyachal Department of Mathematics University of Allahabad Allahabad | 225 |

Selection of Molecular | 231 |

An Analysis of Competition Between | 238 |

PREDATORPREY SYSTEMS 247 | 245 |

RASMUSSEN J B Department of Biology University of Calgary Calgary Alberta | 317 |

HOLT Robert D University of Kansas Museum of Natural History Lawrence | 71 |

Cn the rK Tradeoff in Density Dependent | 72 |

A Test of Ideas About the Evolution | 79 |

Compensatory Strategies of Energy | 85 |

A Geometric Model | 91 |

Necessary Conditions | 98 |

The Evolution of Stable Strategies | 105 |

Forecasting | 114 |

KRISHNAN P Department of Sociology University of Alberta Edmonton Alberta | 122 |

Persistence in Uncertain Environments | 125 |

Lotka Distribution for a Finite | 173 |

A Problem in Nonlinear Age Dependent | 180 |

Coexistence | 187 |

Coevolution | 328 |

A Coexistence Model for NSpecies Using Nearest | 335 |

Periodic LotkaVolterra Systems and Time | 342 |

Stability of Community Interaction | 355 |

Is Dynamical Systems Theory the Best | 366 |

Stability in Compartmental Models | 372 |

Models of Pheromone Release for Pest | 389 |

Harvesting Under Small | 401 |

Resource Recovery Time Just How Destabilizing | 407 |

Influence | 415 |

Interaction of Antitumor Cells | 423 |

A Model for Infection | 429 |

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### Common terms and phrases

Aa AA adult age-structured allele Amer analysis assume assumptions asymptotically asymptotically stable behaviour bifurcation Biol biological birth rate Cantor set chemostat coefficients coexistence competition consider constant convex curve death rate defined denote density dependent differential equations diffusion distribution Ecology ecosystem eigenvalues environment environmental equilibrium error evolution evolutionarily stable strategy example exists expected extinction fecundity Figure fitness-components fluctuations forecasts frequency function gametes genotype given graph growth rate haploid Hassell homozygosity Hopf bifurcation host individuals interaction juveniles larvae Levin limit cycle linear logistic Math matrix mortality obtained optimal oscillations parameters parasitism parasitoid periodic solutions persistence polymorphism population density population dynamics population genetics population models positive predator predator-prey predator-prey system prey r-selection r-strategist random rate of increase recruitment reproduction resource selection simulation species stable strategies stochastic storage effect survival survivorship Theorem theory tion tradeoff trajectory variable variance vector zygote