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Stochastic Population Models

A Compartmental Perspective

  • James H. Matis
  • Thomas R. Kiffe

Part of the Lecture Notes in Statistics book series (LNS, volume 145)

Table of contents

  1. Front Matter
    Pages i-x
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. James H. Matis, Thomas R. Kiffe
      Pages 2-4
    3. James H. Matis, Thomas R. Kiffe
      Pages 5-15
  3. Models for a Single Population

    1. Front Matter
      Pages 15-15
    2. James H. Matis, Thomas R. Kiffe
      Pages 17-29
    3. James H. Matis, Thomas R. Kiffe
      Pages 30-39
    4. James H. Matis, Thomas R. Kiffe
      Pages 40-48
    5. James H. Matis, Thomas R. Kiffe
      Pages 49-71
  4. Models for Multiple Populations

    1. Front Matter
      Pages 100-100
    2. James H. Matis, Thomas R. Kiffe
      Pages 72-99
    3. James H. Matis, Thomas R. Kiffe
      Pages 101-109
    4. James H. Matis, Thomas R. Kiffe
      Pages 110-118
    5. James H. Matis, Thomas R. Kiffe
      Pages 119-136
    6. James H. Matis, Thomas R. Kiffe
      Pages 137-141
    7. James H. Matis, Thomas R. Kiffe
      Pages 142-160
    8. James H. Matis, Thomas R. Kiffe
      Pages 161-171
    9. James H. Matis, Thomas R. Kiffe
      Pages 172-188
  5. Back Matter
    Pages 189-204

About this book

Introduction

This monograph has been heavily influenced by two books. One is Ren­ shaw's [82] work on modeling biological populations in space and time. It was published as we were busily engaged in modeling African bee dispersal, and provided strong affirmation for the stochastic basis for our ecological modeling efforts. The other is the third edition of Jacquez' [28] classic book on compartmental analysis. He reviews stochastic compartmental analysis and utilizes generating functions in this edition to derive many useful re­ sults. We interpreted Jacquez' use of generating functions as a message that the day had come for modeling practioners to consider using this powerful approach as a model-building tool. We were inspired by the idea of using generating functions and related methods for two purposes. The first is to integrate seamlessly our previous research centering in stochastic com­ partmental modeling with our more recent research focusing on stochastic population modeling. The second, related purpose is to present some key research results of practical application in a natural, user-friendly way to the large user communities of compartmental and biological population modelers. One general goal of this monograph is to make a case for the practical utility of the various stochastic population models. In accordance with this objective, we have chosen to illustrate the various stochastic models, using four primary applications described in Chapter 2. In so doing, this mono­ graph is based largely on our own published work.

Keywords

Mathematica Moment bee calculus differential equation equation mathematical modeling mathematical software migration modeling population probability probability distribution software tool

Editors and affiliations

  • James H. Matis
    • 1
  • Thomas R. Kiffe
    • 2
  1. 1.Department of StatisticsTexas A&M UniversityCollege StationUSA
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1244-7
  • Copyright Information Springer-Verlag New York 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-98657-9
  • Online ISBN 978-1-4612-1244-7
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site
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