# Stochastic Population Theories

• Donald Ludwig
Book

Part of the Lecture Notes in Biomathematics book series (LNBM, volume 3)

1. Front Matter
Pages N2-VI
2. Donald Ludwig
Pages 1-31
3. Donald Ludwig
Pages 32-56
4. Donald Ludwig
Pages 57-86
5. Donald Ludwig
Pages 87-102
6. Back Matter
Pages 103-114

### Introduction

These notes serve as an introduction to stochastic theories which are useful in population biology; they are based on a course given at the Courant Institute, New York, in the Spring of 1974. In order to make the material. accessible to a wide audience, it is assumed that the reader has only a slight acquaintance with probability theory and differential equations. The more sophisticated topics, such as the qualitative behavior of nonlinear models, are approached through a succession of simpler problems. Emphasis is placed upon intuitive interpretations, rather than upon formal proofs. In most cases, the reader is referred elsewhere for a rigorous development. On the other hand, an attempt has been made to treat simple, useful models in some detail. Thus these notes complement the existing mathematical literature, and there appears to be little duplication of existing works. The authors are indebted to Miss Jeanette Figueroa for her beautiful and speedy typing of this work. The research was supported by the National Science Foundation under Grant No. GP-32996X3. CONTENTS I. LINEAR MODELS •••••. •••••••••••••••. . ••••••••••••••••••••••••••••••••••••••• 1 1. The Poisson Process ••••••••••••••••••••••••••. ••. •••••••••••. •••••••••• 1 2. Birth and Death Processes 5 2. 1 Linear Birth Process 5 2. 2 Linear Birth and Death Process •••••. ••••••. ••••••••••••••. •••••••• 7 2. 3 Birth and Death with Carrying Capacity ••••••••. •••. ••••••. ••••••. • 16 3. Branching Processes •••••••••••••••••••. •••••••. ••••••••. ••••••••••••••• 20 3. 1 Continuous Time . •••. ••••••••••. •••••••••••••••••••. ••••••••. ••••.

### Keywords

Branching process Derivation Galton-Watson process Poisson process Population Probability theory Stochastischer Prozess equation

#### Authors and affiliations

• Donald Ludwig
• 1
1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-80883-8
• Copyright Information Springer-Verlag Berlin Heidelberg 1974
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-07010-8
• Online ISBN 978-3-642-80883-8
• Series Print ISSN 0341-633X
• Buy this book on publisher's site