Population Projection (UMAP)

Author: Edward L. Keller

This unit examines a model developed by P.H. Leslie and others that uses matrix multiplication to make population projections from one time period to another. The emphasis is on understanding the role of eigenvalues and eigenvectors. Proofs are not emphasized. There are computer exercises in an appendix for those who wish to use them. Students see how a knowledge of eigenvalues and eigenvectors is useful in studying powers of a matrix, and are birefly exposed to some interesting theorems of linear algebra.

Table of Contents:

1. INTRODUCTION

2. THE MODEL
2.1 Population Projection -- An Example
2.2 Extending the Projection
2.3 Powers of the Leslie Matrix
2.4 Another Example

3. THEORETICAL BACKGROUND
3.1 Some Observations
3.2 The Perron-Frobenius Theorem
3.3 An Example with Oscillations
3.4 Summary
3.5 A Simplification Using Left and Right Eigenvectors

4. A HUMAN POPULATION EXAMPLE

5. REFERENCES

6. ANSWERS TO EXERCISES

APPENDIX A

APPENDIX B