Stochastic Population Models

I Introduction.- 1. Overview of Models.- 1.1 Modeling Objectives.- 1.2 Structure of Monograph.- 2. Some Applications.- 2.1 Introduction.- 2.2 Application to Invasion of Africanized Honey Bee.- 2.3 Application to Muskrat Spread in the Netherlands.- 2.4 Application to Bioaccumulation of Mercury in Fish.- 2.5 Application to Human Calcium Kinetics.- II Models for a Single Population.- 3. Basic Methodology for Single Population Stochastic Models.- 3.1 Introduction.- 3.2 Basic Assumptions.- 3.3 Moments and Cumulants.- 3.4 Kolmogorov Differential Equations.- 3.5 Generating Functions.- 3.6 Partial Differential Equations for Generating Functions.- 3.7 General Approach to Single Population Growth Models.- 4. Linear Immigration-Death Models.- 4.1 Introduction.- 4.2 Deterministic Model.- 4.3 Probability Distributions for the Stochastic Model.- 4.4 Generating Functions.- 4.5 Cumulant Functions.- 4.6 Some Properties of the Stochastic Solution.- 4.7 Illustrations.- 5. Linear Birth-Immigration-Death Models.- 5.1 Introduction.- 5.2 Deterministic Model.- 5.3 Probability Distribution for the Stochastic Model.- 5.4 Generating Functions.- 5.5 Cumulant Functions.- 5.6 Some Properties of the Stochastic Solution.- 5.7 Illustrations.- 6. Nonlinear Birth-Death Models.- 6.1 Introduction.- 6.2 Deterministic Model.- 6.3 Probability Distributions for the Stochastic Model.- 6.4 Generating Functions.- 6.5 Cumulant Functions.- 6.6 Some Properties of the Stochastic Solution.- 6.7 Illustrations.- 6.8 Appendices.- III Models for Multiple Populations.- 7. Nonlinear Birth-Immigration-Death Models.- 7.1 Introduction.- 7.2 Deterministic Model.- 7.3 Probability Distribution for the Stochastic Model.- 7.4 Generating Functions.- 7.5 Cumulant Functions.- 7.6 Some Properties of the Stochastic Solution.- 7.7 Illustrations.- 7.8 Appendices.- 8. Standard Multiple Compartment Analysis.- 8.1 Introduction.- 8.2 Deterministic Model Formulation and Solution.- 8.3 Illustrations.- 9. Basic Methodology for Multiple Population Stochastic Models.- 9.1 Introduction.- 9.2 Basic Assumptions.- 9.3 Joint Moments and Cumulants.- 9.4 Kolmogorov Differential Equations.- 9.5 Bivariate Generating Functions.- 9.6 Partial Differential Equations for Generating Functions.- 9.7 General Approach to Multiple Population Growth Models.- 10. Linear Death-Migration Models.- 10.1 Introduction.- 10.2 General Formulation of the Stochastic Model.- 10.3 Direct Solution for Stochastic Migration-Death Model.- 10.4 Mean Residence Times.- 10.5 Appendix.- 11. Linear Immigration-Death-Migration Models.- 11.1 Introduction.- 11.2 Generating Functions for the Stochastic Model.- 11.3 Probability Distribution.- 11.4 Cumulant Functions.- 12. Linear Birth-Immigration-Death-Migration Models.- 12.1 Introduction.- 12.2 Equations for Cumulant Functions.- 12.3 Application to Dispersal of African Bees-Basic Model.- 12.4 Application to Muskrat Spread Data.- 12.5 Appendix.- 13. Nonlinear Birth-Death-Migration Models.- 13.1 Introduction.- 13.2 Probability Distribution for the Stochastic Model.- 13.3 Cumulant Functions.- 14. Nonlinear Host-Parasite Models.- 14.1 Introduction.- 14.2 Proposed Host-Parasite Model.- 14.3 Conclusions and Future Research Directions.- 14.4 Appendix.- References.