Introduction:  This course covers an introduction to population dynamics. It attempts to bridge the gap between mathematics and population Biology. It is intends to introduce modeling in the natural sciences and show students how to apply mathematics to the study of some questions of importance to population biology.

 

Book:  Mathematical Models in Population Biology and Epidemiology by F. Brauer and C. Castillo-Chavez, TAM-40 Springer 2000.

Basics Content

  1. Continuous Population Models (PDF notes  chapter 1)
    1. Exponential Growth  
    2. The Logistic Population Model 
    3. The Logistic Equation in Epidemiology
    4. Quantitative Analysis 
    5. Harvesting in Population Models
      1. Constant Yield Harvesting : Maple worksheet
      2. Constant Effort Harvesting: Maple worksheet
    6. Eutrophication of a Lake: Maple worksheet
    7. Maple worksheet for Lab1     
  2. Discrete  Population Models (PDF notes  chapter 2)
    1. Linear Models
    2. Graphical Solutions of Difference Equations   CODE
    3. Equilibrium Analysis
    4. Period-Doubling and Chaotic Behavior
    5. Discrete Time Metered Models
    6. A Two-Age Model and Delay Recruitment
    7. Systems of Two difference Equations
  3. Introduction and Mathematical Preliminaries (PDF notes chapter 4)
    1. The Lotka-Volterra Equations
    2. The Chemostat
    3. Equilibria and Linearization
    4. Qualitative behavior of Solutions of Linear Systems
    5. Periodic Solutions and Limit Cycles
    6. Appendix: Canonical Forms of 2x2 Matrices
  4. Continuous Model for Two Interacting Populations (PDF notes chapter 5)
    1. Species in Competition
    2. Predator-prey Systems
    3. Kolmogorov Models
    4. Mutualism
    5. The Community Matrix
    6. The Nature of Interactions Between Species
  5. Harvesting in two-species models (PDF note chapter 6)
    1. Harvesting of species in competition
    2. Final Presentation: A class of Predator-Prey Models.