Math/EEB 581 - Fall 2016 Mathematical Ecology I

Course Materials

Offices and Office Hours
Louis Gross: Office is 401B Austin Peay and Office Hours are Mondays 11-1 and Wednesdays 11-12:15, with other hours by appointment. I am often at NIMBioS when not in Austin Peay - my office there is 124 Claxton. Email Dr. Gross to make an appointment.

Assignments
Problem set 1 - part 1: Problems 1.1, 1.2, and 1.3 - these will be due along with problems from Chapters 2 and 3 on approximately September 9. Note that for Problem 1.2 you might find it useful to look at pages such as Paul's notes on solving Bernoulli eq
Problem set 1 - part 2: Problems 2.1, 2,2, 2.3, 2.4, 2.5, 2.6 - these will be due along with problems from Chapters 1 and 3 on approximately September 9.
Assignment for Friday September 2: Read the below listed articles by Chad Brassil and Sebastian Schreiber, and email the instructor any questions you have about these. Note that both articles include topics from models concerning more than one species and we will be discussing these as the term goes on - we have not covered this yet. So please focus on the beginning sections of each article that deal with single species and not the two and higher number of species sections.
Problem set 1 - Part 1 and Part 2 problems from Chapters 1 and 2 above are due on September 12
Problem set 2 - Part 1 from Chapter 3 - do problems #3.1, 3.2, 3.3, 3.4, 3.6, 3.7. These will be due along with problems from Chapter 4 at the end of September.
In class on September 9, I asked you to think about the following Waiting Time problem. Suppose that buses arrive at a bus stop at times that are not a fixed schedule, but according to an exponential distribution with mean time between arrivals of a bus being 1/a (so a is the parameter in the exponential distribution). You arrive at the bus stop without any information about when the last bus stopped there or when the next bus will arrive. How long on average will you have to wait until a bus arrives?
Problem set 2 - Part 2 from Chapter 4 - do problems #4.1, 4.2, 4.3, 4.4. These will be due along with problems from Chapter 3 on October 10.
Assignment for Friday September 30: Read the below article by Jim Cushing, and email the instructor any questions you have about this. Note that this article include topics from models concerning more than one species and we will be discussing these as the term goes on - we have not covered this yet. So please focus on the beginning sections of the article that deal with single species and not the multi-species section.
Problem set 3 - Part 1 from Chapter 5 - do problems #5.1, 5.2 These will be due along with problems from Chapter 6 on November 4.
Problem set 3 - Part 2 from Chapter 6 - do problems #6.1, 6.2, 6.4 and 6.5 These will be due along with problems from Chapter 5 on November 4.

These are additional readings that go along with Chapters 1 and 2 and expand on several topics in these chapters. We will discuss some of the topics in these in class, but not all of them in each paper. The below is the order I suggest you look at them. The links are to the UTK library e-book version for each but they are all taken from the Encyclopedia of Theoretical Ecology (A. Hastings and L. J. Gross, eds.)
Sebastian Schreiber: Ordinary Differential Equations
Fabio Dercole and Sergio Rinaldi: Bifurcations
Karen Abbott and Anthony Ives: Single Species population Models

This additional reading goes along with Chapter 4. Jim Cushing: Difference Equations
This additional reading goes along with Chapter 7. Peter Abrams: Predator-Prey Models
This additional reading goes along with Chapter 12. Priyanga Amarasekare: Two-Species Competition

References Mentioned in Class
Background on modeling trade-offs - this is discussed in Chapter 1 of Evolution in Changing Environments by Richard Levins, Princeton University Press (1968). For a recent discussion and mathematical formulation of these issues, see The structure of tradeoffs in model building by John Matthewson and Michael Weisberg

MATLAB

Single simulation of pure death process (MATLAB .m file)
Simulation of time to extinction of pure death process (MATLAB .m file)
Simulation of mean time to extinction of pure death process (MATLAB .m file)
Simulation of pure birth process with time for pop size to reach a max size (MATLAB .m file)
Simulation of single type branching process (MATLAB .m file)
Illustration of cobwebbing using Logistic map (MATLAB .m file)
2 cycle composition of Logistic map (MATLAB .m file)
Illustration of cobwebbing starting from two initial points using Logistic map - to illustrate sensitive dependence on initial conditions (MATLAB .m file)
Lagged-Logistic map (MATLAB .m file)
Lagged-Logistic map Bifurcation diagram calculation (MATLAB .m file)
Beverton-Holt difference equation model (MATLAB .m file)
Ricker difference equation (MATLAB .m file)
2 cycle composition of Ricker model (MATLAB .m file)
Illustration of cobwebbing using Ricker model (MATLAB .m file)
Simple disc rete-time predator-prey model (MATLAB .m file)

Questions raised by Class Participants (text file)