| Day |
Date |
Lecture |
Topic |
Guest
Lecturer |
Reading |
Homework |
Due Date |
| |
|
|
PART
I: Discrete Math and applications of difference equations |
|
|
|
|
| Thurs |
1/10/2013 |
1 |
Introduction to the class;
the Modeling Cycle; Example 1: the 1st-order difference equation
for modeling population dynamics |
|
Chapter
1.1 |
HW #0 (solution)
|
1/15 |
| Tues |
1/15/2013 |
2 |
Example 1, Cont. + PRIMER: Models and
common sense: dimensions, orders-of-magnitude estimation,
significant figures |
|
Ch. 1.2, 1.5 |
HW#1 (solution) |
1/22 |
| Thurs |
1/17/2013 |
3 |
Second order difference
equations, the superposition principal. Example 2: plant
reproduction from a seedbank |
|
|
|
|
| Tues |
1/22/2013 |
4 |
Coupled linear difference
equations; Bifurcations diagrams: Example 3: populations
with juvenile and adult stages |
|
Ch. 1.3,
1.6 |
HW #2 (solution) |
1/29 |
| Thurs |
1/24/2013 |
5 |
General 2-D systems of
difference equations; Example 4: 3-D system, Characteristic equations giving complex eigenvalues |
|
Ch. 1.4,
1.8 |
|
|
| Tues |
1/29/2013 |
6 |
Project 1 Intro; Parameterizing models with data: maximum likelihood estimation |
|
(not in book) |
Project #1 (corrected) (solution) |
2/12 |
| Thurs |
1/31/2013 |
7 |
Non-linear difference equations: the discrete logistic equation; Cobweb diagrams (free downloadable software for cobwebbing: E&F Chaos) |
|
Ch. 2.1, 2.3, 2.5 |
|
|
| Tues |
2/5/2013 |
8 |
Linearization of non-linear diff. equations: the fundamental theorem of stability |
|
Ch. 2.2 |
|
|
| Thurs |
2/7/2013 |
9 |
Systems of non-linear
difference equations (if interested, see classic paper on chaos in Beetle populations, "Chaotic Dynamics in an Insect population")
|
|
Ch. 2.7,
2.8 |
|
|
| Tues |
2/12/2013 |
10 |
Application: Host-parasite system, Nicolson-Baily model |
|
Ch. 3.2,
3.3, 3.4 |
Review for midterm exam 1 |
|
| Thurs |
2/14/2013 |
11 |
PART
II: Continuous math models & differential equations
Differences between discrete & continuous math: 3 DEQ's everyone should know |
|
Ch. 4.1 - 4.6 |
Midterm practice (solution) |
|
| Tues |
2/19/2013 |
12 |
Phase-plane qualitative analysis: Lotka-Volterra model of pop. Dynamics |
|
Ch 5.1 - 5.5; Ch. 6.1 - 6.2 |
HW #3 (solution)
|
2/26 |
| Thurs |
2/21/2013 |
|
MIDTERM 1 (lectures 1-10, and homeworks 1-2; Project 1) |
|
|
|
|
| Tues |
2/26/2013 |
13 |
Linearization & stability analysis with continuous math |
|
as above;
|
HW #4 (solution) |
3/5 |
| Thurs |
2/28/2013 |
14 |
Matrix approach to stability analysis: variations on Lotka-Volterra |
|
Ch. 4.7-4.9; 5.6-5.8 |
|
|
| Tues |
3/5/2013 |
15 |
L-V competition/mutualism summary; linking ecology to biogeochemistry (background for project
2) |
|
as above |
Project #2 (solution)
|
3/19 |
| Thurs |
3/7/2013 |
16 |
Models with more than two state variables; qualitative
stability analysis: Routh-Hurwitz criteria |
Cushing |
Ch. 6.4 - 6.5 |
|
|
| |
|
|
SPRING BREAK |
|
|
|
|
| Tues |
3/19 |
17 |
Application: Does biological complexity influence
stability? (for those interested, see Robert May's classic 1972 paper, "Will a large complex system be stable?" |
|
as above |
HW 5 (solution) |
3/26 |
| Thurs |
3/21 |
18 |
Epidemiological models of Infectious disease: SIR models |
|
Ch. 6.6 |
|
|
| Tues |
3/26 |
19 |
Epidemiology, continued: unintended
outcomes; review for Exam 2 |
|
Ch. 6.7 |
Review for
exam 2
|
|
| Thurs |
3/28 |
20 |
Oscillations and Limit cycles; Poincare-Bendixson theorem |
|
Ch. 8 (intro); 8.3-8.4 |
|
|
Tues |
4/2 |
|
MIDTERM 2 (Lectures 11-19; homeworks 3-5; Project 2) |
|
|
|
Thurs |
4/4 |
21 |
Application: neuron impulse conduction (Fitzhugh model) |
|
8.5 - 8.8 |
HW #6 (solution) |
4/11 |
Tues |
4/9 |
22 |
Oscillations and Limit cycles: the Hopf bifurcation; chaos in continuous models |
Cushing |
as above |
Project #3 (solution) |
4/23 |
| |
|
|
PART
III: Miscellaneous: Genetics, Max Entropy, and Scaling |
|
|
|
|
Thurs |
4/11 |
23 |
Application: evolution by natural & sexual selection |
|
(not in book) |
|
|
Tues |
4/16 |
24 |
Population Genetics: Hardy-Weinberg equilibria |
Cushing |
Ch 3.6 |
|
|
Thurs |
4/18 |
25 |
Guest lecture for an application from biogeochemical modeling: Predicting Fires in Amazon forests with a simple model (see Chen et al., 2011) |
Randerson |
Chen et al. 2011 |
|
|
| Tues |
4/23 |
26 |
Structural and Dynamical Models of Ecological Networks |
Martinez |
|
HW #7 (optional) (solution) |
5/6 |
| Thurs |
4/25 |
27 |
Macroecology and Maximum Entropy |
|
|
|
|
| Tues |
4/30 |
28 |
Max Entropy 2 and Last Day
Course review |
|
|
|
|
