EC 305: Quantitative Ecology; Module two: Theoretical and Mathematical Ecology
Kavita Isvaran (module one) and Vishwesha Guttal (module two)
Schedule and Venue: Mon: 2:30pm-5:30pm and Wed: 1:30pm to 3:30pm at CES Seminar Hall. In case the seminar hall is booked for seminars on Wednesdays, we will meet at 420 CES (3rd floor).
This is an introductory course in theoretical/mathematical ecology to ecologists/biologists who have no experience in math after their high-school. So the key prerequisites are an enthusiasm to play with numbers, equations and to understand ecology. If you are familiar with basic calculus and programming, that’s a great bonus! If you are good in mathematical skills, I believe you will still learn a lot of fun stuff, both math and ecology — you may be assigned problems to use those skills. If you are concerned about the suitability of this course to you, i.e., if you feel being under- or over-prepared, discuss with me.
You will need to bring your own laptop (or anything else that will be informed) to all sessions.
In this course, I plan to follow a slightly unconventional set of topics, as compared to a regular theoretical ecology course. One of the main aim is to get to a state where one can begin to appreciate latest research literature on at least some topics of theoretical ecology. So we will learn some models and techniques that are current interest in ecology, but starting with very basics!
Tentative syllabus for this half-semester module is to build and play with
1. simple deterministic models of single species population dynamics (discrete logistic, continuous logistic models; fixed points, oscillations, chaos and predictability).
2. simple deterministic models of populations under harvesting (overharvesting, grazing models of May; Tipping points and regime shifts; Bifurcation diagrams).
3. stochastic models of population dynamics
4. animal movement and random ‘drunkard’ walks
5. spatial patterns in ecology, and the issue of scale
6. some elements of evolutionary biology
This is very likely overambitious given that we have only 8 weeks of classes (each with roughly 3 hours lab and 2 lecture hours) and that its meant to be an introductory course to nonspecialists! So we may tweak, skip parts of above list and may add something else as we go along.
Teaching method in this course
This may evolve with the course. But here is the basic idea: Classes will involve computing sessions, lectures or a combination of them. A ‘hands on’ approach will be followed where every class/session students will build and/or play with mathematical models of ecology. Sometimes this may be in groups. In the first few sessions, the calculations will involve calculators, but later on we will move to use computers.
Lectures will be minimal. Typically, an hour after a session of 3 hours of computing sessions.
It turns out that it much easier to modify a code than to write from scratch, especially if you are beginner. So, I will supply with sample codes relevant to an ecological problem in discussion. You may need to modify it during the class.
Computing sessions will predominantly use R as our programing language. This can be on Linux, MacOS or Windows environment.
In class work (20%) + Assignments (30%) + a Project (50%); the numbers in brackets indicate percentage weightage for these two components. This is for module two only.
There will be two to three take-home assignments which needs to be submitted on due dates to be announced later.
Everyone should carry out a small, simple theoretical/computational project that covers an important ecological question. This could be from a current research work you are doing, a topic you came up with, or from a list I am going to provide later. It will involve submission of a short report of less than 2000 words (include programs if you wrote any) and a presentation of 10+5 minutes. More details will be provided before the end of Feb.
Textbook and References
I won’t be following a single book as a Text. Many references will be research papers. I will add more on this when its appropriate.
Students interested in auditing are welcome to attend, but please try to attend all of classes. You are encouraged to submit assignments, but I can’t promise whether they will graded! It is desirable that you also perform a project — that is where I always learnt the most. I can provide comments on that.