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**Course number and title:** EC 201: Theoretical and Mathematical Ecology

**Revised and final times for the class are (applicable from the week of Jan 7th):**

- Wed: 2:45pm to 3:45pm (Discussion of reading materials/home-work assignments).
- Thu: 2:45pm to 4:45pm (Classes/Lectures)
- Fri: 2pm to 5pm (Lab)

Note that this is a 2:1 credit course, meaning 2 lecture hours and 1 lab (of 3 hours). But I will be travelling on two to three weeks during the semester. To compensate for the loss of teaching time during my travelling weeks, we are having an additional hour every week (this will continue until we make up for the losses).

**Venue: **Lotka-Volterra Mathematical Ecology/Computer Lab, Third Floor-A Wing, (new) Biological Sciences Building, IISc.

**Instructor:** Vishwesha Guttal

- Email: vishwesha.guttal at gmail dot com
- Office: TA-10, 3rd floor, (new) Biological Sciences Building.
- Phone: 2360-5797; 2293-2782 (typically, emails are preferred over phone).

**Teaching Assistants:**

- Sabiha Sachdeva: Will be the grader for all assignments.
- Sumithra Sankaran: For general assistance related to the course.

**Description: **This is an introductory course in theoretical/mathematical ecology to ecologists/biologists who have no experience in math after their high-school. At the end of this course, you should develop an ecological intuition that is quantitatively grounded, be able to read and critique mathematical/computational modelling papers, reproduce their results, and possibly even build basic models yourself. This course is also accessible to motivated undergraduate students.

**Tentative topics: **

1) Population dynamics

- Discrete population models (Exponential growth; Carrying capacity with logistic model; Cycles, chaos and unpredictability in population dynamics)
- Continuous population models (Exponential growth; Carrying capacity with logistic model; Allee effect, multiple stable states and catastrophic changes)
- Structured populations.
- Lotka-Volterra predator-prey model

2) Random walks and stochastic population dynamics

- Stochastic population models.
- Random walks and diffusion in animal movement models.

3) Spatial population models

- Single species population dynamics in space.
- Cellular automata and partial differential equation (reaction-diffusion) based models.

4) Evolutionary dynamics

- Random walks, drift and diffusion in evolution.
- Evolutionary game theory (ESS).
- Price equation, altruism and levels of selection.

**References:**

There is no single textbook for this course. But following will be used as references:

1) Intro to mathematics for Life scientists, Batschelet.

2) A Primer of Ecology, Gotelli, 3rd/4th Edition.

3) Population Biology: Concepts and Models, Alan Hastings

4) Mathematical Models of Social Evolution: A guide for the perplexed, McElreath and Boyd

5) Theoretical Ecology, McLean and May.

Ref (1-3) above have been kept as reserved in the CES Library (2nd floor of Biological Sciences Building).

**Prerequisites: **

We will learn most of the required math, computing and ecology “on the fly”. But math at the level of 12th class will be assumed and some programming experience (at least manipulation in Microsoft Excell) will help. I will also assume that you know basic ecology. Real key prerequisites are an enthusiasm to play with numbers, equations and to understand ecology through math. This course is also accessible to motivated undergraduate students.

If you are already good in mathematical skills, I believe you will still learn a lot of fun stuff, both math and ecology — you may be assigned additional 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.

**Teaching method:**

Distinction between classes and lab sessions are hazy, most classes will involve *computing sessions*, *lectures* or a combination of them. A ‘hands-on’ approach will be followed where students will build and/or play with mathematical models of ecology. This may be in groups. In the first few sessions, the calculations will involve calculators, but later on we will move to use computers.

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/lab session.

Computing/programming sessions will predominantly use R as our programing language. CES has a well furnished Lotka-Volterra Mathematical Ecology/Computer Lab where we have already installed linux and R. You are recommended to use these for your computer sessions.

**Grading:**

Will be based on a number of criteria but the relative weight-age of components mentioned below is not set in stone yet but it will be finalized soon.

**1) Assignments (30%):** You can expect an assignment on alternate weeks, and a total of 5 to 7 for the entire semester. Due dates will be announced and late submissions will be penalized (20% for not turning in by the precise time; 50% for next day; no credit for any further delays).

**2) A mid-term exam (30%): **This may be a open-notes or open-book exam. Dates will be announced later.

**3) Project (30%): **Everyone needs to 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 1500 words and a presentation of 15+5 minutes. More details will be provided by the end of Jan. Have a look at this for what we did in the last year.

**4) Class participation (10%):** General participation in the class.

To give you some idea, you should score 90% and above for an S grade, 75% and above for an A grade, and so on. The instructor reserves the right to decide to grading scheme based on difficulty level of exams and overall performance of the class.

**Expectations from students: **

**1) Academic honesty:** Read this page on IISc website. You are welcome to (and recommended to) work collaboratively in solving home-work problems, but final solutions must be your own. Pay attention to what constitutes plagiarism, for both home-work submission and project work and reports.

It is not clear as to what is the policy of IISc in plagiarism in course-work related matters (let me know if you know). For violation of academic honesty, you can expect range of penalty, from your specific assignment given a zero score to a fail grade in the course, depending on the severity of the case. Feel free to discuss any issues related to this.

**2) Late arrival/submissions:** Late arrival into class is strictly not allowed. Assignments must be submitted before the class starts on the due date. Late submissions will attract penalty (20% penalty for 1 minute or more but within class-hours; 30% for the same day submissions but after class-hours; 50% for next day submissions, and 100% for anytime later).

**3) Absence from class:** You are responsible for covering materials in missed classes. Note that the mid-term exam might be open-notes, where you will be allowed to bring your notes only but not photocopies of your friends’ notes.

**4) Auditing students:** Attend classes only if you can come to at least two months (until first mid-term). You are expected to do all homework and submit them so that you are also at the same level of understanding as the rest of the class. I can not, however, assure that they will be graded :-).

Look forward to seeing you in the class!

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