Projects: Jan 2012

Broad expectations: Project is an important part of the course both in terms of learning as well as grades for those who credit. It is really meant to improve your depth of a topic covered in the class, and/or add a breadth to your mathematical modeling skills. As an example of the former, you can study in depth the role of discrete logistic model in enhancing our understanding of biology of populations. For the latter, a good example might be to take up an ecological issue (like competitive exclusion principle), present it mathematically, computationally and show how it sharpens our understanding of the relevant ecology.

Alternatively, you can also do a project on statistical inference, the part that Kavita covered. In fact, if you can integrate both mathematical modelind with statistical inference for your project, that would be ideal.

You could either come with your own project that interests you or select something from the list below. In either case examine the topic in depth, critically analyze the work carried out so far, and develop an understanding of key outstanding issues. Note that we are not just doing a reading project, so you should either do some theoretical analysis, numerical simulations and/or statistical analysis of some dataset (if available). Although entirely reading projects are discouraged, they may be accepted as exceptions if there is something novel about what you plan to do.

You should talk to me to finalize the project before going ahead. Please come with a bullett point write up that presents a broad outline of what you plan to achieve along with some references.

Submission requirements: You should submit a short well-written report (<2500 words) and also present the work (10+5 minutes) you have done.

Timeline:

* Finalize the topic after discussing with me: before 28th March 2012 3rd April 2012.

* Discuss your progress (write a short email with any graphs, equations or references): 6th April 2012 9th April 2012.

* Submit the written report (<2500 words): 18th April 2012.

* Presentations (10+5 minutes): Week of April 23rd (tentative – to be finalized after figuring out your exam schedules).

List of topics (INCOMPLETE; please add your own!). Note that each topic can itself narrow down to different specific projects depending on your interests; so more than one can work on a given topic as long as they take different approaches/aspects of it:

(1) Do real ecological systems exhibit chaos, as predicted a host of simple population models? Simplicity of the discrete time logistic model and other such models, and the fact that real world is so much more complex, could suggest that real world has lots of potential to exhibit chaotic dynamics. Analyze the current state of research in this field. Basically anything (experimental design, underlying theory and implications, statistical methods to detect chaos, etc) that strikes you most.

REF: Some of the assigned reading materials can help you find references.

(2) Predator prey OR Competition models. We did not cover this in the class, but its analysis involves new techniques (using matrices, eigen values) and can help you broaden your mathematical skill-set.

REF: Any standard textbook on ecological modeling. You can start with Alan Hastings book on population biology (available as Reserve in the CES library).

(4) Abrupt ecological transitions. Many ecological systems show abrupt changes in their dynamics (like phase transitions in physics), and in this project you will take further from where we left off in the class on grazing model and how it simple mathematical models can be helpful in developing predictive tools for ecosystems.

REF: Scheffer et al, 2001, Nature. Catastrophic shifts in ecosystems; Scheffer et al 2009; Early warning signals of critical transitions. 

(5) Investigate discrete logistic/ricker model with stochasticity in its parameters to represent the fact that birth and death rates are influenced by environmental stochasticity.

(6) More to be added.

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