Schedule: Jan 2012

Session Date
Topic Covered
Worksheets; Assignments
Due Tasks
20th and 23rd April 2012
Project presentations
-
For those presenting on 20th, the report is due by noon on the 19th. For those presenting on 23rd, the due date is 8am on the 22nd.
11th April 2012
Review and guest lecture by Prof. Srinivas Raghavendra
MSD R code available in materials page
Submit progress report on projects
9th April 2012
Random walks and diffusion.
4th April 2012
Quantifying random walks: mean square displacement and its exponent.
How the exponent could mean different types of foraging strategies; levy flights.
Computing the exponent based on animal movement data.
Qns: 1-3 of assignment#2 is due
2nd April 2012
Quantifying random walks
How to distinguish different movement patterns (like migration and random walks) quantitatively.
Mean square displacement for directed motion and
Assignment #2 is ready!
-
28th March 2012
Model home range patterns.

Last day to finalize projects.
Come prepared to present questions #1,5, and 6 from Assignment #.1
26th March 2012
Animal movement:
(i) Build and simulate a model of animal migration
(ii) Simulate a random walk model.
R code: random_walk
Finalize projects soon.
24th March 2012
(i) Recap single species models.
(ii) Stochastic simulations of May’s grazing/harvesting model.
(iii) Early warning signals of abrupt changes.
R Code: harvesting_model_stochastic_dynamics (This is in google docs but you get a message saying “Preview not available”. You will find a download option under File menu – or press Ctrl S in Windows – and with that you can save the file on your desktop/laptop).
Incorporate stochasticity into the model
21st March 2012
(i) Dynamical simulations of logistic + harvesting model.
(ii) Catastrophic regime shifts and hysteresis.
(iii) Introduction to simulating stochasticity.
R Code: harvesting_model_dynamics (This is in google docs but you get a message saying “Preview not available”. You will find a download option under File menu – or press Ctrl S in Windows – and with that you can save the file on your desktop/laptop).
19th March 2012
(i) Continue with logistic models with grazing. Build and analyze more realistic models.
(ii) Multiple stable states and ecological transitions
(iii) Linear stability analysis for ODE models.
R Code: harvesting_model_fixedpoints
(This is in google docs but you get a message saying “Preview not available”. You will find a download option under File menu – or press Ctrl S in Windows – and with that you can save the file on your desktop/laptop).
Strogatz, Chapters 1-3 (to be scanned).
17th March 2012
Class cancelled.
14th March 2012
(i) Revise stability analysis derivation for the discrete time model.
(ii) Stability analysis for continuous time models – Graphical method.
(iii) Construct logistic model with grazing. Analyze fixed points graphically.
Steve Strogatz, Chapter 2 (to be scanned).
Complete at least a few questions of assignment. Read all of it to ask for any clarifications (UPDATED PDF).
Revise basic calculus.
12th March 2012
 (i) Construct continuous time exponential model.
(ii) Construct continuous time logistic model
(iii) Obtain its long term dynamic as a function of growth parameters.
Alan Hastings, Chapter 2.
7th March 2012
(i) How to analyze a new (discrete time) model of population dynamics: Used Ricker model.
(ii) Stability analysis.
NA
Please revise basic calculus (Derivatives, their definition and what do they mean? Finding maxima and minima of functions)
5th March 201
(i) Looking at time-series to long term dynamics of logistic equation.
(ii) Discover deterministic yet unpredictable and chaotic dynamics in logistic model.
Worksheet NA;
May, 1976 – A classic and highly influential paper.
Assignment #1 partly ready. PDF
Please bring your laptops
29th Feb 2012
(i) Finding fixed points analytically
(ii) Finding fixed points, and analyzing them, graphically
 (iii) ‘Discover’ cycle 2 oscillations and period doubling bifurcation in the discrete logistic model
(iv) Discover that cycles can occur even without periodicity in external forcing: periodic doubling in discrete logistic model
Worksheet #2 (logistic); continued from previous session: PDF
Complete up to 10th generation for the logistic model tasks for both values of R.
27th Feb 2012
(i) ‘Feel’ the exponential growth(ii) Develop discrete time exponential growth population model
(iii) Develop discrete time logistic population model
(iv) A heuristic explanation of fixed points and stability
Worksheet #1 (Exponential): PDF
Worksheet #2 (Logistic):PDF
Please come with calculators (not laptops).

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