Session Date
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Topic Covered
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Worksheets; Assignments
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Due Tasks
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20th and 23rd April 2012
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Project presentations
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–
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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.
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11th April 2012
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Review and guest lecture by Prof. Srinivas Raghavendra
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MSD R code available in materials page
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Submit progress report on projects
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9th April 2012
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Random walks and diffusion.
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—
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4th April 2012
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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.
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—
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2nd April 2012
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Quantifying random walks
How to distinguish different movement patterns (like migration and random walks) quantitatively.
Mean square displacement for directed motion and
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–
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28th March 2012
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Model home range patterns.
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Last day to finalize projects.
Come prepared to present questions #1,5, and 6 from Assignment #.1
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26th March 2012
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Animal movement:
(i) Build and simulate a model of animal migration
(ii) Simulate a random walk model.
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Finalize projects soon.
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24th March 2012
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(i) Recap single species models.
(ii) Stochastic simulations of May’s grazing/harvesting model.
(iii) Early warning signals of abrupt changes.
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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).
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Incorporate stochasticity into the model
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21st March 2012
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(i) Dynamical simulations of logistic + harvesting model.
(ii) Catastrophic regime shifts and hysteresis.
(iii) Introduction to simulating stochasticity.
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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).
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19th March 2012
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(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.
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(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).
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17th March 2012
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Class cancelled.
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14th March 2012
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(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.
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Steve Strogatz, Chapter 2 (to be scanned).
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Complete at least a few questions of assignment. Read all of it to ask for any clarifications (UPDATED PDF).
Revise basic calculus.
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12th March 2012
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(i) Construct continuous time exponential model.
(ii) Construct continuous time logistic model
(iii) Obtain its long term dynamic as a function of growth parameters.
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Alan Hastings, Chapter 2.
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7th March 2012
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(i) How to analyze a new (discrete time) model of population dynamics: Used Ricker model.
(ii) Stability analysis.
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NA
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Please revise basic calculus (Derivatives, their definition and what do they mean? Finding maxima and minima of functions)
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5th March 201
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(i) Looking at time-series to long term dynamics of logistic equation.
(ii) Discover deterministic yet unpredictable and chaotic dynamics in logistic model.
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Worksheet NA;
May, 1976 – A classic and highly influential paper.
Assignment #1 partly ready. PDF
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Please bring your laptops
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29th Feb 2012
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(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
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Worksheet #2 (logistic); continued from previous session: PDF
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Complete up to 10th generation for the logistic model tasks for both values of R.
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27th Feb 2012
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(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
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Worksheet #1 (Exponential): PDF
Worksheet #2 (Logistic):PDF
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Please come with calculators (not laptops).
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