# User:Carl Boettiger/Notebook/Teaching/2010/02/04

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## Early Warning Signals to Regime Shifts Seminar

• I was just responsible for covering a relatively technical paper on the idea of detecting early warning signals to regime shifts. This is a class of about 10 people. First half we took turns on the board, relying entirely on graphical analysis, and going from a birth death model through stability analysis to illustrate bi-stability to the bifurcation diagram and the energy landscape representation. In the second half we explored an individual-based stochastic simulation module in netlogo in which we could move slider bars for parameters and observe the bifurcation and population crash.
• The board work went very well with people taking turns getting us to the next step. I believe it was clear that (a) not everyone understood this analysis at the beginning and (b) were able to figure it out at the board with a little bit of guidance and (c) seemed very engaged in the process. The netlogo activity ended up being done predominately on my machine connected to the projector rather than in pairs at individual computers in front of everyone. Getting groups started on an activity seems to be a challenge to me, and transitioning between little groups and whole class discussion remains something I really need to figure out. In this case the whole-group exploration of the netlogo simulation guided by me was probably best anyway, as I didn't have clear directions or time for people to work in groups.

## Evaluation

• I was also pleased by the prepwork required to do this. Initially it took me about 3 hrs (while stuck on a train) to learn how to get a population model into netlogo. Realizing that I can only do individual-based birth and death rates (so divide the population rates by population size), and learning the  count sheep  command were key steps. I debated coding the dynamics in R, or in C and writing a python interface for slider bars, but the netlogo approach was much easier. Still, I was frustrated by not knowing how to make netlogo do graphs that don't have time on the x axis, or the rather cumbersome way I have to calculate warning signals such as variance. Once I figured out the basics, I was able to write the actual netlogo code we used in about an hour this morning, and guide the board discussion without more than a sketch of my plan.
• I still debate whether interactive learning must involve slower pace and less coverage than traditional approaches. Overall I was happy with how much we covered today and think it successfully facilitated an accelerated discovery process relative to what would happen in normal lecture + homework exercise. The fact that we hardly talked about the article I was supposed to cover notwithstanding...
• On the science side, the simulation did a good job of illustrating a case where there was a mathematical warning signal, in terms of a weakening eigenvalue, (despite the model having the stochasticity built in intrinsically and not just added to the landscape picture), but at the same time it was hard to detect without long-time averages, slow changes, or replicates.

## Going Forward

• Thinking about writing up a little manuscript with the examples and discussion of the theory we covered.
• Trying to figure out what makes this post useful and what just wastes time. Thinking about adding the netlogo code up here, and/or figures covering the examples. Might be better placed in my lab notebook on stochastic population dynamics.