10.24.2015

Modeling an Ecological Phenomenon: Stress

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[Niklas Lollo, ERG graduate student]


One of my very first ERG experiences was a colloquium in spring 2014. On stage was a towering fellow I had met once before by the name of Joe Kantenbacher, PhD. His talk: It’s about time: Linking happiness and the pursuit of sustainability, struck all the right chords in my heart. I had been very focused on work-life balance in what little time I’d had to either work or live. (I’m a spritely 25 year-old!) There’s compelling evidence that life balance has many ancillary benefits, including for your heart, your family, your community and the environment.

Not surprisingly, I have followed the work of Juliet Schor and Giorgios Kallis, both major academic advocates of worktime reduction, for years. Last year, I worked on a campaign that helped pass a flexible worktime policy in the city of Berkeley. In my free time, I swoon over the workplace policies in Europe.

It really shouldn’t be a surprise that this semester has been wildly different from my romantic pre-conceived visions coated with naïveté.
With this in mind, I entered graduate school thinking it would be the serene experience I had romanticized for years: I would blend rigor and pursuit of my passion within a nurturing environment that understands the beauty of balance.

It really shouldn’t be a surprise that this semester has been wildly different from my romantic pre-conceived visions coated with naïveté.

The beginning of the semester launched me into the wild west of selecting classes, going to different lab groups, talking to professors across campus, picking up skills at the D Lab, plotting student groups, toying with the idea of clubs, fiddling with photography, meeting new friends, doing course readings… the list stretches and tumbles. The dust will settle… I was told.

Except that, when the dust settled, rather than finding a field of daisies, before me was a valley of fires. Every task surged with urgency—learning R was no longer one of many programs to mess around with, it was THE one and I needed to do THE analysis right NOW. And the problem sets kept piling, the tasks kept stacking, the bureaucracy kept flowing… until the mother of all stress-inducing activities reared its grotesque, warted head: the NSF GRFP fellowship application.

...I began to wonder (perhaps the first time all semester I was permitted to wonder so freely), what is the nature of this stress? Will it ever end? What might be its functional form?
It was precisely a week ago, as I sat on a plane whipping across fourteen time zones safely freed from my laptop and internet, that I began to wonder (perhaps the first time all semester I was permitted to wonder so freely), what is the nature of this stress? Will it ever end? What might be its functional form?

Full disclaimer: This activity of modeling stress in this blog isn’t entirely removed from the Willy Wonka’s everlasting task-list I describe above—I am in John Harte’s modeling class and we are strongly encouraged to write for this blog.

My first impulse was, Aha! It’s the logistic. So, I drew upon Core Model #2 which is a carrying capacity model. The per capita stress rate depends on the carrying capacity of stress, which is moderated by the physical capacity of projects you could take on. If X were stress and K were carrying capacity of stress (projects), the equation would look like:

dX/dt=rX(1-X/K)

Which is represented by the graph…


So, you see that over time stress reaches a maximum (your limit) and then coasts. This appears reasonable, until I thought, Hey, what about when projects are done? Stress must decrease at that point. To which fellow newbie ERGie, Dan Aas, listening nearby to my thought process, noted, “Maybe it’s sinusoidal.” Which would graphically look like a perfectly wiggled snake.
In order to graph this movement, I figured I might shift to Core Model #4. I wondered if this phenomenon wouldn’t be better modeled as a Lotka-Volterra set of equations. Stress would be the predator (Y) and tasks would be the prey (X).

So,
dX/dt = aX – bXY
dY/dt = cXY – dY

Since the project population tends to experience perturbations from external forces (such as: professors slipping a task or two your way on Friday afternoon), a stability analysis might be able to tell us new information about the resilience of the stress-task ecosystem. I specified the equations (you’ll have to trust me on the math here), and the eigenvalues were both > 0… which looks like this…

Which partially makes sense, the projects do tend to increase in importance over the course of time, but I don’t imagine relaxation also increases with each periodic cycle. Maybe if the periods were semesters, but that resembles a tangent function with vertical asymptotes and I’m not sure we’re making this model as simple and effective as possible.

In any case I lack experience with the end of semesters, so I ventured to ask a few second- and third-years nearby.

“I spent 30 hours per week last winter break glued to Kahn Academy learning statistics while I recovered emotionally from my GSI work and feverishly worked on my Switzer.”

Oh.

I considered adding in time lags of guilt, but then it hit me: maybe the answer has been right in front of my face. And maybe that answer is the one function that Professor Harte says has no representation in nature.

But my economist friends know about exponential growth.

And since I’m pretty confident in the robustness of this model, let’s go back to Joe’s research. What does this say about our happiness and our environmental footprints?

While stress might be increasing, we still need to figure out one crucial thing, and it truly is the unsettled debate of graduate school: are we time affluent or time poor?

Yes, there’s boundless time and open schedules, but with so many great things happening at Berkeley, you just keep can’t keep your hands out of the cookie jar until its too late and the sugar coma hits you.


[Top image source: Sara V.

Note: The views expressed here belong solely to the author of each entry and are not representative of the position of the Energy and Resources Group, UC Berkeley.

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