Resilience indicators: prospects and limitations for early warnings of regime shifts

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Resilience indicators: prospects and limitations for early warnings of regime shifts

This is a paper by Vasilis Dakos, Stephen Carpenter, Egbert van Nes, and Marten Scheffer who investigated ways of measuring resilience in ecosystems and measures that would indicate tipping points in them before they were too late to reverse.

This might seem pretty far out of our wheelhouse, but I think its an important look at some concrete way of attempting to measure resilience.

I often get questions about this, how do you actually measure resilience? And often times the answer begins with looking for sources of adaptive capacity or reserves. But this is an example of very quantitative way, which I think is often what some folks are seeking.

I don’t necessarily think this approach is better, we’ll discuss it’s limitations shortly, but I do think it can serve as a good example of the difficulty of “counting” resilience.

Critical Slowing Down

The authors investigate a measure that can help determine when ecosystems are approaching a “Critical Slowing Down” (CSD) period. This period sometimes occurs as ecosystems make a major shift, essentially from what we think of as good to bad.

The idea is that if we can detect these things (hopefully before it’s too late to do anything about it), then we can intervene. I think this idea is attractive for a lot of us as we explore resilience regardless of the domain.

Many of us had been searching in this sort of direction, discover this resilience stuff, and then want to go find that resilience bit of our system and amplify it. It doesn’t really work like that of course, but the core idea, how can I measure or determine where I, my organization, my system is positioned as it relates to resilience and perhaps tipping points are great questions.

I’m not advocating that everyone go out and make new ecological based grafana dashboards and alerts or anything (though that sounds like a cool experiment), but knowing about how others are assessing complex systems and the difficulty they run into can help you when you want to do the same in your world.

The authors define these tipping points, then shifts as “critical transitions”:

Critical transitions are defined as abrupt qualitative changes in the state of an ecosystem that occur close to bifurcation points

Notice that though this method is quantitative and heavy on math, the shift itself is qualitative. I think this is important to emphasize as an industry, software and tech in general perhaps, can be strongly biased towards that quantitative only.

First, some limitations of this method (and likely any method developed to measure resilience in this way) from the authors:

• Not all shifts in the ecosystem have these indicators because not all shifts occur in the pattern of approaching a tipping point, then essentially falling off of it.
• “Conceptual. CSD detection depends to a great extent on whether the regime shift in question is a critical transition and whether this transition is gradually approached. The ability to unequivocally identify an approaching regime shift is conditional on the underlying mechanism that drives the shift. If such conditions are not met, misunderstandings and misuses of CSD indicators may arise.”
  • Essentially if you misuse the metric, you can get led down the wrong path. Try not to use it when ti doesn’t apply, though of course knowing when it does apply can be difficult.
• “Operational. Operationalizing CSD identification crucially depends on the temporal and spatial scales of the ecosystem in question and our ability to monitor key variables. Highly variable environments, or insufficient monitoring protocols, reduce the ability for monitoring the right variables at the right scale.”
  • If you hardly ever look at the underlying system, its no surprise you might miss whats going on. If you look at too small a time scale, things might look fine. If you look on perhaps too large of a timescale, things again will look different. This looking across scales and perspectives lines up with what we know about resilient systems
• “Methodological. Just like any other quantitative analysis, the sensitivity and significance of CSD indicators largely depend on the quality and quantity of the data as well as the underlying assumptions of the various statistical tools employed.”
  • If you don’t have the data, it’s pretty hard to do math on it.

What’s next?

Well if you want to try it for yourself or see more of the math, then I suggest you check out the paper, but here’s a preview:

Ecological resilience (ecR) depends on the distance to the border of the unstable manifold in state space (ds) and on the distance to the critical threshold (dp) in parameter space [ecR 1⁄4 f (ds,dp)] (a). We can approximate ds as the distance to the border of the attraction basin and dp as the height h of the attraction basin to the alternative state (b,c). Recovery rate (recR) (or engin- eering resilience) depends on the slope of the basin of attraction, which is defined by ds and dp [recR 1⁄4 dp/ds]. This slope can be approximated by the eigenvalue jlj which determines the stability of the current equilibrium of the system [recR;jlj]. CSD occurs as the system approaches the threshold, dp becomes smaller, recovery rate decreases and ecological resilience declines. Although ecological resilience is not approximated completely by jlj, CSD indicates the progressive shrinking of the basin of attraction of the current state. Moreover, the dynamics of the monitored ecosystem differ radically far from and close to the threshold; both variance and autocorrelation increase (d,e).

If you’re less inclined to look at the math, then simply understanding that these measures are being developed, what the limitations and potential problems are are enough. These are good things to know so that when you go to asses your own organization and systems you have a sense of what you’ll be getting into.

Takeaways

• Looking at complex systems, like ecosystems, measures are being developed to try and detect tipping points before system failure.
• These measures don’t work in all cases and are still under development, but provide a window into ways we might measure resilience and what some pitfalls might be.
• Rather than measuring an ecosystem once, it’s better to measure over time.
• The measure may be more effective as a way of comparing systems as opposed to an exact measure for one system.