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How Nature Defies Math in Keeping Ecosystems Stable (quantamagazine.org)
Paradoxically, the abundance of tight interactions among living species usually leads to disasters in ecological models. New analyses hint at how nature seemingly defies the math. Veronique Greenwood, writing for Quantamagazine: Behind the beautiful facade of a rainforest, a savanna or a placid lake is a world teeming with contests and partnerships. Species are competing for space, consuming one another for resources, taking advantage of one another's talents, and brokering trades of nutrients. But there's something funny about this picture. When ecologists try to model ecosystems using math, they tend to find that the more interactions there are among species, the more unstable the system. For a simple ecosystem model to be stable, all the interactions among its species must be in perfect harmony. Maintaining that balancing act gets much harder, however, as the number of coupled species and the strengths of their interactions rise: Any disturbance or imbalance for one couple ripples outward and sows chaos throughout the network.
Bring in mutualisms, relationships in which species contribute directly to each other's survival, and things can really fly off the handle. Pairs of organisms that live off each other sometimes do so well in the mathematical simulations -- thriving exponentially in extreme cases, in what Robert May, the theoretical ecology pioneer, once called "an orgy of mutual benefaction" -- that everything else can go extinct. It seems unlikely that real ecosystems are quite this flimsy. In a new paper in Nature Communications, a pair of theoretical ecologists at the University of Illinois explored more precisely how the give-and-take in mutualism affects ecosystem stability and how, under the right conditions, it might contribute to it. Their result joins previous work in suggesting how real-world communities manage to be more resilient than the models imply.
Bring in mutualisms, relationships in which species contribute directly to each other's survival, and things can really fly off the handle. Pairs of organisms that live off each other sometimes do so well in the mathematical simulations -- thriving exponentially in extreme cases, in what Robert May, the theoretical ecology pioneer, once called "an orgy of mutual benefaction" -- that everything else can go extinct. It seems unlikely that real ecosystems are quite this flimsy. In a new paper in Nature Communications, a pair of theoretical ecologists at the University of Illinois explored more precisely how the give-and-take in mutualism affects ecosystem stability and how, under the right conditions, it might contribute to it. Their result joins previous work in suggesting how real-world communities manage to be more resilient than the models imply.
All of the unstable ecosystems have failed, and their participants extinct or changed. That's the crazy part of hundreds of millions or billions of years of adaptation and evolution and environmental change - there are probably trillions of ecosystems that became unstable and collapsed - they just happened long before scientists showed up to track things.
Which isn't to say that collapses can't happen again (or that ecosystems don't fail on a daily basis) but the ones still around have whatever "secret sauce" nature requires for those groups to survive and even thrive. So far...
Reading code is like reading the dictionary - you have to read half of it before you can go back and understand it.
Chaos is merely order beyond comprehension.
Is there anything news worthy about the notion that our models might be incomplete?
Mod me down with all of your hatred and your journey towards the dark side will be complete!
If you want to go that way, you got the wrong gas. It's a giant machine built to generate and consume O2. We can see this clearly in the oxidization of atmosphere when chlorophyll was introduced and spread among the early life forms on the planet, which enabled existence of essentially all other life (barring the few exceptions that exist in closed systems like subterranean volcanoes).
CO2 emissions by these life forms were utilization of the fact that atmosphere was now rich in O2. Your version puts the cart before the horse.
When I teach my students about the MVC paradigm I describe the model component this way:
The model is the simplified representation of reality that describes those things which are important to your application.
For example, a maintenance work scheduling application for a school probably needs to know how many display screens are in a classroom, and maybe their positions. Suppose that the decision was made that it does not need to know the make, model and version of the multimedia control panel at the instructor workstation.
Now, if somebody came along and tried to make maintenance purchasing decisions to replace the multimedia control panel based on just the number of display screens in the classroom, they might find the decisions to be faulty because of the lack of information. That does not mean that the lecture hall defied the model. It just means that when the model was developed, the important aspects of the reality being modeled were not considered properly and some were left out. In this example, somebody would need to walk to the classroom and look at the actual control panel to be replaced and gather information on that.
It could be that perhaps the researches described in the article need more detailed models to accurately describe the behaviors they are interested in for these systems.
Comprehension is merely the delusion that complete understanding could ever occur.
Math does not describe the universe we inhabit, but all possible universes. We have to search to find which mathematical system accurately describe what we see around us.
I'm sure there is a mathematics that properly describes ecosystems. When we one day find it, the practical implications will be enormous. It will explain why all those activist predictions of species collapse and environmental disaster in response to this or that specified kind of external pressure keep failing to happen. It could tell us more about where else in the universe life could exist. If it uncovers negative climate feedbacks we never know were occurring, it will finally lead to accurate climate models.
This immediately makes me think of humans and the species we have domesticated. It's not just humans who are thriving exponentially and driving thousands of other species to extinction. It's humans plus wheat, rice, cows, pigs, and a handful of other species. Millions of square miles of the most productive land in the world have been taken over by us and our mutualists. The group of us seem like the perfect example of what they've found in their simulations.
I hate headlines like this. Nature didn't defy anything. Nature pointed out that the model being used wasn't anything like up to the challenge.
This is, frankly, perfectly normal.
The only people who are surprised are the headline writers who apparently can't remember the last x thousand times that something was thought to be understood turned out not to be.
A thousand pounds of wood moving at 300 feet per minute. Don't get in the way.
Most ecologists I've read the work of have said that the more interactions, the more stable. This is because the models that work best - nonlinear dynamics that are sensitive to initial conditions - are only stable if you have large numbers of Strange Attractors.
Daisyworld is the best example. As you increase daisy species from two to 200, stability goes up exponentially. Provided, and this is important, three conditions are met.
First, each component must possess a negative feedback loop. It can possess positive feedback as well, but it must have negative feedback.
Second, for all species A, there must exist at least one species B with whom at least one form of resource consumption or other pressure is in a closed loop.
Third, you need large numbers. Simulations of a goldfish pond filled with five examples each of a hundred species won't be stable.
You can simulate twenty, two hundred or two thousand species on your computer and get absolutely stable (albeit chaotic) results, if you do it right - i.e.: the way you'd get in a naturally balanced forest, for example.
What the researchers have shown is that you can make this entire dynamic violently unstable by reducing scale, breaking cycles or doing other stupid things. That chaotic systems aren't self-restoring if they're messed up.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
Yes, there is nothing newsworthy about the notion and the scientific journals are full of incomplete models. There is nothing wrong with that as long as people realize that the models are incomplete. It becomes a problem when the newspapers start spouting off about how some incomplete model predicts something---and something needs to be done NOW about the predicted outcome.
This just in from the Devil's Dictionary:
Ecology — the formal study of insufficient models and their mutinous deficits.
Unless you are modelling every single animal on the planet,
Even the butterflies? What effect does a butterfly have, I wonder?