How Nature Defies Math in Keeping Ecosystems Stable (quantamagazine.org) 103
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.
Only The Stable Ones Are Still Around (Score:5, Insightful)
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...
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The point is that mechanistic analysis, in the form of 'modeling' can never delve far enough into the real world. Not some warmed over 'survival of the fittest' pabulum.
There are trillions of interactions within 'the ecosystem' to a degree that it simply can't be described or completely understood. To the degree that it's a little conceited to call it 'the ecosystem' as if we have enough grasp of it to even call it a system.
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That's actually my assumption to, but I'd be less sanguine about "can be modeled", as model implies that you have appropriately included all the important features, and this is an area where we don't really know what all is important. It could turn out that the survival of a visible ecosystem is dependent on the presence of a particular mix of microorganisms, and we don't even know most "species" of bacteria.
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The reality is that DNA that's crap at surviving doesn't stick around to
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I think the best guess is that they are not only incomplete and missing a lot of data, but some of the assumptions that they do make are probably wrong. Figuring out which ones, though, won't be easy.
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Yes, the scientists here appear to have forgotten evolution, in several ways. Both, as you say, how all the failures are quickly forgotten and taken over by the successes, but also that the lifeforms that compete do not stand still; they evolve continuously, adapting to the unstable ecosystems.
Mathematical models without generations, where the offspring is always different from its parents, are not going to reflect what happens in nature.
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Ecosystems are large things, and don't arise quickly (though they can move location quickly on an evolutionary time scale.)
Because of this an eco-system collapse can be dramatic. It can also be sudden, taking only days, though that's a rather extreme case.
Part of the problem here is that eco-systems are invisible. All we can see are their component parts, and not all of them. So we often don't notice when they are tottering on the edge of collapse, but let me give you an example of one.
Aphids are mutuali
Re: Of course (Score:2, Interesting)
Chaos is merely order beyond comprehension.
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Comprehension is merely the delusion that complete understanding could ever occur.
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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 car
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No, when photosynthetic plants came into existence and started consuming CO2, their waste product was O2. As it accumulated in the environment it created a "market" for organisms that could inhale O2 and convert it back into CO2.
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>their waste product was O2
Great. Now note the ORDER:
>Basically a giant machine purpose built to generate and consume CO2.
Do you understand where you and original poster went wrong?
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Before oxygen consumers evolved, plant life led to steadily accumulating O2 in the atmosphere, a concentration eventually reaching 35% in the Carboniferous:
https://en.wikipedia.org/wiki/... [wikipedia.org]
After that, animals came to the rescue and began consuming more oxygen, the percentage ticked down to today's 21%.
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Apply reading comprehension. Thank you.
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If you want to go that way, you got the wrong gas. It's a giant machine built to generate and consume O2.
No, life thrived for about half a billion years before the oxygen catastrophe.
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It did. And then it was snuffed out by the extinction event that was caused by much more energetic lifeforms that outcompeted. If you don't win the competition for survival, you die.
That is the way of evolution. Always has been. Something that young city-dwelling folks need harsh reminder of, as life in many of the modern Western cities has allowed many to forget that the cycle keeps going, and doesn't care about their feelings. And it will keep going long after they are devoured by their own gut bacteria.
Re: Hint: Applies to global warming as well (Score:2)
And then it was snuffed out by the extinction event that was caused by much more energetic lifeforms that outcompeted.
It was? Weird. I could swear I've seen at least a few trees in my lifetime ...
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That moment when someone thinks they're smarter than you, because they weren't smart enough to understand what you wrote.
Ok.
Re: Hint: Applies to global warming as well (Score:2)
Yeah that must be it.
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Nobody doubts the Earth will survive. Humans might not, but the planet will be fine.
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Your intelligent robots are still just robots, ridiculously simplistic compared to even a single animal cell and not alive by measure. Entropy will kill them in non-geographic time. You are describing the path to a dead, desolate world, not the legacy of humanity.
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Right now they are, but look at the rate of change.
Re: Hint: Applies to global warming as well (Score:2)
On the contrary.
The models are stable and scaleable. And they show that the current destabilization through deforestation plus CO2 levels is going to lead to collapse.
So...incomplete models? (Score:5, Insightful)
Is there anything news worthy about the notion that our models might be incomplete?
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No, but considering the incredible amount of young people who seem to be genuinely indoctrinated to think that "scientific modelling" is the same thing as "truth", it may be a necessary reminder that modelling is one of the least accurate forms of scientific quest for better understanding of reality.
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I'm still not going to call you back after fucking you in that thread. No matter how much you bitch about it.
Re:So...incomplete models? (Score:5, Insightful)
"Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful." - George E. P. Box
Nothing newsworthy, but... (Score:3)
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.
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''Is there anything news worthy about the notion that our models might be incomplete?''
Yes, if it also provides the seed for an idea on how to make one particular model more complete and therefore more accurate.
Re: Stability is a fallacy (Score:2)
Beware of confusing dynamic equilibria with static equilibria. Both are stable, but in different ways.
Nature doesn't defy math...your model is deficient (Score:3)
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.
Re: Nature doesn't defy math...your model is defic (Score:2)
Natural models have worked fine and have been scaleable since 1968.
The model you described is discrete time. Nature doesn't use discrete time so much, although you can simulate it with a very short time base or by having each entity on an independent concurrent thread. Either way, you get a smoother time.
This is important. The equations of the models are non-differentiable at any point because there's no deterministic value between any two points. For that reason, there's no integral. If there's no integral
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Implementation errors are not specification errors.
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When reality defies equations: error between world and (momentarily) conical graphite core. There is no hubris in this world quite like reality leaving a cossetted wonk slack-jawed.
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This just in from the Devil's Dictionary:
Ecology — the formal study of insufficient models and their mutinous deficits.
We have to decide WHICH math to use (Score:3, Insightful)
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.
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I am not saying that climate change isn't a fact. The greenhouse effect of CO2 is quite straightforward physics. But I doubt that the complex climate models are much better than the simplest formulas. We know something will happen. And it is probably better not to find out what. In the long run the Earth will most likely fix itself, but in the short run it can go through a
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Earth will most likely fix itself, but in the short run it can go through all kind of unpleasant changes. Historically humanity develops best in the quiet phases of climate changes, we live in such a quiet time.
What does it mean for earth to fix itself? That the environment remained conducive to life and for ecosystems to remain sufficiently stable in the past is guaranteed by the anthropic principle. That is we could not have evolved to observe it unless the conditions in the past facilitated our evolution. The anthropic principle says nothing about the future however. In the long run (~billion years) the sun will get hot enough to vapourise the oceans. Currently, temperature rise is unusually rapid. It wou
Re: We have to decide WHICH math to use (Score:2)
I think it could also take longer until things get back to what it was, if the temperature rise triggers other changes. But such slow changes shouldn't matter.
Well, there is a reason why the changes within a century are always discussed. These are the
Re: We have to decide WHICH math to use (Score:1)
How many people earth can feed in this time is the important question, which I think is hard to answer.
It can be broadly answered with "more". Increased CO2 is a good thing for the things we eat. So is more heat. Lack of water might become an issue but we can solve that with desalination and irrigation, so it's only really a problem for dirt poor places which can't manage to implement the needed technology. Which is the crux of the matter; global warming is primarily a problem for places which are already pretty shitty, and will get much shittier. We will either have to help them, or we will be facing w
Re: We have to decide WHICH math to use (Score:2)
We've had such maths since 1968. Works fine, when applied correctly. Edward Lorenz studied it extensively, as did James Lovelock. Their models all work fine and Lovelock's models increase in stability exponentially as you scale them up.
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I'm sure there is a mathematics that properly describes ecosystems.
Chaos theory?
Domestication as mutualism (Score:4, Insightful)
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.
Crap headlines (Score:5, Insightful)
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.
Constant change (Score:1)
Re: Failed model, not cheating (Score:2)
Maths is exactly what the universe speaks. Dig beneath matter and energy, and you'll find maths alone, the most fundamental form of the universe.
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Unless you are modelling every single animal on the planet,
Even the butterflies? What effect does a butterfly have, I wonder?
Color Me Shocked.. (Score:1)
Oh..you were defining "Human readable" as "ecologists and climate scientists can understand it"...oh...ahahahahaha.
Seriously though, this result would be obvious to anyone with distributed system design experience. We don't have the computational power on Earth (outside of the actual ecosystem) to model the whole system. Hell, even with a mult
Nature does not defy the math (Score:2)
Re: Nature does not defy the math (Score:2)
Our models are right. They work just fine when applied right, as shown by Daisyworld getting more stable as you increase species and decrease abstraction.
A.K. Dewdney's Bugs shows the same behaviour as well.
The problem is the way they're being applied. They're non-linear dynamic systems that are sensitive to initial conditions, non-differentiable and turbulent.
As you'll be aware from Gleik's book on Chaos, you have to be within certain parameters before this becomes a dynamic equilibrium. Outside of that, i
Quite the opposite (Score:3)
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.
Stability or stagnation? (Score:2)
What is 'stability' in this context? It seems like biologists/ecologists would define it differently from physicists and mathematicians. Maybe chemistry would be somewhere in the middle?
With a shit-eating title like this (Score:2)
I won't even read the summary
Nature knows no competition; humans do (Score:1)
Gaia Theory (Score:2)
I am very much aware that the Gaia Theory receives a very skeptical view from the broader scientific community. I am certainly not making any claim as to its veracity here, but there do seem to be interesting parallels between the Gaia theory and the observed results.
It's important to note, however, that Gaia breaks down, potentially significantly,
Mutualisms (Score:2)
Doesn't this describe the relation between humans and its favored species (chickens, pigs, cows, etc.)? Those species thrive in vast numbers, as do the humans that feed on them, at the cost of everything else. The simulations seem to be spot on in that sense.