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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.
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.
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.
Nobody doubts the Earth will survive. Humans might not, but the planet will be fine.
sub f{($f)=@_;print"$f(q{$f});";}f(q{sub f{($f)=@_;print"$f(q{$f});";}f});
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.
Real ecosystems are constantly adjusting. It sounds as if the model is not sophisticated enough to deal with dynamic systems.
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.
So it's tough to boil down a huge parallelized system with radically different compute nodes to a single Human-readable equation? Well, can't say that's shocking.
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 multi-acre closed environment like Biosphere 2 it still took decades to get a self-stable model working with more limited nodes (species, interactions, resources, etc.) Next someone will post an article acting shocked that they can't model the whole universe on an Arduino...
Rather what we think "the math" is, is wrong. Nature is right. Always
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.
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)
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.
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)
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, then it's meaningless to take aggregate time as though it meant anything.
The model isn't the problem, it's aggregating time that's the problem.
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)
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.
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)
Beware of confusing dynamic equilibria with static equilibria. Both are stable, but in different ways.
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)
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?
I won't even read the summary
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.
>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?
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.
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/...
After that, animals came to the rescue and began consuming more oxygen, the percentage ticked down to today's 21%.
Why use human's ugly greed/selfishness to describe evolution. Nature just plays; celebrates as one whole. I believe the human hemoglobin molecule structure is present likely even in a mosquito or any oxygen breathing living thing. The point is Nature like a mathematician explores the universe/nature/it-self. It doesn't think of species1 is exploiting species2.. in fact even a grass may be happier if it ends up in the stomach of a goat. The phrases like 'survival of the fittest' etc comes from a sick mind (mine bigger than yours mindset). Think of one global Oneness, expanding playing with itself. Even after E=mc^2 and how all are connected what is the this talk of xyz riding over abc bs.
The Gaia Theory/Principle/Hypothesis - see href="https://en.wikipedia.org/wiki/Gaia_hypothesis">here, suggests one possible answer for the observed data.
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, with edge cases. For example, the introduction of the Lion Fish to the Caribbean - an area where it has no natural predators - has resulted in a largely un-checked population explosion; the same is true of Crown-of-Thorns starfish. So it is possible that Gaia breaks down either where one species is introduced to an otherwise relatively stable ecosystem, or where an apex predator is introduced that has or develops the ability to consume multiple different species for food.
This is somewhat different from the idea of mutualism, but I'd still be interested in seeing an attempt to apply Gaia theory to the observed data.
Implementation errors are not specification errors.
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)
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.
This just in from the Devil's Dictionary:
Ecology — the formal study of insufficient models and their mutinous deficits.
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.
Right now they are, but look at the rate of change.
Unless you are modelling every single animal on the planet,
Even the butterflies? What effect does a butterfly have, I wonder?
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 ...
Apply reading comprehension. Thank you.
That moment when someone thinks they're smarter than you, because they weren't smart enough to understand what you wrote.
Ok.
Yeah that must be it.
What are you trying to say. You don't seem to be using any words and what you are saying seems to be completely the opposite of how history happened.
-- ssoorrrryy,, dduupplleexx sswwiittcchh oonn.. -Quote found on actual fortune cookie.