The Modeled Economy
The same three levels as the other ecological panels, with one thing added: a finite pool of matter that every living thing has to draw from and eventually gives back.
Layer 1 of 2 · the accepted science
The classical picture
Ecologists describe a food chain in two ways that are easy to confuse. Energy flows through it: sunlight is captured by plants, and most of it is lost as heat at every step up, never to return. That is the view Raymond Lindeman founded in his 1942 paper "The trophic-dynamic aspect of ecology". Matter cycles through it: the nitrogen or phosphorus in a plant passes to a grazer, a predator, dead material, and back into the soil, where plants take it up again. This panel models the second view. There is one currency here, and it is conserved.
The standard way to write the second view is a compartment model: every place the nutrient can sit is a compartment, and every flow out of one compartment is a flow into another. With N for nutrient in the soil, P plants, H grazers, Z predators and D dead material:
Add the five lines and every term cancels: d(N + P + H + Z + D)/dt = 0. The total amount of nutrient, T, never changes.
Why these terms
- Uptake and eating are products, g N P, a P H, b H Z. This is the law of mass action: meetings happen in proportion to how much of each party there is.
- An efficiency, ε. Only a fraction of what is eaten becomes the eater. In a nutrient model the rest is not destroyed; it goes to dead material, which is why the books still balance.
- Losses, μ. Upkeep and death move nutrient out of living tissue and into dead material.
- Decomposition, δ D. Dead material returns to the soil, which is what closes the cycle.
What the equations predict
- Conservation constrains everything. Because T is fixed, the system can never leave the set of states with that total, and every balance point, including whether one exists at all, depends on T.
- More at the base supports more levels. Lauri Oksanen and colleagues' 1981 "exploitation ecosystems" argument is that the productivity available at the base of a food chain determines how many trophic levels it can hold. A top level appears only once enough flows up the chain to cover its losses.
- More is not always safer. Michael Rosenzweig's 1971 "paradox of enrichment" showed that in predator-prey models, enriching the prey's resource can turn a steady balance into swings large enough to drive populations toward extinction.
- Somewhere to hide stabilises. Georgy Gause's 1934 experiments with the protist Paramecium and its predator Didinium, and Carl Huffaker's 1958 experiments with predatory and prey mites, both found that predator and prey persist longer when the prey have places the predator cannot easily reach.
Where the classical equations stop
The equations assume a well-mixed world, smooth quantities and constant conditions. The panel below is a lattice with whole animals that move, reproduce by handing over part of their own body, and pay an upkeep that rises in winter. It keeps the conservation law exactly and drops the rest. One simplification to know about: in real soils, much of what an animal respires returns to inorganic form directly, while here all of it passes through dead material first. Where the panel and the equations agree, and where they do not, is measured in the wrapped layer at the bottom of this page.
STACK §5.2 · BPP §10.8.1). An authored design claim, not a measurement.
STACK §5.2). A closed loop rather than a ladder: the top of the stack returns to the bottom, and matter is conserved exactly around the whole circuit.
SOV §7.2), what this
panel supplies, not how it scored- exercised 1 · Recursion lock. The loop either closes or it does not. Matter has to make it all the way round, ground to plant to grazer to predator to dead and back to ground, and you can watch a run fail to close it and lose a level.
- exercised 2 · Internal recurcline persistence. The running three-level economy is the candidate attractor; the brushes that move matter without adding or removing any are bounded perturbations of it, and the sliders change the rules it runs under; twelve worlds held all three levels for 1500 steps, and raising winter severity to 0.90 removed the top level in six worlds out of six at the first deep winter. Caveat: The update runs synchronously at u=1, so part of the temporal order is supplied by the clock.
- out of scope 3 · Boundary retention. No boundary is modeled. Cell states are trophic roles, not a membrane, and the lattice wraps. The sanctuaries are terrain a predator cannot enter, which is a constraint on movement rather than a boundary a structure maintains.
- exercised 4 · Maintenance-bearing continuation. This is the one panel in the gallery where persistence is paid for. Every transaction splits a conserved quantity instead of creating one, upkeep is debited every step and respired back to the dead pool, offspring are transferred out of the parent, and the readout audits the total every step. Caveat: The economy is authored, not ontic. Satisfying a cost schedule that was written down here is not the same as producing one, and the declared items are listed in the panel's purpose.md.
No sovereignty verdict is claimed here or anywhere in this gallery. The Sovereign column is empty, and that emptiness is the honest reading: no panel here has been shown to produce its own order.
What you are looking at
A landscape seen from above, divided into patches. Each square is one patch of ground, not one organism. At any moment a patch is in one of four states:
- Green, plants. They draw matter out of the ground to grow.
- Gold, grazers. They eat plants.
- Red, predators. They eat grazers.
- Black, bare ground. Nothing living there, though there may be a great deal of matter in it.
- Blue outline, sanctuaries. Ground a predator cannot enter. Plants grow there and grazers live there unharried.
Underneath the four states, every patch also carries three invisible quantities: how much matter is in the soil there, how much is in dead material waiting to break down, and how much is in the body of whatever is living on it. Use the show control on the panel to look at each of those layers directly. They are where most of the world actually is.
The rules
There is a fixed quantity of matter, and it never leaves. It only moves:
- A plant is one unit of matter taken out of the ground. Bare ground next to a plant can grow a new plant, but only if there is enough matter in the soil right there.
- Eating splits what was eaten. When a grazer eats a plant, part of the plant becomes grazer and the rest falls to the ground as dead material. The same when a predator eats a grazer. Nothing is destroyed and nothing is created.
- Staying alive costs matter every step, and what is spent is breathed back out into the dead pool. An animal that cannot pay dies, and its whole body joins that pool.
- Offspring are paid for out of the parent. A grazer or predator hands over a fixed amount of its own body to make a new one. It is a transfer, not a gift from nowhere.
- Dead material rots back into the soil, a little each step, where plants can draw on it again. That is what closes the loop.
The fraction of a meal that becomes the eater is the transfer efficiency, and it starts at 30%. The other 70% is not wasted, it just goes back to the ground rather than up to the next level. That single number, applied twice, is the whole reason the levels come out the sizes they do.
The Modeled Economy
The audit line is the point. Total matter must not move unless you move it. The two brush tools that add or remove matter from outside are counted separately, so the audit still balances after you use them. If that line ever stops saying balances, the ledger has a hole in it and nothing else on this panel can be trusted.
Space is kept honest: the lattice runs on
Duncan(√5), whose
anisotropy 𝒜 is shown above (admissible ≤ 0.02).
What to notice first
Most of the world is in the ground. Switch show to matter in the ground. Roughly half of all the matter in the system is sitting in soil at any moment, and another large share is in dead material. Everything alive, all three levels together, is a minority of the total. This is true of real ecosystems and it is almost never what a diagram of a food chain suggests.
The levels come out roughly a factor of ten apart. After a few hundred steps you should see something near 4,700 plants, 500 grazers and 40 predators. Nothing in the model was set to produce those numbers. They are what a 30% transfer efficiency does when it is applied twice.
An ecological pyramid is the picture you get when you stack the levels of a food chain by how much of each there is. It narrows sharply going up, because most of what is eaten never becomes the eater.
The predators are always the fragile ones. Watch the red line on the whole-run view. It swings much harder than the others in relative terms and it comes closest to zero. When a level is lost here, it is almost always the top one.
Three things to try
Each of these was run before it was written down, and the numbers quoted are what came out.
1. Make the winters harder
Press harsh winter, or drag winter severity from 0.35 to 0.90. Then let it run past step 600.
What happens: the predators go extinct, and they do it on schedule. Across six runs from six different starting worlds, every single one lost the top level between step 610 and step 660, which is the first deep winter. At the default severity, five of the six lost nothing in 5,000 steps.
Why it matters: the top level has the thinnest margin, because it is living on what is left after two rounds of transfer loss. A stress that the plants and grazers absorb without much trouble is the one that removes the predators. The failure is not gradual and it is not random, it is timed to the hardest part of the year.
2. Make the predators better at their job
Press efficient predators, or raise predator transfer efficiency from 30% to 60%. Reset, and watch several runs.
What happens: the predators do worse. Doubling how much of each meal they keep took survival from five runs out of six down to two out of six.
Why it matters: this is the result most people do not expect, and it is worth sitting with. More efficient predators convert prey into more predators faster, the grazer population is driven down harder, and then there is nothing left to eat. Efficiency raises the peak and deepens the trough that follows it, and it is the trough that ends the run. Being better at extraction is not the same as being better at persisting.
3. Take away the sanctuaries
Press remove the sanctuaries. This one resets the world, because the sanctuaries are laid out when the world is built.
What happens: the top level gets noticeably more fragile. Over ten worlds run 2,500 steps, all ten kept every level at the shipped seven sanctuaries, and eight of ten kept every level with none. The lowest predator count the average world touches falls from about seven to about three. Push the slider the other way and it keeps going: twelve sanctuaries hold that floor near twelve, sixteen hold it near fifteen. This is the largest single stabiliser on the panel.
Why it matters: a place the predators cannot reach is the textbook stabiliser for exactly this kind of system, and here the textbook is right. What is worth knowing is which part of a sanctuary does it. A sanctuary in this rule set does four separate things: it bars predators, it grows plants forty percent faster, it lets a plant start on less ground, and the world is laid out denser inside one at reset. Switch each off on its own and only the first matters at all. With the bar removed and the other three left in place, the panel reads exactly as if the sanctuaries were not there.
And one distinction worth holding onto: the sanctuaries raise the level, but at the shipped seven they do not change how well it comes back. Remove seventy percent of the predator mass and the population returns to about three quarters of its unkicked value either way, with or without them. What changes is where that three quarters starts from, and how often an undisturbed world loses a level on its own. Altitude and restoring force are different things, and the first is easy to mistake for the second.
An earlier version of this section said the sanctuaries barely moved the outcome. That reading came from six worlds, which cannot separate a two-in-ten difference in failure rate from noise. Ten worlds separate it cleanly. The model did not change; the measurement was under-powered, and the claim is corrected here rather than quietly dropped.
4. Change the length of the year
Press the bad year length, watch for a few thousand steps, then press very short years. Or drag year length yourself.
What happens: not what the other sliders have taught you to expect. Every control above this one gets worse in one direction and better in the other. This one is worst in the middle. At the default 900 steps the top level holds comfortably. Shorten the year toward 450 and its floor drops by about a factor of ten, close to the point of losing the level altogether. Keep shortening, and it comes back: at 90 steps the floor is the highest anywhere on this panel, roughly triple the default.
Why it matters: a long year is tracked as it goes, and a very short one is over before starvation compounds, so the damage averages away. In between is the bad case, where winter lasts long enough to starve the top level and returns often enough to keep doing it. That reading is offered as a reading; what was measured is the shape.
And the part that took longest to learn: whether the depressed level actually dies depends on how big the world is. On a lattice four times this one the floor still drops by the same factor in the same band, but the level survives it. The depression is a property of the dynamics. The extinction is a property of a small board, and this board is small. So read the dip as real and the deaths as partly an artifact of the window you are looking through.
This slider did not exist until the year length was measured properly. It had been a constant since the panel was built, frozen at a value that happens to sit in a safe region, which is the easiest way to hide a parameter that matters. An earlier record of this panel described the safe range as an interval with a cliff below it. It is a band with safety on both sides, and four sample points could not tell those two shapes apart.
How this panel differs from the others in the gallery
Nothing is free here. In the Tri-Trophic Stack, a grazer beside a plant simply takes that cell, and a plant colonises bare ground out of nothing. Those panels are honest about it: each one says so on its own disclosure card. What they cannot show is what changes when the accounting is enforced, and that is the only thing this panel exists to show.
The counts and the mass disagree, and the disagreement is informative. The other panels count cells, so a predator that takes a cell has gained area without paying for it. Here a predator holds a quantity of matter that it had to acquire and has to keep paying to hold. Read the two readouts side by side: the pyramid by count and the pyramid by mass are not the same shape, and neither one is wrong.
It still is not a real ecology. There is one currency where a real system has many, the transfer efficiency is a single number where a real one varies by tissue and by season, and the grazers and predators have no strategy at all: when they cannot feed they move somewhere adjacent at random. Adding a preference would make them look cleverer and would quietly add one more piece of authored structure to declare. Undirected is the honest default.
Layer 2 of 2 · the framework's reading
The wrapped reading
For readers following the framework
Everything the substrate hands this panel is supposed to be declarable, and here the declared items are: the size of a plant, the transfer efficiencies, the upkeep rates, the cost of an offspring, the decomposition rate, the seasonal drive, and the sanctuary layout. That list is the point. A structure that persists against a declared economy is showing something different from one that persists because the accounting was never done, and the difference is checkable rather than asserted. What it is not is a sovereignty result: an economy you authored and then satisfied is still an economy you authored. The Modeled Economy page sets out that distinction and why the ledger is kept in one place.
The Shape of the Basin
Every number in this section and the next was measured against the shipped rule set, unchanged: twelve worlds per setting on this 90 by 90 board, defaults unless stated. The record is kept with the panel's other measurements.
What runs settle on is a yearly cycle, not a point. The seasons are forced from outside, so a settled run never comes to rest. It repeats a pattern each year. Averaged over settled years, plants peak near 6,200 early in the year and fall to about 2,900 late in it, grazers swing between about 440 and 980 in the opposite direction, and predators run from about 105 down to about 25. Year to year the pattern is loose rather than exact: across worlds and years, the yearly low in predators ranged anywhere from 1 to 36. The candidate attractor is that repeating yearly pattern of the three levels. Its basin is the set of starting states that lead there.
This basin is a matter of odds. The rules are probabilistic, and every count below is a rate over the runs tried, not a boundary drawn through the state space. Every rate is also for this board; as "Change the length of the year" records, on a board four times larger a depressed top level survives where it dies here. Even undisturbed at the defaults, one world in twelve lost its predators within 5,000 steps.
Total matter decides which basin you are in. Matter is conserved, so every run lives at one fixed total. The brushes divide cleanly on this. Clear a patch and seed plants move matter from one place to another without changing the total, so they are pushes inside this basin. Enrich the ground and strip the ground change the total, so they do not push the run; they move it to a different world with its own attractor and its own basin. That belongs to the Morph below.
Starting states barely matter, with one exception. With total matter held fixed:
| starting state | held all three levels for 3,000 steps |
|---|---|
| the panel's default start | 11 of 12 |
| plants cut to 2% of open ground | 12 of 12 |
| plants raised to 50% of open ground | 11 of 12 |
| predators cut to 0.1% of open ground | 10 of 12 |
| predators raised to 2% | 9 of 12 |
| predators raised to 5% | 2 of 12 |
Worlds that held settled to about the same levels whatever they started from. The exception is too many predators: at 5%, ten worlds in twelve lost their predators, nine of them within 180 steps, after the predators ate through the grazers before the run could settle.
Pushes, and how the season changes them. Settled worlds had a share of their predator mass removed the way the clear brush removes it, with the bodies left as dead material, once in mid-summer and separately in mid-winter. Each was followed for two years. Eleven worlds per row; the twelfth had already lost its predators before the push.
| predator mass removed | summer: some predators left / came back | winter: some predators left / came back |
|---|---|---|
| 50% | 11 / 11 | 10 / 9 |
| 70% | 11 / 11 | 10 / 10 |
| 90% | 11 / 10 | 8 / 7 |
| 99% | 7 / 4 | 1 / 0 |
"Some predators left" counts worlds where the removal did not take every last predator. Worlds that came back reached, in the second year after the push, predator numbers close to the year before it (on average between 0.85 and 1.2 times).
The season moves the edge. A settled world holds 41 to 160 predators at mid-summer and only 1 to 49 at mid-winter. The same share removed in winter leaves far fewer animals, and more often none: most of the winter failures above are removals that took the last predator outright. So this basin's edge is not a fixed line. It comes closest to the settled pattern every winter.
The edge written into the rules, and the edge that is measured. No rule creates a predator from nothing, so a predator count of zero is permanent. That edge is authored. What is measured is how close to it a run can be pushed and still come back: a summer world came back from losing 90% of its predator mass ten times in eleven, and from 99% four times in the seven where any predators were left. The status line's at-risk reading is the same edge seen from the other side: at six or fewer predators, 57% of states lost a level within 300 steps, against 5% above six (17,703 step-states). As "Take away the sanctuaries" puts it, altitude and restoring force are different things.
The Morph of the Basin
Every slider changes the rules. Moving a slider does not push the economy; it gives it a different law, and runs settle onto whatever attractor that law has. The four experiments above are this panel's Morph, each measured before it was written down: "Make the winters harder", "Make the predators better at their job", "Take away the sanctuaries" and "Change the length of the year".
Total matter as a dial. Starting the world with a different amount of matter in the ground, the same as enriching or stripping the whole board before the run begins:
| total matter | held all three levels for 3,600 steps | settled levels (plant / grazer / predator) | predators after settling |
|---|---|---|---|
| half | 0 of 12 (predators lost by step 437) | none | none |
| three quarters | 10 of 12 | 2,210 / 685 / 28 | lows of 2 to 5 |
| default | 11 of 12 | 4,499 / 683 / 57 | lows of 1 to 26, highs of 132 to 182 |
| one and a quarter | 11 of 12 | 5,332 / 801 / 71 | highs of 184 to 240 |
| one and a half | 11 of 12 | 5,611 / 922 / 77 | highs of 197 to 298 |
| double | 8 of 12 | 6,002 / 998 / 88 | highs of 208 to 314 |
Too little matter cannot support a top level at all. More matter raises every level, and it also makes the predators swing harder: at double the default, four worlds in twelve lost them. That is qualitatively like the paradox of enrichment in the classical layer, measured with twelve runs per setting, so it is a pattern worth noting rather than a demonstrated effect.
What the morph can and cannot say here. This is the one panel in the gallery where upkeep, birth and eating all move a represented, conserved quantity, so it is the one place a basin can be asked whether it holds when holding has a cost. Every one of those costs is still authored: the rates were written down here, and satisfying a written cost schedule is not the same as producing one. That is why condition 4 on the disclosure card is marked exercised with a caveat rather than met.