Species are to ecosystems as cells are to the human body, according to a mathematical model
This is interesting. Sounds like a mathematical evidence for the "Gaia theory" - not the more philosophical approach about Gaia/Earth being sentient or conscious, but about it being basically a living being or organism as a whole. As Earth as a whole is a system of connected ecosystems forming a global ecosystem, if the species (and maybe on a more detailled level also individuals) form the cells, then rivers, oceans and air literally are the nutrient flows, forming the "blood vessels" and rocks give the whole system the physical shape and determine local functions (like a skeleton). Very cool.

And an interesting part was this:
Humans have managed to eliminate the threat of predators (and equivalents) - so we are in that trap somehow - sadly the model does not describe what the species in that predicament can do - create a new predator or something that simulates this? Our hope is, that human intelligence can replace the predator - let's hope this works out. Up to now it has not done so. Though stress (career stress, financial stress etc) seems to be sort of a good "predator equivalent" for western civilization. A lot of people actually die from it but most of all it is a main contributor to reduced population growth (choosing career over children, having not enough money to afford children, fearing for potential childrens economical future). Another large one surprisingly is selfishness and individualism (prefering to have enough time and money to go on many vacations over having children).

Really? I always thought we were most related to a cell-consuming virus. :/

Actually, a large factor in limiting population growth is women becoming educated. Women who go to university tend to have children far later than those who only have a high school education, or less - which makes sense, as they are having children later in life. Also, education tends to go hand in hand with having access to birth-control - most women, when they have that access, also limit the number of children they have, instead of just playing Russian roulette every time they have sex with a man. Big reason why having six children is no longer considered normal.

Although, I'm confused - given we are all facing overpopulation, why on earth would you call not having children 'selfish'?

I never liked that analogy. My analogy is that that humans are indeed part of the larger organism, but that we have developed a mutation. Naom Chomsky recently wrote about it as "intelligence as a lethal mutation", I personally would rather say that the mutation is not genetically but memetically, that we have developed some memes that are a mutation, namely what Daniel Quinn calls "totalitarian agriculture" and other forms of belief that we are entitled to take whatever we can get at the expense of others and even exterminating others on purpose. Plus some other memes that are part of what we call civilization. These memes turn the cell that is human beings int he larger organism that is the Earth into a cancer because they literally cause this cell to multiply and take over other parts of the body.
I think there certainly would be other sets of memes that would allow humans to be a benign species, maybe even a benign tumor (which in that analogy would be a small civilization that does not take away so much of the larger organism to threaten it).

Indeed that is one factor, though I think it is more a correlation than the cause. What really helps is empowerment of women (even uneducated ones) relative to men plus birth control. In both cases, women will make decisions on children according to sane and sensible planning. The "having children later" argument is not so much of a gamechanger. It has an influence on generation times, which only then has a positive effect if a women has more than 2.1 children. If she has more children, then reducing generation times has a delaying effect on population growth, otherwise not. The main goal thus has to be to reduce children per women to 2 (or below). Paradoxically in a society with traditionally fast generation times, a reduction in children per women would have a much faster effect than in slower societies...

No, I meant it the other way around. Often a reason for women not to have children are selfish or stress related ones, like making more money, having a better career, spending more time on exotic vacations, being free of the duties of family life. The second class of reasons is not really selfish but focussed on the well being of the family (selfish in context of kinship), meaning one is worried about the kids future, economic stability, education opportunities,... And only fewer women in western industrial societies actually make a decision not to have children because of the overpopulation, carrying capacity of Earth or therelike.
I extrapolated this from surveys in Germany, so maybe in other countries the numbers may be shifted, but I doubt they are significantly different. Here is a related article that explains this in more detail for those interested, this is a bit off topic for this thread though: Fewer Germans consider children essential part of life - The Local

You are implying organisms have a purpose, or that they remain static over time, when neither is true.

Other than that, it's actually interesting, the claims of Earth being a nonsentient organism actually make more sense than the sentience claims, but just because something works in a similar manner doe not imply it is one. Certainly, it's a complicated system that arose over time and has specialised functions and, in effect, a form of homoeostasis occurs, but that doesn't mean it is an actual organism as such.
either way, I hope something useful comes of this, perhaps better modelling of effects

Well - i guess one would have to think about what an organism is.
A complicated system made of smaller parts that is organic and has grown organically and adapted to the circumstances it exists in certainly sounds like what one would call an organism.

The discussion in the other thread (about Eywa as a fungal organism) about Earth as a sentient organism is more a philosophical exploration than anything scientific. This one here is scientific - probably more to your liking, HNM