First, I think we're using the word "civilization" in different senses. You're talking about the global single human civilization where civilization means having running water and taking tea in the afternoon. I'm talking about multiple civilization which are, basically, long-lived cultural agglomerations (e.g. there is a Western civilization but China isn't part of it).
I would say that the whole global system is so intermingled and global right now that a complete collapse of civilization of the type I am talking about would likely have to include the entire world if it happened at all. 1500 years ago Roman civilization could fall without badly hurting Chinese civilization, but I don't think that's true anymore.
In any case, I find complete human extinction as the result of the civilization collapse to be highly unlikely. There are peoples who haven't changed much for thousands of years -- would they even notice?
In the kind of global demographic overexertion and resource exhaustion leading to a total collapse that we're talking about, a lot of traditional food sources would be exhausted before the collapse. In the face of impending global starvation, I would expect every major fishery in the world to be rapidly wiped out, I would expect the rainforests to be burned for more farmland, I would expect decent soil and easily available water to be completely exhausted, ect. I would expect that process would take away most of the resources that people need to survive, and that people living in a traditional hunter-gather existence or a traditional subsistence farming existence would probably had their land and resources taken from them before the end. If we're talking about billions of people facing potential starvation, I suspect that all thought of environmental preservation or sustainability would go right out the window, as well as concern for the well-being of aboriginal people.
There might be some pockets of people left living traditional lifestyles somewhere (that's actually what I was thinking about when I put the extinction possibility at 25%, instead of higher), but even they would also be affected by global environmental destruction. (And, of course, small pockets of humans surviving on their own can have issues from lack of genetic diversity and such.)
Moreover, let's even say 99% of the North American population will die. OK. But what would kill the remaining 1%?
What would they live on?
When the Roman Empire collapsed, the population of Europe dropped dramatically, perhaps by half according to some estimates, but people still remembered how to farm using old iron-age technology, people still had the knowledge of how to build houses out of wood and straw when better building materials stopped coming from distant parts of the Empire, ect. It was a catastrophe, but people still had enough knowledge of how to survive without the civilization to hang on.
How many people in North America today do you think have the knowledge of how to farm without any technology at all? How many have the knowledge to forge their own farming tools? A few do; but places known to have organic farms or traditional farming knowledge (the Amish, for example) would likely be swamped by millions of starving refugees. And besides that, once a stretch of land has been farmed using industrial farming techniques for several decades, it is very hard to change it back into something that can be farmed with old-fashioned techniques; the soil is basically completely exhausted of all it's natural nutrients by that point, and only can be farmed with advanced techniques.
Total human extinction might not be the result, but I wouldn't rule it out as a significant possibility.
And even if we didn't end up with total extinction, remember that an existential risk is anything that prevents mankind from achieving it's potential; you have to not just consider the risk of extinction, but then try to estimate the chances of us re-developing advanced technology after a collapse. That's harder to estimate, but I don't think it's 100%.
In an unrelated thread, one thing led to another and we got onto the subject of overpopulation and carrying capacity. I think this topic needs a post of its own.
TLDR mathy version:
let f(m,t) be the population that can be supported using the fraction of Earth's theoretical resource limit m we can exploit at technology level t
let t = k(x) be the technology level at year x
let p(x) be population at year x
What conditions must constant m and functions f(m,k(x)), k(x), and p(x) satisfy in order to insure that p(x) - f(m,t) > 0 for all x > today()? What empirical data are relevant to estimating the probability that these conditions are all satisfied?
Long version:
Here I would like to explore the evidence for and against the possibility that the following assertions are true:
Please note: I'm not proposing that the above assertions must be true, only that they have a high enough probability of being correct that they should be taken as seriously as, for example, grey goo:
Predictions about the dangers of nanotech made in the 1980's shown no signs of coming true. Yet, there is no known logical or physical reason why they can't come true, so we don't ignore it. We calibrate how much effort should be put into mitigating the risks of nanotechnology by asking what observations should make us update the likelihood we assign to a grey-goo scenario. We approach mitigation strategies from an engineering mindset rather than a political one.
Shouldn't we hold ourselves to the same standard when discussing population growth and overshoot? Substitute in some other existential risks you take seriously. Which of them have an expectation2 of occuring before a Malthusian Crunch? Which of them have an expectation of occuring after?
Footnotes:
1: By carrying capacity, I mean finite resources such as easily extractable ores, water, air, EM spectrum, and land area. Certain very slowly replenishing resources such as fossil fuels and biodiversity also behave like finite resources on a human timescale. I also include non-finite resources that expand or replenish at a finite rate such as useful plants and animals, potable water, arable land, and breathable air. Technology expands carrying capacity by allowing us to exploit all resource more efficiently (paperless offices, telecommuting, fuel efficiency), open up reserves that were previously not economically feasible to exploit (shale oil, methane clathrates, high-rise buildings, seasteading), and accelerate the renewal of non-finite resources (agriculture, land reclamation projects, toxic waste remediation, desalinization plants).
2: This is a hard question. I'm not asking which catastrophe is the mostly likely to happen ever while holding everything else constant (the possible ones will be tied for 1 and the impossible ones will be tied for 0). I'm asking you to mentally (or physically) draw a set of survival curves, one for each catastrophe, with the x-axis representing time and the y-axis representing fraction of Everett branches where that catastrophe has not yet occured. Now, which curves are the upper bound on the curve representing Malthusian Crunch, and which curves are the lower bound? This is how, in my opinioon (as an aging researcher and biostatistician for whatever that's worth) you think about hazard functions, including those for existential hazards. Keep in mind that some hazard functions change over time because they are conditioned on other events or because they are cyclic in nature. This means that the thing most likely to wipe us out in the next 50 years is not necessarily the same as the thing most likely to wipe us out in the 50 years after that. I don't have a formal answer for how to transform that into optimal allocation of resources between mitigation efforts but that would be the next step.