I have read and reread Charles Galton Darwin (CGD)’s 1952 book The Next Million Years. This book may be in a thousand years in the future valued as a much more important than his grandfather Charles Robert Darwin (CRD)‘s book Origin of Species.
The reason I suspect that CGD’s book Million Years will be considered important is that it not only applies observations based on long-term past behavior of living things, as does CRD’s, but it also projects these ideas into the long-term future of humanity. In CGD’s analysis, it all boils down to food and the realization that no matter what the technical improvements in our food supply the population will soon adapt to equal the new food supply. In a period of several generations, a population will begin to librate about the carrying capacity of the earth’s food supply.
Starvation will probably not bring Homo sapiens to extinction, because there will usually be local populations with a few survivors who will reproduce and repopulate the planet. However, as the population nears an upper population limit, and before a general famine strikes the whole world, there will be starving margins of people. When that condition of severe shortage is local to an area there will be starvation and death of those marginal people.
At the present time, we have a system of worldwide distribution of food, and an abundance of food, but even so there are isolated groups that are on the edge of famine. When the worldwide distribution system is stressed there will be local famines, and when it becomes nonexistent there will be severe shortages and some localized starvation.
Species that lack predators, such as humans, have a tendency to boom and bust, but because humanity is widely spread across most of the Earth it is unlikely that a general supply disruption would occur everywhere and that would result in pockets of survivors.
One factor that is always there but swept under the hopeful idealist’s table is a massive war using atomic weapons. The Wikipedia article List of states with nuclear weapons states “the worldwide total inventory of nuclear weapons as of 2019 stood at 13,865” atomic weapons. That is only half as many as in the early 1960s but is probably still enough to kill almost everyone.
After the war, starvation and disease set in and only pockets of humans will survive.