What happens when a population cannot be maintained? Collapse. Whether by resource starvation (the poorest and most vulnerable go first) or conflict (populations invest in warfare.)
For students of history/lit, it may be anecdotal to know that "Odysseus" doesn't mean adventurer who goes around trying to find his way home it means "child of anger." Why was our hero named so? "For there are so many people in the world, and it makes me so very angry" (the uncle of Odysseus upon his naming.)
So according to some accounts, the Trojan war and many other conflicts of those times (the "sea people"), were cataclysms instigated by excessive populations for those times in human societal (technological) evolution.
Too bad we can't anthromorphize evolution, else I'd say: maybe that was evolution's "idea" / "gamble" to begin with. Evolve the being that evolves everything "evolution" (nature) itself hasn't. Pyramids, skyscrapers, suburbs, machinery, poetry, computation, computation devices.. entirely abstract pure-thought-stuff machines aka programs.. abstract machines that "evolve" new ones.. and whatever stems from that when we/they get there.
But.. evolution doesn't have ideas or plans. Right? Nevermind that we, a self-proclaimed product of evolution, do. Did we even invent (create / evolve) .. the idea of "ideas" and "plans" there? Who could tell, other than some big overseer of it all =)
What does "outpacing natural evolution" even mean once non-random-mutation-based change makers .. just naturally evolved via the natural evolutionary mechanisms? Everything they (we) do then is "natural evolution" by extension / implication. Genes and fitness "came up with" (or randomed up) us doing all that, even us wondering and worrying whether we're "outpacing natural evolution".
Curious food for thought!
Do you mean what happens if we grow faster than we can adapt to, or that our ability to exploit natural resources can support?
If so, then what happens is pretty clear: population collapse.
The bigger scare is when our technological output (toxic waste?) hurts our ability to evolve.
When you have different bacteria stems and limited resources, then they'll fight for it with weapons (their antibiotics). Bacteria stem that is fast enough to use up resources will survive, while the slow ones will go extinct.
If, now, you think of humanity as different bacteria stems, it will be the same. A few human stems have resources and access to it, other dont. That corresponds to economy (or to countries with economy) for resource production.
So, "if the grow rate exceeds natural evolution" - first, it needs to be analysed what that means. In Europe, Japan, actually everywhere in the rich western world, the birth rates of woman go down. In poor countries, the kids are mostly birthed as a security for later years or for getting the work done.
So, there's your answer. The rich world with resources will keep the resources closed and inaccessible as the bacteria also do. The poor world will produce even more kids that can't be fed solely by the poor countries resources and go extinct by used up resources, or they use their weapons to get resources of others, which of course will use their weapons.
We'll see a lot of migration until the times the borders close. After that time wars for resources will start and will become even worse as the resources decline.
You can't talk about rapid growth of knowledge, technology or economics, without taking into account, that the growth is happening unequal in pace and amount through different parts of the world. We still haven't realized that concurrency is the problem. And the economy as we know it today is even more a problem.
But, don't ask me please. I don't have an answer or solutions to that problems. At least, none acceptable ones.
Prepare, it'll start in a few decades, when the earth don't have nutrients anymore, the clear water is not clear and the droughts have made yields go down.
In what units are you going to compare those apples and… rackoons?..
We've outpaced genetics alone long ago, using our brains and dexterity to hunt, make fire, create clothing for most of the world's biomes, sail across the seas, etc. It's a sort of cultural evolution that continued where genetic selection slowed down. You can see lighter versions of that in animals, like chimp tribal cultures, raven sub groups (and language "dialects"), learned tool use passed down across generations in otters, etc.
But semantics aside, if our population grows faster than we can adapt, well, either we catch up (with better medicine, food, shelter, economics, agriculture, distribution, climate mitigations, etc.) or people start dying. Usually the poorer people in developing countries.
It's incredibly difficult to model human population collapse because there's so many more unknowns with us than other, more predictable species. If a supervolcano goes off and we suddenly face a global crop failure and massive food shortages, maybe the remaining countries will all try to work together to work out a new production and distribution system like we did with COVID. Or maybe the rich countries will start hogging all the resources, like we also did with COVID. If Putin nukes Europe tomorrow, that would change things, or if some high schooler gets fusion to net positive energy in her friend's garage, a lot of things would get easier. If ChatGPT goes Skynet on us next year, maybe we'll be all killed, or eaten, or saved. Who knows.
In the meantime, most countries don't have population control programs (the way China did a few decades ago) so people keep popping them out, especially in areas with either high poverty (needing child labor) or high infant mortality (gotta make a bunch in case a few die young). On the other hand birth rates are slowing down, or already negative, in many developed economies because a lot of people have trouble affording kids (in time or money), for example, or don't want to bring them into this world. I guess there's some hopelessly slim chance of a Star Trek style "fully automated luxury space communism" future, but more likely you'll have a few rich powerful people and everyone else working for pittances, with people dying left and right but enough getting made to replace them in the commodity labor market. We already have most of that system in place today.
And nature? An afterthought, until it isn't, at which point the survivors will adapt anew and we'll go through similar boom and bust cycles again and again... yay, the circle of life and all that.
Just look at the news. (Gaza, Ukraine, Syria, Libia, Yemen, a good part of Africa and so on) /s