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I only skimmed this paper, but as far as I can tell it never responded to one of the most central reasons for why a Malthusian model makes sense, which is selection effects and evolutionary pressure. The paper brings this up themselves, but then doesn’t seem to do anything with that:
Over the course of hundreds of generations, we should expect huge memetic and genetic selection towards higher fertility rates, so it seems pretty implausible to me you end up with a population permanently substantially below carrying capacity, unless you also posit the development of some enforcement mechanism that prevents people from having children.
I don’t really know why we should assign much validity to the alternative population models you outline, on the timescales that we are talking about (100,000+ years). The basic selection effect argument seems much stronger than the support for these other models on their long-run fit, so it seems pretty confused to me to consider them seriously.
Thanks – this is a very important point and I am glad that you raised it! Overall, I think we should be very uncertain about what the long-run population dynamics might be after a catastrophe. I am not sure how much we disagree, but I tried to add some thoughts below (Note: Maya might not necessarily agree with my thoughts on this issue).
As you point out, we write in the paper that Malthusian population dynamics may reemerge in the long run and that evolutionary pressures are one of the main reasons to expect that this might happen. We do not directly argue that such reemergence won’t happen, but in the footnote that follows immediately after that passage you quoted we write:
Here’s an attempt to quickly explain Arenberg et al.’s argument: Arenberg et al. point out that we “should not conflate higher fertility within a heterogeneous population with high or above-replacement fertility: it is an empirical question whether future higher-fertility sub-populations will have above replacement fertility”. They then argue that “there is strong historical and global evidence that even higher-fertility groups will eventually trend to near or below replacement fertility”. Drawing on these insights, they introduce a model indicating that “long-term population growth can be negative even with both strong heritability and an above-replacement-fertility sub-population”.
Now, it could reasonably be argued that evolutionary pressures will nonetheless determine fertility rates on 100,000+ year timeframes. However, even if this is correct, such timeframes are only relevant if there is at least a decent probability that humanity will still be around in 100,000 years (conditional on surviving this century). This is not obvious; for instance, if the background probability of human extinction is 1% in each century, then the probability that humanity is still around after 100,000 years is only 0.004%. It is therefore not clear to me that the Malthusian model is correct, so it seems sensible to take other models of fertility seriously.
Thanks again for engaging with the paper!