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I read this and laughed “Reductions in child mortality rates can lead to parents having less children overall (as they know that the per-child odds of their children making it to adulthood have substantially increased).” Do you actually think people having numerous kids in third world countries are trying to have more kids they already can’t feed in case some of them strave to death?

Absolutely.

The percentage of children making it to adulthood is a very powerful driver of reduced population growth rates. There's good self-interested reasons why this is so.

See, parents in the poor countries depend on having a number of children make it to adulthood, in order for those children to then support their parents in their old age. The higher the percentage who die in the childhood years, the more children parents must have in order to ensure that some actually make it to adulthood.

If child mortality rates are 50%, a couple might have a dozen children in the hopes that at least some will survive. And, with a 50% child mortality rate, on average 6 of them will survive -- albeit only 3 in some families, while 9 in others, etc.

Now, if the child mortality rate in only 1%, a couple might only have 3 kids, safe in the knowledge that the odds are very high that all 3 will make it to adulthood.

That's the way it works. God read up on demographics -- reduced child mortality rates almost always precede reduced numbers of children per family, and therefore reduced population growth. (With individual exceptions to the rule, here and there; some families just want 18 kids).