Is there any peer reviewed analysis that actually demonstrates that correlation? It strikes me as obviously untrue.
That depends if you take the libertarian stance that things like taxes and other government policy interventions are "force." If you do, then I don't know where in the world you expect to live, because I don't know of any functional societies that don't have a government which exerts some regulatory control over their economy.
If you don't, I think things like a more progressive tax system, making the minimum wage a living wage, and investing more in public education would help.
I thought it was common knowledge concerning poverty versus population. One could logically theorize it but here are some articles as you wanted.
Population and poverty
Population growth and poverty in the developing world. - PubMed - NCBI
I come from a used-to-be third world nation that had to control it's cultural behavior on population to better control it's economic growth. A generation ago, it was common for families to have up to 10 children because the children was viewed as a workforce for the families to survive. The government aggressively marketed and enforced rules to favor less children in the hopes to better it's economy. It succeeded due to this and other factors. I'm Vietnamese...
Two-child policy - Wikipedia
I'm not so much a libertarian as I agree there should be oversight and regulations against businesses. Possibly I should rephrase the the ideology of force as more of violent force which some socialists tend to agree with more. Again, being able to have possession is a right. The question is how much that can be very subjective. Purex tends to argue that people have no right to be rich or successful. It can be seen as unfair at face value that one person owns more resources than another but if we lose the ability to own, then why would we choose to be productive to gain resources only for it to be lost.
I came to America as a very poor refugee. Actually, my family escaped a communistic regime by boat. We came here with literally nothing, and yet, we were able to pull out of poverty and become successful. We actually flourished more than our native counterparts, especially more so in the 80s and 90s. Without certain rights, we would not have been able to achieve our success. Many here theorize certain governments between socialism and capitalism. I and my family actually lived it with enough real-world results to know better.