Practitioners of a scientific discipline know that the first mistake outsiders often make is a failure to familiarize ones self with the often quite large body of peer reviewed published research in that field. The economists who authored the original article have fallen into that common blunder here.
When two disciplines come into conflict it is often a good idea to pay heed to the discipline whose field of expertise and history of research best covers the bone of contention. The central conflict here is over two variables - genetic diversity, and population density at various times in history and prehistory. Anthropologists have a long established, peer reviewed record of research into genetic diversity and human migration; economists do not. Anthropologists (specifically, archaeologists) have a long established, peer reviewed record of research on population estimation throughout history and prehistory across the globe; economists do not.
As a result, the economists who wrote the original paper got both their genetic diversity AND population density estimates wrong, so their work is essentially worthless. The rebuttal by the anthropologists goes ino great detail on these errors often resulting from long outdated sources or complete lack of awareness of published literature in the relevant areas of research.
N.B. dupe since I unintentionally wasn't logged in originally