“If high status Muslim men have dozens of children, and monopolize the most desirable women, and similar American non-Muslim men have one or no children, and you continue this for centuries, you get the transformation of the Eastern Roman Empire into the Caliphate.”
Yes, that’s assuming no other conditions.
I know birthrate has a big impact.
But polygamy does not work, mathematically. There are not enough wives for the men within a generation. The boys get essentially thrown out.
Also, practicing Muslims marry their cousins a lot and that creates many problems.
Also, the use of houris and lots of homo sex makes STDs rampant, which of course result in death and sterility.
Also, the jihad mentality means a lot of men get lost in war.
So there are other factors than just the high status Muslim.
‘There are not enough wives for the men within a generation. The boys get essentially thrown out. . . . . the jihad mentality means a lot of men get lost in war.’
So one of the problems leads to its own solution, with the side benefit of large armies, whose soldiers can die without leaving orphans. This process worked pretty well to transform the people of North Africa, Asia Minor, the Middle East, Central and much of South and Southeast Asia, Malaysia and Indonesia (most populous of all Muslim countries) from non-Muslim to Muslim, in only 1000 years.