This article from Ohio State suggests that more than a million Europeans were enslaved by Muslims from the Barbary Coast between 1530 and 1780. My question is whether the slaves were ever bred to produce new slaves or whether the slaves were not bred and the slave population would entirely be dependent on newly captured slaves.
I know that in America and other places, slaves were bred and that slavers actually supported the end to Atlantic slave trade so that they could get more money selling slaves that they had bred on their own plantations. Did something similar happen on the Barbary Coast? Are there any populations in that area which are descended from slaves that were captured centuries ago?
Part 1 - Numbers
When I read 'more than a million Europeans' I knew that Robert Davis would be here somewhere! Before I jump into the topic, I should note some terminology. You use the term slaves and I will use the term slaves, captives and prisoners interchangeably but we should be aware of some distinctions. The majority of male slaves captured from the mid-17th century by North African pirates were what we would consider to be prisoners of war, involved in armed conflict against North African states. Many of these prisoners were returned (following payment) to their host countries as European states could not afford to lose skilled sailors and gunners lightly. I will also talk about North African 'pirates' but often these were ships engaged in warfare of state sanctioned privateering as opposed to any sort of illegal activity.
Now about those one million slaves... Peter Earle (who studies both Maltese and North African pirates) rather pithily states that Davis' figures "sound a bit dodgy and I think he may be exaggerating". Nabil Matar has a rather more comprehensive breakdown of some of Davis' evidence that should demonstrate that we are looking at far lower numbers of people. Davis uses the eighteenth century consul Joseph Morgan as a source. He mentioned a:
List, printed in London in 1682 of 160 British ships captured by Algerians between 1677 and 1680. Considering what the numbers of sailors who were taken with each ship was likely to have been, these examples translate into a probable 7,000 to 9,000 able-bodied British men and women taken into slavery in those years.
As mentioned in that link you provided, Davis uses sources like these to come up with a figure of 8,500 captives taken between 1530 and 1780. Now let's unpick just this quote of Davis here. We actually have access to the original document from 1682 that Joseph Morgan refers to - this document mentions only 91 ships not 160. 50 of those ships had fewer than ten people on the ship. In total there were 918 peoples on those ships not '7,000 to 9,000'. To put it bluntly, Davis is exaggerating his numbers and using sources poorly to try and reach as large a figure as possible. North African pirates did do coastal raids but the majority of their captives were taken at sea. These ships which were raided had smaller crews because out of necessity it was easier for a ship from Algiers to take captives from a smaller vessel with ten sailors than from a larger vessel with 100.
There are other problems with the sources Davis uses to reach his number. A French consul in Algiers would have good reason to exaggerate the number of captives there are in Algiers so that he can gain greater resources to assist in their redemption. In cases of shipwreck off the North African coast would be included in potential lists of captives even though many would likely have drowned instead. You are right to ask the question about why there are not these communities in North Africa in the same way as there are across the Atlantic. One of the main reasons is because there were not one million slaves.