How did slave populations change during the early to mid nineteenth century?

Assuming this question is referring to the United States, there were several ways the enslaved population changed throughout the first half of the nineteenth century. One was that it became almost totally indigenous. This was because almost no enslaved people were brought from Africa after 1808, when American participation in the international slave trade was banned. So very few people from Africa (or, for that matter, the West Indies) entered the country, and none did so legally.
Despite this fact, the population of enslaved people changed in another important way during this time: put simply, it grew dramatically in number. In 1800, just over 850,000 slaves lived in the United States. By 1860, this number had increased to around 3.9 million. The slave population of the United States also spread territorially. In 1800, most slaves lived in a small band from the Low Country of South Carolina to the Chesapeake in Virginia. By 1860, the population had spread into Texas and especially Alabama, Mississippi, and Georgia, a so-called "black belt" where cotton was cultivated. The invention of the cotton gin led to the rapid spread of slavery into these areas. So being sold away from one's plantation and family became a fact of life for many slaves in the South as a domestic slave trade flourished.
http://faculty.weber.edu/kmackay/statistics_on_slavery.htm

https://www.smithsonianmag.com/history/maps-reveal-slavery-expanded-across-united-states-180951452/