So to what do you attribute the growth in the black population of Illinois between 1820 and 1860? At a time when the free black population of southern states like Louisiana, Mississippi, and Arkansas was declining?
Births to blacks already there plus the successful movement of blacks there in violation of the state's laws. In a similar pattern, it is currently illegal for people to immigrate into the United States without going through customs. Even so, the illegal mexican population here grows by several million every decade.
At a time when the free black population of southern states like Louisiana, Mississippi, and Arkansas was declining?
A quick comparison from 1850 to 1860 indicates the states of Maryland (where almost half of the black population was free), Virginia, Tennessee, South Carolina, North Carolina, Missouri, Kentucky, and Delaware ALL had net gains in the number of free blacks over the decade. Florida remained the same. You are also incorrect about Louisiana, which went from 17,462 to 18,647.