Final answer:
Increased births and decreased immigration are the two sets of changes most likely to cause a population to remain stable.
Step-by-step explanation:
Increased births and decreased immigration are the two sets of changes most likely to cause a population to remain stable. When there is an increase in births, the population size increases. On the other hand, when there is a decrease in immigration, fewer individuals are added to the population. This balance between population increase through births and population decrease through decreased immigration helps maintain a stable population size.