Most of the migrant families whose children are being separated from their parents at the southern U.S. border come from Honduras, Guatemala and El Salvador, Central American nations plagued by grinding poverty and some of the worst criminal violence in the world, experts say.

“They are coming for a mix of reasons, some because of fear of extreme violence and some looking for better economic opportunities,” says Andrew Selee, president of the Migration Policy Institute, a Washington-based think tank.

Analysts...