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“Going to Ecuador is the easiest way right now to get out of Cuba,” said Andy Gomez, a senior political fellow at the University of Miami’s Institute for Cuban and Cuban-American Studies.

“For the majority, Ecuador is a stopping point, but they have to come up with the money to get to their final destination, the United States.”

According to Ecuadorean official figures, 106,371 Cubans entered the country legally and 97,923 left legally between 2007 and February 2012. It is unclear what happened to the other 8,448.

In Ecuador, many Cubans work to save money to pay smugglers to take them to Mexico’s border with the United States, a route shared with many Central American migrants who have to cross territory controlled by drug traffickers and who often face extortion and kidnapping.

Few, though, cross the Darien, one of the world’s most rain-drenched regions. While several thousand indigenous people live along its trails and rivers, the jungle is so dense, the ground so swampy or mountainous, that the few attempts to cross it by car or motorcycle take weeks or months.

That terrain, and fears of environmental damage to its wild ecosystem, have continued to frustrate planners trying to link South and North America with the Pan-American Highway.

Panamanian authorities began noticing five years ago that the Darien Gap was being used by smugglers, usually to move people from Asia and Africa who had traveled by boat from Brazil, said Jose Mulino, Panama’s public safety minister.

That has tapered off. Panamanian immigration officials have detained just 97 non-Cuban migrants in the area since the start of the year.

“That traffic of Africans and Asians has considerably decreased, and the big problem we have now is the flow of Cubans who are coming through the jungle,” Mr. Mulino said.

Drug smugglers and rebels

The Cuban migrants are sharing dangerous paths used by drug traffickers and rebels of the leftist Revolutionary Armed Forces of Colombia, Mr. Mulino said, That has sometimes caused problems for local law enforcement.

Police recently had to call off a drug raid after spotting a group of Cubans near the border, Mr. Abrego said.

“We had to get them out of there and take them to Panama City,” he said. “We lost the raid’s effectiveness.”

Authorities have yet to determine if their guides work for either group, Mr. Mulino said.

“It’s not clear if the rebels, or the drug traffickers, or both, are the ones guiding the migrants,” he said. “Someone is helping them, and those people are the ones who walk that area.”

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