One of the cousins, Ibrahim Annus, 20, said, “Ask him to pick between his wife and his pigeons — he’ll pick the pigeons for sure.”

The men laughed out loud. Their relative, they were sure, would slip into Turkey at another spot.

Syria’s pigeon collectors, hamemati as they are known back home, are among the most ardent in the Arab world. They do not breed or race them. They will trade and sell them, but mostly they just keep them as treasured pets. So it comes as little surprise that some have gone to great lengths to pursue their hobby in exile, especially since no one expects Syria’s two-and-a-half-year civil war to end anytime soon.

A coop atop a trailer in a refugee camp; a flock of pigeons circling above a building in a neighborhood with Syrian newcomers. These are the telltale signs of the hamemati in Turkey, Lebanon and Jordan, the nations with the most Syrian refugees. Even if the collectors have not managed to resume their hobby yet, any Syrian will immediately identify the local hamemati, who often gather together and endlessly swap pigeon stories.

Like most Syrian refugees, the hamemati tend to oppose President Bashar al-Assad. But some express a more visceral opposition to the Syrian government, adding pigeons to the long list of losses they say they have suffered at the hands of Mr. Assad and his forces.

“They shoot both pigeons and people for fun,” said Yasseen Taha Atra, 29, a refugee in Wadi Khalid, in northern Lebanon. “I hate Bashar so much.”