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Mr. Staples pointed out the bullet holes as proof of the escalating threat along the border. Webb County Sheriff’s Department spokeswoman Maru De La Paz, however, said there was no evidence tying the shooting to suspected drug traffickers.

Several growers and ranchers say their jobs started becoming more dangerous about two years ago.

An Arizona rancher was gunned down in 2009 while checking water lines on his property, in what authorities suspect was a killing carried out by a scout for drug smugglers. No arrests have been made. Apart from that incident, Arizona agricultural leaders say they’ve heard of no direct threats toward their farmers and ranchers.

In Texas, the run-ins with traffickers are largely anecdotal. Border Patrol spokesman Mark Qualia said any confrontations would be investigated by local law enforcement, but added that landowners “haven’t been expressing those feelings to us.”

Mr. Staples said farmers are scared to speak out. Two weeks ago, a 2½-hour meeting between Mr. Staples and about 20 farmers was closed to reporters over concern farmers wouldn’t otherwise attend.

“I told [farmers] we have to tell this story so our policymakers understand the critical nature of what’s being said,” he said. “It is a process that we have to continue to tell it until we get the help we need.”

• AP writers Sommer Ingram and Amanda Lee Myers contributed to this report.