“It’s for both security and companionship,” he said as Julia nuzzled his leg, looking like a gentle enough companion. But when an intruder emerged near the tennis court of his estate, all it took was one command, “Packen!” (the bite command from the German word for “seize”), to send Julia racing across the lawn.

She sunk her teeth into the intruder’s arm, which was encased in padding for a demonstration, and hung on even as he lifted her off the ground in a vain attempt to shake free of her. She let go only upon being commanded and then stood guard over her new prisoner, barking and threatening to bite again whenever he made a move to escape, which he wisely did not try.

Julia’s was a controlled ferocity, which trainers distinguish from the anger manifested by ordinary dogs. When two dogs try to intimidate each other, they stiffen, growl, bare their teeth and stare intently. Protection dogs are trained to continue looking around and protecting their owners, not establish their own dominance.

And, when commanded, they are supposed to switch instantly from attack mode to pet mode.

“The dog has to get along with children,” Mr. Prather said. “The client is often a guy on his second family. He travels a lot, leaves his wife alone with the kids in a large house — maybe 30,000 square feet, so big you don’t even know what’s going on at the other side of the house. He wants peace of mind and a dog that his wife can handle. We don’t sell tank-stoppers.”

The price tag for a protection dog has risen because of increasing demand in the United States, Latin America (especially Mexico), the Middle East, Asia and other places, said Mr. Prather and Wayne Curry, the owner of Kraftwerk K9 in Rochester, Wash.

“I’ve turned down offers of more than $200,000 for one of my champion dogs,” said Mr. Curry, who added that he knew of a dog that had sold for more than $400,000 because of its bloodline and breeding potential. (Although Julia’s offspring most likely would have commanded top prices, Mr. Johnson said he had no time to breed her and instead had her spayed shortly after buying her in January.)