With the fruit in short supply, official figures showed that local avocado prices smashed records in May. The average cost was five New Zealand dollars, or $3.30, per avocado, a 37 percent increase over last year.

The country cannot look overseas: Because of its strict biosecurity laws, New Zealand does not import avocados. But enterprising, law-abiding New Zealanders are looking to solve the shortfall themselves, and there are now waiting lists for avocado trees at garden centers.

Those who invest in a tree might also want to consider how best to guard it.

Bret Glazer, who lives in the Auckland suburb of Sandringham, recently spent more than $500 on a security system for his avocado tree after multiple thefts. The 30-foot tree produces 500 avocados a season, most of which Mr. Glazer gives away to neighbors, colleagues and friends. Last year, his tree was “professionally harvested” of several hundred fruit in one night, he said.

In April, Mr. Glazer’s partner caught two thieves red-handed — “older men,” he said — as they tried to strip the tree, wielding a long stick with a hook on the end for reaching the upper branches. When confronted, he said, they fled, one of them on a mobility scooter.

Last month, a grower in the upper New Zealand region of Northland said 70 percent of his avocados had been stolen, a loss worth $66,000. The grower, Graham Burgess, told The New Zealand Herald that the theft was “pointless” because the fruit was months from being ready to harvest and would go to waste.

Mr. Macmillan, the police officer, said he knew of “half a dozen” cases that resulted in charges. But he said gathering evidence could prove difficult, since some crops were only checked every few weeks and growers might not know when a theft had occurred.

“So already the investigation cycle has been slow to begin, and the baddies get three or four weeks’ head start,” he said. “The evidence would be well and truly devoured by then.”