The number of alpaca farms has surged in the U.S., and Sen. Jeff Flake thinks he’s figured out the reason: incredibly generous federal tax breaks that literally pay Americans to raise the animals.

It’s become one of the odder dodges in a tax code littered with loopholes and workarounds.

Collecting chicken poop to turn into energy, allowing professional gamblers to write off massive losses, or “moving” to Puerto Rico to keep U.S. citizenship but avoid mainland U.S. income taxes are also on Mr. Flake’s list of areas where the federal government encourages bizarre behavior through its tax code.

“This is not an exhaustive list nor the worst loopholes, but rather anecdotes intended to show how the complexity of the tax code provides shelters for nearly any industry, interest, activity or individual,” Mr. Flake said in his latest report Wednesday.

Compiled from public reports and government documents, his analysis identified more than 200 tax breaks that short the government $1.23 trillion a year in money it could collect, but for the loopholes. The ones Mr. Flake highlighted average $5 billion a year.

The alpacas write-off applies to small business owners of all stripes, letting them speed up depreciation write-downs of business expenses, such as equipment. Alpacas were treated the same way — because they were expensive but low maintenance, and could live in relatively small areas, they made for wonderful tax breaks, Mr. Flake said.

One Vermont couple he documented paid $10,000 for an alpaca, and earned a $4,000 write-off. The Pennsylvania Alpaca Owners and Breeders Association says alpacas can help earn write-offs for barns, fences and other spending, too.

“Let Uncle Sam buy your alpacas for you!” exclaimed one alpaca selling operation Mr. Flake highlighted. Another owner said online that she bought $300,000 worth of alpacas, and said even though the sales from the fleece weren’t enough to break even, the depreciation of the cost left her with “a huge carry over loss, allowing my income to be below zero … and therefore no tax liability.”

She also said keeping the animals meant her property was deemed agricultural, saving her another $10,000 a year in property taxes. And since her income showed as zero, she qualified for massive assistance in sending her children to college.

The Alpaca Owners Association said Mr. Flake was besmirching hard-working small business owners with the report. The association said alpaca owners are only claiming the same tax benefits that other livestock owners claim, and said it was unfair to single the farmers out for scrutiny.

“Alpacas are a business venture that people have made a successful living from,” the association said. “When compared to other livestock, alpacas are a safe animal for children to work with as well — the entire family can get involved. It is a shame that during these difficult economic times, the senator cannot celebrate the fact that Americans are succeeding in a business that makes them happy.”

Mr. Flake said alpacas are attractive because their high initial cost makes them a good write-off, and their low maintenance costs make them easier to maintain than other agricultural write-offs.

The expensing provision was designed to be a short-term boost to the economy in Bush-era tax cuts, but has been extended repeatedly.

Gamblers, meanwhile, are benefitting from provisions that allow business losses to be written off. That includes travel expenses to reach a casino or racetrack, the cost of meals and entertainment, Mr. Flake said.

But the real scam comes in non-winning scratch-off lottery tickets, which the IRS says can count as proof of gambling losses. Professional gamblers have taken to buying non-winning tickets on eBay and Craigslist, using them to reduce their taxable income from their winnings.

Mr. Flake said gamblers claimed nearly $19 billion in deductions for gambling losses in 2015, costing the government as much as $2.8 billion in lost revenue.

“Our outdated tax code provides shelters for nearly any industry, interest, activity or individual,” Mr. Flake said. “Scrubbing the tax code for other unfair tax expenditures would undoubtedly identify many more loopholes costing hundreds of billions of dollars that could be closed with the savings more evenly distributed.”

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