"We just don't see people walking up, looking for jobs like they used to," he says. Now he has to pay a labor contractor to find enough people to tend his 2,200 furrowed acres under the harsh Sonoran sun near Yuma, in the southwestern corner of Arizona.
The dwindling supply of labor available to Mr. Dunn illustrates a significant shift in migration from Mexico, which has caused illegal immigration to drop to its lowest levels.
Even as states loudly debate new immigration restrictions – including Arizona's proposed armed, all-volunteer state militia to keep Mexicans from sneaking across the US-Mexican border – research suggests the illegal immigration has slowed.
The migration explosion that since the 1970s had pushed millions of men, women, and children into the United States has fizzled, says Douglas Massey, a sociologist at Princeton University and codirector of the long-term, binational Mexican Migration Project. "We're at a turning point, and what unfolds in the future remains to be seen. But I think the boom is over."
Mr. Massey's research shows that after the US recession hit, the illegal population fell from about 12 million to 11 million, where it has hovered since 2009. (About 60 percent of the illegal population is Mexican.)
Similarly, Homeland Security estimates released in March suggest that while the number of unauthorized immigrants living in the US grew 36 percent between 2000 and 2011, from 8.5 million to 11.5 million, that growth plateaued in 2010 and 2011.
"With no change in either direction, we're roughly at a net zero," says Massey, and adds that it's something unseen since the late 1950s.
The 2004 movie "A Day Without a Mexican," in which the state of California grinds to a halt when Mexican laborers suddenly disappear, satirized a thesis that is now a subject of real-life debate among experts.
What if the workers that farmers, hotels, and restaurants have relied on for decades don't come back? Will crops rot, beds stay unmade, and dirty dishes pile high in restaurants? Those sectors can't outsource labor; so will they slow, downsize, and will that create ripple effects across the already straitened US economy?
Experts agree that illegal immigration has declined sharply in recent years and cite the overall lack of work as the main reason many Mexicans choose to stay home.
But the big debate is how permanent the trend is. Most experts expect the flow to return once the US economy rebounds. But some say there are other factors at play that could keep Mexicans home, including more access to legal US work visas, border enforcement efforts on the US side and drug-war insecurity on the Mexican side, demographic shifts in Mexico, and growing economic incentives there.
The shrinking labor pool already is having an impact in agricultural fields scattered throughout the US, some say. For example, a University of Georgia report projects that, when 2011 figures are tallied, the state economy will show a $391 million loss due to farm labor shortages. Georgia is one of several states that – following Arizona's footsteps – recently passed laws aimed at illegal immigration. Farmers across the country are experiencing near-term crop losses and scaling back operations, confirms Libby Whitley, president of Mid-Atlantic Solutions in Lovingston, Va. Her company handles visa applications for 600 employers who use temporary legal workers, mostly from Mexico.
In the more than a dozen states that require businesses to confirm employment eligibility through the Internet-based federal program E-Verify, employers are in a corner. "The em-ployers just really don't have an option," Ms. Whitley says. She adds that the farm labor workforce is 75 percent illegal.
Whitley has noticed growing interest in the H-2A visa program that brings in temporary seasonal farmworkers. But many employers still shun these visas, saying the program – which requires housing provisions and set wages – is too bureaucratic and costly. Advocacy groups long have maintained the program is fraught with employer abuse.
Massey says spot shortages are possible in sectors that employ large numbers of Mexican workers, particularly agriculture, but he believes that a gradual shift toward the use of guest workers may offset any potential labor deficiencies.
Mexicans in growing numbers are securing visas that allow them to hold temporary US jobs legally, says Massey. "The workers that are coming into the United States are not just agricultural workers, they're workers in the non-agricultural sector, and increasingly, they're skilled workers."
The US State Department reports a 53 percent increase in temporary visas for seasonal farm work issued between 2006 and 2010. And other visa categories are driving the expansion, too, including those for professional health and technology workers under the North American Free Trade Agreement.
But even with the visas, the farm labor situation suffers, says David Dyssegaard Kallick, a senior fellow at the Fiscal Policy Institute, a nonpartisan think tank in New York. "Those jobs really do seem to go begging when immigrants are pushed out, at least temporarily."
In the long run, Mr. Kallick says, the US labor market probably would adapt: "Maybe wages and working conditions would go up enough to make the jobs more attractive, or maybe some farms would close up shop. Basically, though, I don't think dishes wouldn't be washed in restaurants without immigrants to do it."
He says the flow of immigrants will return when the demand for workers is back, although "we're not anywhere near there" yet.
"As long as the large wage differences between Mexico and the US exist, there will be incentives for people to endure the real risks of crossing illegally," says Judith Gans, manager of an immigration policy program at the University of Arizona in Tucson. She says that as jobs do become available, the pressure on the border will correspondingly increase.
In the long term, the changes in Mexico and shifts in migration in all of Latin America may ease the pull north of the border, Ms. Gans adds.
The impact of fewer illegal immigrants coming into the US will depend on how long it takes for the economy to bounce back, says Audrey Singer, a senior fellow at the Brookings Institution, a Washington public policy group.
"In the intervening time, a lot can happen in a place like Mexico, where unemployment is relatively low right now," she says. "Birthrates have dropped and the demand for workers has been rising. For young people entering the workforce, it may mean more opportunities and less reason to leave."
• Sara Miller Llana contributed to this article from Mexico City.