Mr. Gaffner pays close attention to South American conditions because of the new reality facing U.S. farmers: America’s agricultural dominance has eroded.

Brazil overtook the U.S. as the world’s biggest soybean exporter in 2012-13, according to the U.S. Department of Agriculture. It’s projected to be the second-largest corn exporter, on the heels of the U.S., this season. As of the last crop year, Russia now beats America in shipments of wheat.

It’s a reversal for a country that has long identified as the world’s bread basket. America’s share of global corn, soybean and wheat exports has shrunk by more than half since the mid-1970s, the USDA says. In soybeans, the most exported U.S. crop, U.S. supplies make up about 40% of world exports, down from more than 70% three decades ago.

Other countries’ rising share of global trade and their bin-busting harvests have helped fuel a multiyear downturn in crop prices that is pushing some U.S. farmers out of business.

“We’re going to have to learn the table manners of sitting at a bigger table,” says Mr. Gaffner, whose soybeans often make their way down the Mississippi to be shipped overseas from New Orleans ports. For U.S. farmers, he says, “that’s hard for our psyche.”

American farmers’ fates are inextricably tied to the broader economy. Farmers produce three-quarters of the nation’s food. U.S. agricultural exports in 2015, the latest year for which data is available, generated more than $300 billion in economic output and directly supported more than one million jobs, according to the USDA.

Agriculture is among the few U.S. industries that exports more goods than it imports, helping to narrow the nation’s overall trade deficit, which last year hit its largest point since 2012, the Commerce Department says.

U.S. taxpayers are tied to farming through the billions spent each year by the government to help insure farmers against crop shortfalls or lost income. For the 12 years ending in 2027, the USDA is expected to spend nearly $87 billion to help protect farmers, according to estimates from the Congressional Budget Office.

Rural communities likely will bear the brunt of the continued pressure on farmers, as job losses and lower farmland values cut the tax base for schools and other public services.

Anxiety over the U.S. role in agricultural trade has grown in recent months amid moves by President Donald Trump to withdraw the U.S. from the Trans-Pacific Partnership, which was backed by many farm groups, and potential changes to the North American Free Trade Agreement, which they say helped develop exports to Canada and Mexico.

Russia over the past decade boosted its wheat harvests by 61%, the USDA forecasts. Corn acreage has nearly tripled in Russia, and more than doubled in Ukraine. Brazil and Argentina have also ramped up output of the grain.

Foreign farm powers in South America and Eastern Europe owe some of their grain-market victories to favorable exchange rates—a strong dollar, the currency used for global trade, means foreign grain priced in local currencies can reap bigger profits.

Other countries have structured trade policy to benefit their farm sectors and have invested in infrastructure such as barge terminals and railroad networks to cut transport costs.

In the U.S., about one-third of the corn crop is used for fuel production, and conservation programs have removed land from farming.

The shift has benefited global food security. Having multiple, strong exporters of grain around the world can help prevent supply disruptions due to weather or trade, farm economists say.

Also part of the silver lining: booming international revenue for U.S. companies such as Monsanto Co., Deere & Co. and Mosaic Co., who sell genetically engineered seeds, satellite-guided tractors and fertilizer to farms outside America. In some cases, U.S. companies design products and seeds specifically for foreign markets.

Bruno Gilioli, who grows soybeans near the heart of Brazil’s vast grain belt, is running out of room to store his huge crops. A concrete shelter the size of a football field holds less than half of this year’s harvest; the rest has been squeezed into nearby storage bins or trucked to a far-off grain elevator.

“The past five years have been very good for us,” he says.

Using high-tech machinery and the advanced seeds and chemicals common on U.S. farms, Mr. Gilioli, 37, has pulled record yields from his 5,000 acres in Brazil’s Goiás state.

“Inside the farm, it looks just like the U.S.,” says Mr. Gilioli, who wears an Iowa State Cyclones hat, Levi’s T-shirt and Wrangler bluejeans. Mr. Gilioli lived on a farm in Iowa for a year as an exchange student and has made four visits to tour farms across the Midwest.

He plans to trade in a still-shiny 3-year-old Case IH harvesting combine for a newer model.

Brazil’s agricultural growth-spurt began about four decades ago, as farmers were lured north to its sweeping savanna, known as the cerrado, by the promise of cheap land and climbing soybean demand and prices.

The region stretches over 500 million acres, an area three times the size of Texas and nearly 50% bigger than all the land in the U.S. used to grow crops.

Armed with soil treatments like lime and fertilizer, settlers brought huge tracts of scrubland—once considered ill-suited for growing crops—into cultivation. Farm operations can dwarf U.S. counterparts in size, including some with multiple parcels that when added up are larger than Yosemite National Park.

Farmers have been aided by Brazil’s lower land costs, macroeconomic reforms and a year-round growing season, which allows them to stack soybean and corn crops back to back.

Low crop prices are hurting farmers in Brazil, but other financial factors have worked in their favor in recent years. Farmers are typically paid in dollars for their grain, but pay about 38% of their expenses in reais, which dropped sharply against the dollar in 2015.

As a result, when crop prices fall, Brazilian farmers can book profits for longer than U.S. farmers, according to J.P. Morgan analysts. Soybean futures currently trade around $9.50 a bushel.

Brazil has less-developed infrastructure. Heavy rains routinely trap trucks shuttling soybeans single-file down poor roads in the country’s north, requiring bulldozers to wrench them from the mud. Earlier this year, wet weather hobbled transport on BR-163, a key agricultural thoroughfare, stranding ships at Brazil’s northern ports for weeks before forcing some to reroute south to collect soybeans, according to Michael Cordonnier, president of Soybean and Corn Advisor Inc., an Illinois-based agricultural consulting firm.

Still, Mr. Cordonnier predicts Brazil will grow into an ever more powerful agricultural player. “They have the weather, the know-how and the area,” he says.

U.S. companies have helped develop the sector. Global grain giants Cargill Inc., Bunge Ltd. and Louis Dreyfus Commodities dotted the countryside with soybean processing plants in the 1970s and ’80s, and built export terminals at the country’s ports. Some grain companies offered financing to farmers.

Equipment manufacturers such as Deere and CNH Industrial NV since 2000 have set up Brazilian factories and assembly lines to roll out tractors.

Farmers in Africa must accept the concept of owning a modern tractor on their farms.

Minnesota-based Mosaic agreed to buy most of Brazilian miner Vale SA’s fertilizer business for $2.5 billion last year to produce in the country.

After Brazil gave farmers the green light to grow genetically modified crops in 2003, seed giants Monsanto and DuPont Co. ramped up production and research there.

In 2013, Monsanto introduced a soybean gene designed to repel pests common to Brazilian fields, their first biotech seed specifically designed for the Latin American market.

The world’s largest seed company by sales now generates about 11% of its revenue from Brazil. It plans to roll out a new genetically engineered soybean by 2021 to resist a wider range of bugs that bedevil crops in South America, says Leonardo Bastos, who leads Monsanto’s product management in South America.

Back in Illinois, the largest soybean-producing state in the U.S., Mr. Gaffner is adapting his operation to ensure his farm, in the family since the 1930s, survives the worst slump in decades. He is focused on keeping costs down on his 1,000 acres.

He buys 10-year-old farm machinery and keeps the equipment running. He uses GPS technology to avoid blanketing fertile areas of fields with unneeded nutrients. Similar systems help measure the exact number of seeds he needs to plant per row.

“That’s enabled us to stay ahead of the financial distress,” says Mr. Gaffner, 51. He considered trying his hand at farming in Brazil two decades ago but ultimately decided against it.

He has also built an array of steel storage bins behind his family’s farmhouse. With profit margins so tight, and price shifts so rapid, Mr. Gaffner says the space provides flexibility to stash crops until prices turn favorable.

He has had to spend more money for extra herbicides to fight palmer amaranth and waterhemp, weeds that have developed resistance to a herbicide, widely used with the genetically engineered seeds that revolutionized farming in the 1990s.

Seed costs are higher. The price of soybean seeds for U.S. farmers has more than quadrupled in the past 20 years, according to USDA data. Some farmers are settling for older, cheaper versions of seeds, though they may not produce as many beans.

“That’s not going to be a good thing for us in competition with other countries,” says Tommy Young, an Arkansas farmer who represents his state on the U.S. Grains Council, an export-focused body for U.S. farmers.

Income in the U.S. farm sector will decline for a fourth year this year, falling to $62.3 billion, half of the record $123 billion farmers earned in 2013, the USDA projects. The last time income fell four years in a row was in the mid-1970s.

U.S. growers are adding soybean acres, wagering that robust demand from China and other importers will make soybeans more profitable than corn. The USDA projects a record 89.5 million U.S. acres will be planted with soybeans and that U.S. exports will expand modestly over the next decade. Soybeans mostly are processed into meal to feed livestock and poultry, as well as into oil used in cooking and food products like margarine.

Farmers could also dedicate more fields to specialized soybeans, tailored to yield healthier oils for processed foods, which can fetch a higher price. “Twenty years from now we may not be focused on squeezing more bushels out of each acre but on growing a more nutrient-dense crop,” says Jim Sutter, chief executive of the U.S. Soybean Export Council.

Over all, U.S. farmland has shrunk by 12%, or 46 million acres, since 1982, partly due to urban development. In contrast, in Brazil, about 150 million more acres in the cerrado could eventually come under the plow, as farmers convert more pasture into fields for crops, according to the USDA. Brazil’s agricultural expansion has drawn criticism for deforestation, though over the past decade, farmers have boosted production largely by converting pasture land and increasing crop yields, instead of knocking down rain forest, according to the Nature Conservancy, a conservation group that has worked with grain companies.

Mr. Gilioli says his family farm has grown 10-fold since the late 1990s, when his father bought the first 500 acres with proceeds from the sale of his seed business, and he may expand further.

“It’s easy to open new land,” Mr. Gilioli says, gesturing toward a wide expanse of pasture land from the cab of his Ford pickup truck. “In two or three years, that will all be soybeans.”