States such as Missouri, Kentucky and Minnesota have seen increases in their Amish populations of more than 130 percent. The Amish now number an estimated 227,000 nationwide, up from 123,000 in 1992, according to researchers from Elizabethtown College's Young Center for Anabaptist and Pietist Studies.
Over the same period, Amish settlements have been established in seven new states, putting them in at least 28 states from coast to coast. The new states are: Arkansas, Colorado, Maine, Mississippi, Nebraska, Washington and West Virginia.
"When we think they might be dying out or merely surviving, they are actually thriving," said Elizabethtown professor Don Kraybill, a leading expert on the Amish who shared his research from an upcoming book with The Associated Press.
Also known as Anabaptists, most Amish reject modern conveniences and rely on horse-drawn carriages. They began arriving in eastern Pennsylvania around 1730. Along with English, they speak a German dialect called Pennsylvania Dutch or Pennsylvania German.
Amish couples typically have five or more children. With more than four out of every five deciding in young adulthood to remain within the church, their population has grown steadily. More than half the population is under 21.
A small portion of the increase is also due to conversions to the faith.
The Amish are attracted to areas with relatively cheap farms, a rural lifestyle and nonfarming jobs such as construction or cabinet making that fit their values and allow them to remain independent. In some cases, they have migrated to resolve leadership problems or escape church-related disputes.
In Intercourse, a town just east of Lancaster popular with tourists, Amish goat farmer Lester Stoltzfus said a number of area families had moved recently to other states in search of affordable farmland.
"It's fine with me if people move out," Stoltzfus, 37, said from his farm along a country lane hemmed in by cornfields. "There are too many people living here anyway."
Down the road at Fisher's Tin Shop, where stove pipes and decorative items fashioned out of tin hung on the walls, Ben Fisher could not offer any explanation for why the Amish are doing so well. But he said families are on the move all the time.
"They've got to go somewhere," Fisher said.
As they move into new areas, some of the conflicts that occurred years earlier in established Amish settlements are playing out again, often involving issues such as building codes or waste treatment.
In Mayfield, Ky., an area into which a few hundred Amish have moved in recent years, nine men are fighting charges they operated horse-drawn buggies without the flashing lights or orange safety triangles that state law requires.
"They are moving into new states and settling or establishing new settlements in communities where local officials aren't acquainted with them. That creates some misunderstanding on zoning issues or other unique factors in Amish practice," Kraybill said.
At the same time, some businesses have been glad to accommodate the Amish. In Mayfield, hardware store owner Dan Falder said his business is one of several to install hitching posts where the Amish can tie up their horses.
Now when Falder looks across the parking lot, he sees horse manure. "That's new within the last few years," he said.
Pennsylvania, Ohio and Indiana continue to be the geographic center for the Amish, accounting for about two-thirds of the faith's population. They also accounted for more than half of the total population gain.
But eight states with at least 1,000 Amish residents had higher rates of growth, led by Kentucky, which saw its population jump 200 percent, from 2,835 to 8,505, the study found.
The number of Amish "districts" - congregations that usually consist of two or three dozen families - has increased by 84 percent in the past 16 years, from 929 to 1,711.
The arrival of the Amish can raise land prices, and their self-reliance translates into a relatively low burden on public services.
Dennis Hubbard, a government official in Sheldon Township, Wis., said the newcomers seldom appear in the court system, require long-term care or attend public schools.
"As they live their lives, they really do not become very involved with government," said Hubbard, whose state has seen its Amish population climb 117 percent since 1992.
At least 350 Amish families migrated into Missouri, New York or Wisconsin between 2002 and 2007. Over the same period, about 520 families moved out of Ohio and some 470 left Pennsylvania.
"One family doesn't go - there is a group of them that goes, like two or three or four," said Fannie Erb-Miller, national editor of The Budget, a weekly newspaper serving the Amish that is based in Sugarcreek, Ohio.
Once a settlement has six families and at least one minister, it qualifies to send The Budget dispatches about its activities, often with an invitation for others to join it.
"They can continue to let people know: We're here, come visit us, how the land is, the orchards do great or whatever," Erb-Miller said.
Kraybill said only families who use horse-drawn buggies and call themselves Amish were considered Amish for purposes of his research.
Researchers combed Amish publications and mined other sources to determine where new settlements were being established and to count the total number of districts.
They used a figure of 135 people per church district to calculate population estimates, but the study cautions that its method could result in numbers that are too high for newer settlements and too low in long-established Amish communities.
In Ontario, Canada, the only Amish community outside the United States also is growing. It consists of about 4,500 people, up from 2,300 in 1992.
The Amish have noticed their changing demographics. The population boom is posing practical challenges for a people who, for example, often pay non-Amish "taxis" - private vehicles - to take them on longer trips.
"An Amish woman said, 'We joke among ourselves, if we keep growing at this rate, soon half the world will be Amish and the other half will be taxi drivers,'" Kraybill said.