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Frontier Thesis

Article by D.R. Owram

Published Online February 7, 2006

Last Edited December 16, 2013

The Frontier thesis was formulated 1893, when American historian Frederick Jackson Turner theorized that the availability of unsettled land throughout much of American history was the most important factor determining national development. Frontier experiences and new opportunities forced old traditions to change, institutions to adapt and society to become more democratic as class distinctions collapsed. The result was a unique American society, distinct from the European societies from which it originated. In Canada the frontier thesis was popular between the world wars with historians such as A.R.M. LOWER and Frank UNDERHILL and sociologist S.D. CLARK , partly because of a new sense of Canada's North American character.

Since WWII the frontier thesis has declined in popularity because of recognition of important social and cultural distinctions between Canada and the US. In its place a "metropolitan school" has developed, emphasizing Canada's much closer historical ties with Europe. Moreover, centres such as Montréal, Toronto and Ottawa had a profound influence on the settlement of the Canadian frontier. Whichever argument is emphasized, however, any realistic conclusion cannot deny that both the frontier and the ties to established centres were formative in Canada's development.

See also METROPOLITAN-HINTERLAND THESIS .

Recommended

Laurentian thesis.

Metropolitan-Hinterland Thesis

How the Myth of the American Frontier Got Its Start

Frederick Jackson Turner’s thesis informed decades of scholarship and culture. Then he realized he was wrong

Colin Woodard

On the evening of   July 12, 1893, in the hall of a massive new Beaux-Arts building that would soon house the Art Institute of Chicago, a young professor named Frederick Jackson Turner rose to present what would become the most influential essay in the study of U.S. history.

It was getting late. The lecture hall was stifling from a day of blazing sun, which had tormented the throngs visiting the nearby Chicago World’s Columbian Exposition, a carnival of never-before-seen wonders, like a fully illuminated electric city and George Ferris’ 264-foot-tall rotating observation wheel. Many of the hundred or so historians attending the conference, a meeting of the American Historical Association (AHA), were dazed and dusty from an afternoon spent watching Buffalo Bill’s Wild West show at a stadium near the fairground’s gates. They had already sat through three other speeches. Some may have been dozing off as the thin, 31-year-old associate professor from the University of Wisconsin in nearby Madison began his remarks.

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Turner told them the force that had forged Americans into one people was the frontier of the Midwest and Far West. In this virgin world, settlers had finally been relieved of the European baggage of feudalism that their ancestors had brought across the Atlantic, freeing them to find their true selves: self-sufficient, pragmatic, egalitarian and civic-minded. “The frontier promoted the formation of a composite nationality for the American people,” he told the audience. “In the crucible of the frontier, the immigrants were Americanized, liberated and fused into a mixed race, English in neither nationality nor characteristics.”

The audience was unmoved.

In their dispatches the following morning, most of the newspaper reporters covering the conference didn’t even mention Turner’s talk. Nor did the official account of the proceedings prepared by the librarian William F. Poole for The Dial , an influential literary journal. Turner’s own father, writing to relatives a few days later, praised Turner’s skills as the family’s guide at the fair, but he said nothing at all about the speech that had brought them there.

Yet in less than a decade, Turner would be the most influential living historian in the United States, and his Frontier Thesis would become the dominant lens through which Americans understood their character, origins and destiny. Soon, Jackson’s theme was prevalent in political speech, in the way high schools taught history, in patriotic paintings—in short, everywhere. Perfectly timed to meet the needs of a country experiencing dramatic and destabilizing change, Turner’s thesis was swiftly embraced by academic and political institutions, just as railroads, manufacturing machines and telegraph systems were rapidly reshaping American life.

By that time, Turner himself had realized that his theory was almost entirely wrong.

American historians had long believed that Providence had chosen their people to spread Anglo-Saxon freedom across the continent. As an undergraduate at the University of Wisconsin, Turner was introduced to a different argument by his mentor, the classical scholar William Francis Allen. Extrapolating from Darwinism, Allen believed societies evolved like organisms, adapting themselves to the environments they encountered. Scientific laws, not divine will, he advised his mentee, guided the course of nations. After graduating, Turner pursued a doctorate at Johns Hopkins University, where he impressed the history program’s leader, Herbert Baxter Adams, and formed a lifelong friendship with one of his teachers, an ambitious young professor named Woodrow Wilson. The connections were useful: When Allen died in 1889, Adams and Wilson aided Turner in his quest to take Allen’s place as head of Wisconsin’s history department. And on the strength of Turner’s early work, Adams invited him to present a paper at the 1893 meeting of the AHA, to be held in conjunction with the World’s Congress Auxiliary of the World’s Columbian Exposition.

The resulting essay, “The Significance of the Frontier in American History,” offered a vivid evocation of life in the American West. Stripped of “the garments of civilization,” settlers between the 1780s and the 1830s found themselves “in the birch canoe” wearing “the hunting shirt and the moccasin.” Soon, they were “planting Indian corn and plowing with a sharp stick” and even shouting war cries. Faced with Native American resistance—Turner largely overlooked what the ethnic cleansing campaign that created all that “free land” might say about the American character—the settlers looked to the federal government for protection from Native enemies and foreign empires, including during the War of 1812, thus fostering a loyalty to the nation rather than to their half-forgotten nations of origin.

He warned that with the disappearance of the force that had shaped them—in 1890, the head of the Census Bureau concluded there was no longer a frontier line between areas that had been settled by European Americans and those that had not—Americans would no longer be able to flee west for an easy escape from responsibility, failure or oppression. “Each frontier did indeed furnish a new field of opportunity, a gate of escape from the bondage of the past,” Turner concluded. “Now … the frontier has gone, and with its going has closed the first period of American history.”

When he left the podium on that sweltering night, he could not have known how fervently the nation would embrace his thesis.

Like so many young scholars, Turner worked hard to bring attention to his thesis. He incorporated it into the graduate seminars he taught, lectured about it across the Midwest and wrote the entry for “Frontier” in the widely read Johnson’s Universal Cyclopædia. He arranged to have the thesis reprinted in the journal of the Wisconsin Historical Society and in the AHA’s 1893 annual report. Wilson championed it in his own writings, and the essay was read by hundreds of schoolteachers who found it reprinted in the popular pedagogical journal of the Herbart Society, a group devoted to the scientific study of teaching. Turner’s big break came when the Atlantic Monthly ’s editors asked him to use his novel viewpoint to explain the sudden rise of populists in the rural Midwest, and how they had managed to seize control of the Democratic Party to make their candidate, William Jennings Bryan, its nominee for president. Turner’s 1896 Atlantic Monthly essay , which tied the populists’ agitation to the social pressures allegedly caused by the closing of the frontier—soil depletion, debt, rising land prices—was promptly picked up by newspapers and popular journals across the country.

Meanwhile, Turner’s graduate students became tenured professors and disseminated his ideas to the up-and-coming generation of academics. The thrust of the thesis appeared in political speeches, dime-store western novels and even the new popular medium of film, where it fueled the work of a young director named John Ford who would become the master of the Hollywood western. In 1911, Columbia University’s David Muzzey incorporated it into a textbook—initially titled History of the American People —that would be used by most of the nation’s secondary schools for half a century.

Americans embraced Turner’s argument because it provided a fresh and credible explanation for the nation’s exceptionalism—the notion that the U.S. follows a path soaring above those of other countries—one that relied not on earlier Calvinist notions of being “the elect,” but rather on the scientific (and fashionable) observations of Charles Darwin. In a rapidly diversifying country, the Frontier Thesis denied a special role to the Eastern colonies’ British heritage; we were instead a “composite nation,” birthed in the Mississippi watershed. Turner’s emphasis on mobility, progress and individualism echoed the values of the Gilded Age—when readers devoured Horatio Alger’s rags-to-riches stories—and lent them credibility for the generations to follow.

But as a researcher, Turner himself turned away from the Frontier Thesis in the years after the 1890s. He never wrote it down in book form or even in academic articles. He declined invitations to defend it, and before long he himself lost faith in it.

For one thing, he had been relying too narrowly on the experiences in his own region of the Upper Midwest, which had been colonized by a settlement stream originating in New England. In fact, he found, the values he had ascribed to the frontier’s environmental conditioning were actually those of this Greater New England settlement culture, one his family and most of his fellow citizens in Portage, Wisconsin, remained part of, with their commitment to strong village and town governments, taxpayer-financed public schools and the direct democracy of the town meeting. He saw that other parts of the frontier had been colonized by other settlement streams anchored in Scots-Irish Appalachia or in the slave plantations of the Southern lowlands, and he noted that their populations continued to behave completely differently from one another, both politically and culturally, even when they lived in similar physical environments. Somehow settlers moving west from these distinct regional cultures were resisting the Darwinian environmental and cultural forces that had supposedly forged, as Turner’s biographer, Ray Allen Billington, put it, “a new political species” of human, the American. Instead, they were stubbornly remaining themselves. “Men are not absolutely dictated to by climate, geography, soils or economic interests,” Turner wrote in 1922. “The influence of the stock from which they sprang, the inherited ideals, the spiritual factors, often triumph over the material interests.”

Turner spent the last decades of his life working on what he intended to be his magnum opus, a book not about American unity but rather about the abiding differences between its regions, or “sections,” as he called them. “In respect to problems of common action, we are like what a United States of Europe would be,” he wrote in 1922, at the age of 60. For example, the Scots-Irish and German small farmers and herders who settled the uplands of the southeastern states had long clashed with nearby English enslavers over education spending, tax policy and political representation. Turner saw the whole history of the country as a wrestling match between these smaller quasi-nations, albeit a largely peaceful one guided by rules, laws and shared American ideals: “When we think of the Missouri Compromise, the Compromise of 1850, the Kansas-Nebraska Act, as steps in the marking off of spheres of influence and the assignment of mandates [between nations] … we see a resemblance to what has gone on in the Old World,” Turner explained. He hoped shared ideals—and federal institutions—would prove cohesive for a nation suddenly coming of age, its frontier closed, its people having to steward their lands rather than striking out for someplace new.

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Colin Woodard | | READ MORE

Colin Woodard is a journalist and historian, and the author of six books including Union: The Struggle to Forge the Story of United States Nationhood . He lives in Maine.

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2 The Making of a National Identity: The Frontier Thesis

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Frederick Jackson Turner's frontier thesis became a significant force in shaping the national identity of the U.S. The ideologies incorporated into Turner's frontier thesis were not only meant to provide a historical interpretation of how the U.S. came into being but also satisfied the national need for a “usable past.” This frontier thesis was able to transmit a series of symbols that became imbedded in the nation's self‐perception and self‐understanding: Virgin land, wilderness, land and democracy, Manifest Destiny, chosen race. Race must be understood as an important piece of this developing national identity because the idea of “purity” of race was used as a rationalization to colonize, exclude, devalue, and even exterminate the native borderlands people.

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British Columbia - Documents - Frontier

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• Frontier Thesis

1920 Turner's Frontier Thesis

Source:(New York: Henry Holt and Company, 1920, 1947; reprinted by Holt, Rinehart and Winston Inc., 1962), pp. 257-262.

The Turner's Frontier Thesis is a seminal work of American history, written by historian Frederick Jackson Turner in 1893. In his thesis, Turner argued that the existence of a continuously expanding frontier in the American West was a defining characteristic of American democracy and society. Turner argued that the frontier was not just a physical place, but a symbol of the American spirit of individualism, democracy, and self-reliance. He believed that the frontier had shaped American democracy by creating a unique American character that was egalitarian, independent, and democratic. Turner's thesis also suggested that the closing of the frontier in 1890 marked the end of a crucial period in American history. He argued that the end of the frontier would lead to the decline of the American character and democracy, and that America needed to find new ways to maintain its democratic ideals in the absence of the frontier. The Frontier Thesis was highly influential in shaping American history and historiography. It has been debated, discussed, and analyzed by historians and scholars for over a century, and its impact can still be seen in American culture and politics today.

Frederick Jackson Turner

The Frontier in American History

(New York: Henry Holt and Company, 1920, 1947; reprinted by Holt, Rinehart and Winston Inc., 1962), pp. 257-262.

The last chapter in the development of Western democracy is the one that deals with its conquest over the vast spaces of the new West. At each new stage of Western development, the people have had to grapple with larger areas, with bigger combinations. The little colony of Massachusetts veterans that settled at Marietta received a land grant as large as the State of Rhode Island. The band of Connecticut pioneers that followed Moses Cleveland to the Connecticut Reserve occupied a region as large as the parent State. The area which settlers of New England stock occupied on the prairies of northern Illinois surpassed the combined area of Massachusetts, Connecticut, and Rhode Island. Men who had become accustomed to the narrow valleys and little towns of the East found themselves out on the boundless spaces of the West dealing with units of such magnitude as dwarfed their former Experiences. The Great Lakes, the Prairies, the Great Plains, the Rocky Mountains, the Mississippi and the Missouri, furnished new standards of measurement for the achievement of this industrial democracy. Individualism began to give way to cooperation and to governmental activity.

Even in the earlier days of the democratic conquest of the wilderness, demands had been made upon the government for support in internal improvements, but this new West showed a growing tendency to call to its assistance the powerful arm of national authority. In the period since the Civil War, the vast public domain has been donated to the individual farmer, to States for education, to railroads for the construction of transportation lines. Moreover, with the advent of democracy in the last fifteen years upon the Great Plains, new physical conditions have presented themselves which have accelerated the social tendency of Western democracy.

The pioneer farmer of the days of Lincoln could place his family on a flatboat, strike into the wilderness, cut out his clearing, and with little or no capital go on to the achievement of industrial independence. Even the homesteader on the Western prairies found it possible to work out a similar independent destiny, although the factor of transportation made a serious and increasing impediment to the free working-out of his individual career. But when the arid lands and the mineral resources of the Far West were reached, no conquest was possible by the old individual pioneer methods. Here expensive irrigation works must be constructed, cooperative activity was demanded in the utilization of the water supply, capital beyond the reach of the small farmer was required. In a word, the physiographic province itself decreed that the destiny of this new frontier should be social rather than individual.

Magnitude of social achievement is the watchword of the democracy since the Civil War. From petty towns built in the marshes, cities arose whose greatness and industrial power are the wonder of our time. The conditions were ideal for the production of captains of industry. The old democratic admiration for the self-made man, its old deference to the rights of competitive individual development, together with the stupendous natural resources that opened to the conquest of the keenest and the strongest, gave such conditions of mobility as enabled the development of the large corporate industries which in our own decade have marked the West.

Thus, in brief, have been outlined the chief phases of the development of Western democracy in the different areas which it has conquered. There has been a steady development of the industrial ideal, and a steady increase of the social tendency, in this later movement of Western democracy. While the individualism of the frontier, so prominent in the earliest days of the Western advance, has been preserved as an ideal, more and more these individuals struggling each with the other, dealing with vaster and vaster areas, with larger and larger problems, have found it necessary to combine under the leadership of the strongest.

This is the explanation of the rise of those preeminent captains of industry whose genius has concentrated capital to control the fundamental resources of the nation. If now in the way of recapitulation, we try to pick out from the influences that have gone to the making of Western democracy the factors which constitute the net result of this movement, we shall have to mention at least the following:--

Most important of all has been the fact that an area of free land has continually lain on the western border of the settled area of the United States. Whenever social conditions tended to crystallize in the East, whenever capital tended to press upon labor or political restraints to impede the freedom of the mass, there was this gate of escape to the free conditions of the frontier. These free lands promoted individualism, economic equality, freedom to rise, democracy. Men would not accept inferior wages and a permanent position of social subordination when this promised land of freedom and equality was theirs for the taking. Who would rest content under oppressive legislative conditions when with a slight effort he might reach a land wherein to become a co-worker in the building of free cities and free States on the lines of his own ideal?

In a word, then, free lands meant free opportunities. Their existence has differentiated the American democracy from the democracies which have preceded it, because ever, as democracy in the East took the form of highly specialized and complicated industrial society, in the West it kept in touch with primitive conditions, and by action and reaction these two forces have shaped our history.

In the next place, these free lands and this treasury of industrial resources have existed over such vast spaces that they have demanded of democracy increasing spaciousness of design and power of execution. Western democracy is contrasted with the democracy of all other times in the largeness of the tasks to which it has set its hand, and in the vast achievements which it has wrought out in the control of nature and of politics. It would be difficult to over-emphasize the importance of this training upon democracy. Never before in the history o the world has democracy existed on so vast an area and handled things in the gross with such success, with such largeness of design, and such grasp upon the means of execution.

In short, democracy has learned in the West of the United States how to deal with the problems of magnitude. The old historic democracies were but little states with primitive economic conditions.... Western democracy has been from the time of its birth idealistic. The very fact of the wilderness appealed to men as a fair, blank page on which to write a new chapter in the story of man's struggle for a higher type of society. The Western wilds, from the Alleghanies to the Pacific, constituted the richest free gift that was ever spread out before civilized man. To the peasant and artisan of the Old World, bound by the chains of social class, as old as custom and as inevitable as fate, the West offered an exit into a free life and greater well-being among the bounties of nature, into the midst of resources that demanded manly exertion, and that gave in return the chance for indefinite ascent in the scale of social advance.

"To each she offered gifts after his will".

Never again can such an opportunity come to the sons of men. It was unique, and the thing is so near us, so much a part of our lives, that we do not even yet comprehend its full significance. The existence of this land of opportunity has made America the goal of idealists from the days of the Pilgrim Fathers. With all the materialism of the pioneer movements, this idealistic conception of the vacant lands as an opportunity for a new order of things is unmistakably present....

Cite Article : www.britsihcolumbiahistory.ca.com/sections/documents

Reference: Article by (Staff Historian), 2023

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Was Frederick Jackson Turner’s Frontier Thesis Myth or Reality?

Two scholars debate this question.

Written by: (Claim A) Andrew Fisher, William & Mary; (Claim B) Bradley J. Birzer, Hillsdale College

Suggested sequencing.

• Use this Point-Counterpoint with the  Frederick Jackson Turner, “The Significance of the Frontier in American History,” 1893  Primary Source to give students more background on individualism and western expansion.

Issue on the Table

Was Turner’s thesis a myth about the individualism of the American character and the influence of the West or was it essentially correct in explaining how the West and the advancing frontier contributed to the shaping of individualism in the American character?

Instructions

Read the two arguments in response to the question, paying close attention to the supporting evidence and reasoning used for each. Then, complete the comparison questions that follow. Note that the arguments in this essay are not the personal views of the scholars but are illustrative of larger historical debates.

Every nation has a creation myth, a simple yet satisfying story that inspires pride in its people. The United States is no exception, but our creation myth is all about exceptionalism. In his famous essay, “The Significance of the Frontier in American History,” Frederick Jackson Turner claimed that the process of westward expansion had transformed our European ancestors into a new breed of people endowed with distinctively American values and virtues. In particular, the frontier experience had supposedly fostered democracy and individualism, underpinned by the abundance of “free land” out West. “So long as free land exists,” Turner wrote, “the opportunity for a competency exists, and economic power secures political power.” It was a compelling articulation of the old Jeffersonian Dream. Like Jefferson’s vision, however, Turner’s thesis excluded much of the nation’s population and ignored certain historical realities concerning American society.

Very much a man of his times, Turner filtered his interpretation of history through the lens of racial nationalism. The people who counted in his thesis, literally and figuratively, were those with European ancestry—and especially those of Anglo-Saxon origins. His definition of the frontier, following that of the U.S. Census, was wherever population density fell below two people per square mile. That effectively meant “where white people were scarce,” in the words of historian Richard White; or, as Patricia Limerick puts it, “where white people got scared because they were scarce.” American Indians only mattered to Turner as symbols of the “savagery” that white pioneers had to beat back along the advancing frontier line. Most of the “free land” they acquired in the process came from the continent’s vast indigenous estate, which, by 1890, had been reduced to scattered reservations rapidly being eroded by the Dawes Act. Likewise, Mexican Americans in the Southwest saw their land base and economic status whittled away after the Treaty of Guadalupe Hidalgo that nominally made them citizens of the United States. Chinese immigrants, defined as perpetual aliens under federal law, could not obtain free land through the Homestead Act. For all these groups, Euro-American expansion and opportunity meant the contraction or denial of their own ability to achieve individual advancement and communal stability.

Turner also exaggerated the degree of social mobility open to white contemporaries, not to mention their level of commitment to an ideology of rugged individualism. Although plenty of Euro-Americans used the homestead laws to get their piece of free land, they often struggled to make that land pay and to keep it in the family. During the late nineteenth century, the commoditization and industrialization of American agriculture caught southern and western farmers in a crushing cost-price squeeze that left many wrecked by debt. To combat this situation, they turned to cooperative associations such as the Grange and the National Farmers’ Alliance, which blossomed into the Populist Party at the very moment Turner was writing about the frontier as the engine of American democracy. Perhaps it was, but not in the sense he understood. Populists railed against the excess of individualism that bred corruption and inequality in Gilded Age America. Even cowboys, a pillar of the frontier myth, occasionally tried to organize unions to improve their wages and working conditions. Those seeking a small stake of their own—what Turner called a “competency”— in the form of their own land or herds sometimes ran afoul of concentrated capital, as during the Johnson County War of 1892. The big cattlemen of the Wyoming Stockgrowers Association had no intention of sharing the range with pesky sodbusters and former cowboys they accused of rustling. Their brand of individualism had no place for small producers who might become competitors.

Turner took such troubles as a sign that his prediction had come true. With the closing of the frontier, he said, the United States would begin to see greater class conflict in the form of strikes and radical politics. There was lots of free land left in 1890, though; in fact, approximately 1 million people filed homestead claims between 1901 and 1913, compared with 1.4 million between 1862 and 1900. That did not prevent the country from experiencing serious clashes between organized labor and the corporations that had come to dominate many industries. Out west, socialistic unions such as the Western Federation of Miners and the Industrial Workers of the World challenged not only the control that companies had over their employees but also their influence in the press and politics. For them, Turner’s dictum that “economic power secures political power” would have held a more sinister meaning. It was the rise of the modern corporation, not the supposed fading of the frontier, that narrowed the meanings of individualism and opportunity as Americans had previously understood them.

Young historian Frederick Jackson Turner presented his academic paper, “The Significance of the Frontier in American History,” at the World’s Columbian Exposition in Chicago on July 12, 1893. He was the final presenter of that hot and humid day, but his essay ranks among the most influential arguments ever made regarding American history.

Turner was trained at the University of Wisconsin (his home state) and Johns Hopkins University, then the center of Germanic-type graduate studies—that is, it was scientific and objectivist rather than idealist or liberal. Turner rebelled against that purely scientific approach, but not by much. In 1890, the U.S. Census revealed that the frontier (defined as fewer than two people per square mile) was closed. There was no longer an unbroken frontier line in the United States, although frontier conditions lasted in certain parts of the American West until 1920. Turner lamented this, believing the most important phase of American history was over.

No one publicly commented on the essay at the time, but the American Historical Association reprinted it in its annual report the following year, and within a decade, it became known as the “Turner Thesis.”

What is most prominent in the Turner Thesis is the proposition that the United States is unique in its heritage; it is not a European clone, but a vital mixture of European and American Indian. Or, as he put it, the American character emerged through an intermixing of “savagery and civilization.” Turner attributed the American character to the expansion to the West, where, he said, American settlers set up farms to tame the frontier. “The existence of an area of free land, its continuous recession, and the advance of American settlement westward, explain American development.” As people moved west in a “perennial rebirth,” they extended the American frontier, the boundary “between savagery and civilization.”

The frontier shaped the American character because the settlers who went there had to conquer a land difficult for farming and devoid of any of the comforts of life in urban parts of the East: “The frontier is the line of most rapid and effective Americanization. The wilderness masters the colonist. It finds him a European in dress, industries, tools, modes of travel, and thought. It takes him from the railroad car and puts him in the birch canoe. It strips off the garments of civilization and arrays him in the hunting shirt and the moccasin. It puts him in the log cabin of the Cherokee and Iroquois and runs an Indian palisade around him. Before long he has gone to planting Indian corn and plowing with a sharp stick; he shouts the war cry and takes the scalp in orthodox Indian fashion. In short, at the frontier the environment is at first too strong for the man. He must accept the conditions which it furnishes, or perish, and so he fits himself into the Indian clearings and follows the Indian trails.”

Politically and socially, according to Turner, the American character—including traits that prioritized equality, individualism, and democracy—was shaped by moving west and settling the frontier. “The tendency,” Turner wrote, “is anti-social. [The frontier] produces antipathy to control, and particularly to any direct control.” Those hardy pioneers on the frontier spread the ideas and practice of democracy as well as modern civilization. By conquering the wilderness, Turner stressed, they learned that resources and opportunity were seemingly boundless, meant to bring the ruggedness out of each individual. The farther west the process took them, the less European the Americans as a whole became. Turner saw the frontier as the  progenitor  of the American practical and innovative character: “That coarseness and strength combined with acuteness and acquisitiveness; that practical, inventive turn of mind, quick to find expedients; that masterful grasp of material things, lacking the artistic but powerful to effect great ends; that restless, nervous energy; that dominant individualism, working for good and for evil, and withal that buoyancy and exuberance which comes with freedom – these are trains of the frontier.”

Turner’s thesis, to be sure, viewed American Indians as uncivilized. In his vision, they cannot compete with European technology, and they fall by the wayside, serving as little more than a catalyst for the expansion of white Americans. This near-absence of Indians from Turner’s argument gave rise to a number of critiques of his thesis, most prominently from the New Western Historians beginning in the 1980s. These more recent historians sought to correct Turner’s “triumphal” myth of the American West by examining it as a region rather than as a process. For Turner, the American West is a progressive process, not a static place. There were many Wests, as the process of conquering the land, changing the European into the American, happened over and over again. What would happen to the American character, Turner wondered, now that its ability to expand and conquer was over?

Historical Reasoning Questions

Use  Handout A: Point-Counterpoint Graphic Organizer  to answer historical reasoning questions about this point-counterpoint.

Primary Sources (Claim A)

Cooper, James Fenimore.  Last of the Mohicans (A Leatherstocking Tale) . New York: Penguin, 1986.

Turner, Frederick Jackson. “The Significance of the Frontier in American History.”  http://sunnycv.com/steve/text/civ/turner.html

Primary Sources (Claim B)

Suggested resources (claim a).

Cronon, William, George Miles, and Jay Gitlin, eds.  Under an Open Sky: Rethinking America’s Western Past . New York: W. W. Norton & Company, 1992.

Faragher, John Mack.  Women and Men on the Overland Trail . New Haven, CT: Yale University Press, 2001.

Grossman, Richard R, ed.  The Frontier in American Culture: Essays by Richard White and Patricia Nelson Limerick . Berkeley, CA: University of California Press, 1994.

Limerick, Patricia Nelson.  The Legacy of Conquest: The Unbroken Past of the American West . New York: W. W. Norton & Company, 1987.

Limerick, Patricia Nelson, Clyde A. Milner II, and Charles E. Rankin, eds.  Trails: Toward a New Western History . Lawrence, KS: University Press of Kansas, 1991.

Milner II, Clyde A.  A New Significance: Re-envisioning the History of the American West . New York: Oxford University Press, 1996.

Nugent, Walter.  Into the West: The Story of Its People . New York: Knopf, 1991.

Slotkin, Richard.  The Fatal Environment: The Myth of the Frontier in the Age of Industrialization, 1800-1890 . Norman, OK: University of Oklahoma Press, 1998.

Suggested Resources (Claim B)

Billington, Ray Allen, and Martin Ridge.  Westward Expansion: A History of the American Frontier . Albuquerque: University of New Mexico Press, 2001.

Etulain, Richard, ed.  Does the Frontier Experience Make America Exceptional?  New York: Bedford/St. Martin’s, 1999.

Mondi. Megan. “’Connected and Unified?’: A More Critical Look at Frederick Jackson Turner’s America.”  Constructing the Past , 7 no. 1:Article 7.  http://digitalcommons.iwu.edu/constructing/vol7/iss1/7

Nelson, Robert. “Public Lands and the Frontier Thesis.”  Atlas of the Historical Geography of the United States , Digital Scholarship Lab, University of Richmond, 2014.  http://dsl.richmond.edu/fartherafield/public-lands-and-the-frontier-thesis/

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17.9: The West as History- the Turner Thesis

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In 1893, the American Historical Association met during that year’s World’s Columbian Exposition in Chicago. The young Wisconsin historian Frederick Jackson Turner presented his “frontier thesis,” one of the most influential theories of American history, in his essay “The Significance of the Frontier in American History.”

Turner looked back at the historical changes in the West and saw, instead of a tsunami of war and plunder and industry, waves of “civilization” that washed across the continent. A frontier line “between savagery and civilization” had moved west from the earliest English settlements in Massachusetts and Virginia across the Appalachians to the Mississippi and finally across the Plains to California and Oregon. Turner invited his audience to “stand at Cumberland Gap [the famous pass through the Appalachian Mountains], and watch the procession of civilization, marching single file—the buffalo following the trail to the salt springs, the Indian, the fur trader and hunter, the cattle-raiser, the pioneer farmer—and the frontier has passed by.” 26

Americans, Turner said, had been forced by necessity to build a rough-hewn civilization out of the frontier, giving the nation its exceptional hustle and its democratic spirit and distinguishing North America from the stale monarchies of Europe. Moreover, the style of history Turner called for was democratic as well, arguing that the work of ordinary people (in this case, pioneers) deserved the same study as that of great statesmen. Such was a novel approach in 1893.

But Turner looked ominously to the future. The Census Bureau in 1890 had declared the frontier closed. There was no longer a discernible line running north to south that, Turner said, any longer divided civilization from savagery. Turner worried for the United States’ future: what would become of the nation without the safety valve of the frontier? It was a common sentiment. Theodore Roosevelt wrote to Turner that his essay “put into shape a good deal of thought that has been floating around rather loosely.” 27

The history of the West was many-sided and it was made by many persons and peoples. Turner’s thesis was rife with faults, not only in its bald Anglo-Saxon chauvinism—in which nonwhites fell before the march of “civilization” and Chinese and Mexican immigrants were invisible—but in its utter inability to appreciate the impact of technology and government subsidies and large-scale economic enterprises alongside the work of hardy pioneers. Still, Turner’s thesis held an almost canonical position among historians for much of the twentieth century and, more importantly, captured Americans’ enduring romanticization of the West and the simplification of a long and complicated story into a march of progress.

Why Was the Frontier So Important in American History?

The American frontier was a significant period in the history of America. It represented a time when American pioneers pushed westward and established new communities, creating a vast and diverse country that we know today. The frontier was so important because it shaped the American identity and created a unique culture that is still celebrated to this day.

Manifest Destiny

The idea of Manifest Destiny was the driving force behind American expansionism in the 19th century. Americans believed that it was their divine right to expand westward and claim new territory. This belief led to the Louisiana Purchase in 1803, which doubled the size of the United States, as well as other land acquisitions such as Florida, Texas, and California.

Pioneers were people who traveled westward to settle new areas. They were often seeking new opportunities or looking for a better life. These pioneers faced many challenges, including harsh weather conditions, disease, and attacks from Native Americans.

Homesteading

Homesteading allowed people to claim land in the West and make it their own. The Homestead Act of 1862 provided settlers with up to 160 acres of land for free if they could live on it for five years and make improvements to it.

In 1848 gold was discovered in California which led to one of America’s biggest migration periods where miners rushed westward hoping to strike gold and become rich.

Native Americans

Native Americans had been living on these lands long before settlers arrived. The settlers’ arrival led to tension between Native Americans and newcomers; sometimes this tension resulted in violence.

The Dawes Act of 1887 aimed at assimilating Native Americans into white culture by dividing up tribal lands into individual plots for each family. This led to further conflict and the loss of Native American land.

Cultural Impact

The frontier had a significant impact on American culture. It created a sense of individualism and self-reliance that is still celebrated today. The cowboy, for example, is an iconic figure in American culture that came out of the frontier era.

Western Movies

Western movies have played an important role in shaping American culture. They celebrate the rugged individualism of the frontier era and often feature cowboys, gunslingers, and outlaws.

Cowboy Culture

Cowboy culture has had a lasting impact on American fashion with cowboy hats, boots, and jeans being popular items of clothing today.

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The Importance of Frontiers

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In the summer of 1893, at the Chicago World’s Columbian Exposition, Frederick Jackson Turner a minor academic in the new discipline of social science, presented his now-famous paper on the closing of the American frontier. What came to be known as the Turner Thesis (1893) forever changed thinking about the influence and importance of the frontier and how dramatic changes of the frontier profoundly impact future economic and social issues. His thesis was deemed so significant that it is still taught at colleges and universities today.

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Gregg, J. (2021). The Importance of Frontiers. In: The Cosmos Economy. Copernicus, Cham. https://doi.org/10.1007/978-3-030-62569-6_4

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Original research article, assessment of tradeoffs between ecosystem services in large spatially constrained forest management planning problems.

• 1 Forest Research Center and Associated Laboratory TERRA, School of Agriculture, University of Lisbon, Tapada da Ajuda, Lisbon, Portugal
• 2 College of Agriculture and Environmental Sciences, University of Gondar, Gondar, Ethiopia
• 3 Research Centre for Mathematics and Applications, University of Évora, Colégio Luis Verney, Évora, Portugal
• 4 Department of Industrial Engineering, University of Chile and Institute for Complex Engineering Systems (ISCI), Santiago, Chile
• 5 Center for Mathematics, Fundamental Applications and Operational Research, Faculty of Sciences, University of Lisbon, Lisbon, Portugal
• 6 School of Electrical Engineering and Computer Science, The Pennsylvania State University, University Park, PA, United States

Forests provide multiple ecosystem services, some of which are competitive, while others are complementary. Pareto frontier approaches are often used to assess the trade-offs among these ecosystem services. However, when dealing with spatial optimization problems, one is faced with problems that are computationally complex. In this paper, we study the sources of this complexity and propose an approach to address adjacency conflicts while analyzing trade-offs among wood production, cork, carbon stock, erosion, fire resistance and biodiversity. This approach starts by sub-dividing a large landscape-level problem into four smaller sub-problems that do not share border stands. Then, it uses a Pareto frontier method to get a solution to each. A fifth sub-problem included all remaining stands. The solution of the latter by the Pareto frontier method is constrained by the solutions of the four sub-problems. This approach is applied to a large forested landscape in Northwestern Portugal. The results obtained show the effectiveness of using Pareto frontier approaches to analyze the trade-offs between ecosystem services in large spatial optimization problems. They highlight the existence of important trade-offs, notably between carbon stock and wood production, alongside erosion, biodiversity and wildfire resistance. These trade-offs were particularly clear at higher levels of these optimized services, while spatial constraints primarily affected the magnitude of the services rather than the underlying trade-off patterns. Moreover, in this paper, we study the impact of the size and complexity of the spatial optimization problem on the accuracy of the Pareto frontiers. Results suggest that the number of stands, and the number of adjacency conflicts do not affect accuracy. They show that accuracy decreases in the case of spatial optimization problems but it is within an acceptable range of discrepancy, thus showing that our approach can effectively support the analysis of trade-offs between ecosystem services.

1 Introduction

Worldwide demographic, socio-economic and environmental changes over the last three decades have led to a shift in forestry from a purely timber production focus toward the consideration of a broader range of ecosystem services. Simultaneous provision of multiple services in forest management is a complex problem where many trade-offs need to be considered. Some objectives are competitive, while others are complementary ( Tóth et al., 2006 ). As a result, harmonizing ecological, economic, and sociocultural values of forest ecosystems and simultaneously managing multiple services poses a considerable challenge to forest managers ( Baskent et al., 2020 ).

The complexity of this problem prompted the development of decision support tools to examine trade-offs among objectives. In the literature, one can find examples of the application of several multiple-criteria decision analysis (MCDA) approaches to help solve multiple objective forest management planning problems (e.g., Mendoza and Martins, 2006 ; Ananda and Herath, 2009 ; Borges et al., 2014 , 2017 ). Moreover, several MCDA-based decision support tools are available that can help users and scientific researchers both to learn and understand the impacts of management plans on the provision of forest ecosystem services ( Baskent and Jordan, 2002 ; Baskent et al., 2014 ).

A Pareto frontier approach does not require the definition of ecosystem service targets a priori , i.e., does not information about potential supply values or trade-offs among those services. The approach provides the decision-maker with information about (i) the production possibilities (i.e., the potential of the landscape to provide ecosystem services) and (ii) the extent to which increasing the supply of an ecosystem service requires accepting reduction in the provision of others ( Borges et al., 2017 ). This method thus provides decision-makers with the information needed to assess the trade-offs between ecosystem services and to set supply targets aligned with their preferences. The approach integrates the functionality of both mathematical programming and interactive decision-maps techniques to compute and display the Pareto frontier when considering two or more ecosystem services ( Borges et al., 2014 ). In particular, the Pareto frontier approach discussed in Tóth and McDill, (2009) , Borges et al. (2014) is a linear programming-based technique that can consider both continuous and integer variables. Nevertheless, the generation of Pareto frontiers of integer or mixed integer optimization problems requires a substantial computation effort ( Marques S, et al., 2021 ). Most applications of Pareto frontier techniques in forest management consider continuous variables (e.g., Tóth and McDill, 2009 ; Borges et al., 2014 , 2017 ; Marques et al., 2017 , 2020 ; Abate et al., 2022 ). There are very few applications to forest management problems with integer variables (e.g., Tóth et al., 2006 ; Marques S, et al., 2021 ). Furthermore, addressing forest management questions related to a wider range of ecosystem services requires spatial optimization models ( Borges and Hoganson, 2000 ). The latter considers both integer variables as well as spatial constraints (e.g., adjacency constraints) but the end result is a computationally complex optimization problem (e.g., McDill et al., 2002 ; Murray and Weintraub, 2002 ; Constantino et al., 2008 ; Könnyu and Tóth, 2013 ; Constantino and Martins, 2018 ).

Computational complexity of spatial optimization problems is the limiting factor for the use of Pareto frontier methods that are based on solving of integer or mixed integer programs ( Tóth et al., 2006 ; Marques S, et al., 2021 ). When addressing large and complex problems, decomposition methods are commonly employed to circumvent this problem. Existing techniques such as the Branch and Price decomposition ( Barnhart et al., 1998 ) and the more recent method by Meselhi et al. (2022) known as the Decomposition of Overlapping Functions (DOV) method have been exploited to solve such problems. However, these have only been applied to single-objective optimization rather than to the generation of the Pareto frontier in scenarios involving multiple objectives. Recent work by Marques S, et al. (2021) showcased an approach for constructing the Pareto frontiers of large integer problems derived from the Pareto frontier of smaller sub-problems. Riffo (2020) emphasized the challenge in creating Pareto frontiers for integer problems that incorporate adjacency constraints. While he suggested decomposing large problems into smaller, more manageable components, his approach produces infeasible optimization problems when applied to the construction of the Pareto frontier for large landscape problems bound by adjacency constraints. Hence, the challenge remains, namely, how to address the adjacencies between stands bordering the sub-problems. Our study aims at addressing this challenge. It proposes an approach that builds from information about trade-offs of ecosystem services in smaller spatial optimization sub-problems that may be solved independently. The emphasis is thus on building the frontier from smaller sub-problems that are designed so that there are no violations of adjacency constraints. A case study in the Northwest of Portugal is used for testing and demonstration purposes.

2.1 Case study area

A forested landscape located in Paiva County in northwest Portugal ( Figure 1 ) was used for testing our approach. Its area extends over 7,487 ha and was partitioned into 686 homogeneous units, each of which is a forest stand with the same cover type (e.g., forest species), age and productivity. The stands are mainly pure eucalypt ( Eucalyptus globulus L.) covering 6,428 ha, with some stands being a mixture of eucalypt and maritime pine ( Pinus pinaster Ait.). The latter extends over 611 ha. The landscape includes too pure chestnut ( Castanea sativa Mill.) and cork oak ( Quercus suber L.) stands extending over 23 ha. Moreover, some of the land (347 ha) is currently bare and available for new plantations. A recent wildfire has burned about 46% of the area. The landscape has the potential to provide several ecosystem services. In the work described in this paper, we leverage the information on the preferences of stakeholders reported in Marques M, et al. (2021) and consider wood as well as cork production, biodiversity conservation, erosion protection, carbon storage, and wildfire prevention as objectives to be taken into consideration. We also rely on the work developed by Marques M, et al. (2021) to simulate species conversions and changes in the area occupied by each species that might reflect the preferences of stakeholders outlined by these authors.

Figure 1 . Location of the case study area.

2.2 Forest management prescriptions, simulations, and ecosystem services estimation

The 686 homogeneous land units were assigned to different management prescriptions based on a forest inventory coordinated by the authors and conducted by the Forest Owner Association [Associação Florestal de Vale do Sousa (AFVS)], an association responsible for the development of a joint management plan for the forested landscape. The definition of the silvicultural options to be considered when simulating prescriptions that can be used to manage each homogeneous unit was made in cooperation with AFVS. This involved the definition of rotation ages, thinning regimes, shrub cleaning periodicity, and cork oak extraction schedules (only for cork oak). Specifically, according to AFVS, eucalypt stands are to be managed through coppicing, encompassing three cutting cycles, each cycle spanning over 10 to 12 years. Rotations of pine and chestnut stands extend from 40 to 55 years and from 35 to 50 years, respectively, and include different levels of thinning intensity. Pedunculate oak ( Quercus robur L.) management includes clear-cut ages from 40 to 60 years, along with different thinning ages and intensities. Cork oak silviculture involves thinning at different ages, without harvesting options. In the case of homogeneous units with eucalypt and pine, the prescriptions also include species conversion options, e.g., conversion to maritime pine (from eucalypt), chestnut, cork oak, or pedunculate oak. Bare land units may be converted into pure maritime pine stands, pure pedunculate oak stands, pure chestnut stands and pure cork oak stands. The landscape includes riparian buffers along water streams. All possible management prescriptions, including harvesting ages and species conversion options, have been identified through collaborative discussions sponsored by AFVS with relevant stakeholders. The combination of management alternatives and land units resulted in a total of 47,448 prescriptions.

The study focuses on six ecosystem services or indicators thereof: wood, cork, carbon, biodiversity, fire resistance and soil erosion. Wood and cork are examples of provisioning services. Carbon stock is considered as an indicator for the climate regulation service, while fire resistance and soil erosion are among the indicators of regulatory services. Furthermore, biodiversity stands as the foundational element underpinning all these services.

Several approaches were employed for estimating these ecosystem services. Specifically, growth models and simulation tools were used to estimate wood and cork production and carbon stocks ( Marques S, et al., 2021 ). Other ecosystem services were estimated using the approaches by Ferreira et al. (2015 ; fire resistance), Rodrigues et al. (2021 ; soil erosion), and Botequim et al. (2015 ; biodiversity). In summary, a wildfire resistance indicator, crafted by Ferreira et al. (2015) , was used to gauge the vulnerability of forest stands to wildfires. This indicator integrates wildfire occurrence and damage models developed for the most important forest species in Portugal ( Ferreira et al., 2015 ). It considers further spatial information such as the configuration of the stand as well as stand adjacency relations ( Ferreira et al., 2015 ). The values of this indicator range from 1 (low resistance) to 5 (highest resistance). For soil erosion assessment, the methodology ( Rodrigues et al., 2021 ) considers the yearly fluctuations in the cover-management factor ( C ) within the Revised Universal Soil Loss Equation (RUSLE) to estimate the annual soil loss. The C factor is a function of average crown diameter and other biometric characteristics of the stand. The biodiversity indicator considers the tree species composition (e.g., maritime pine, eucalypt, chestnut, pedunculate oak, cork oak, and riparian trees), stand age, and understory coverage ( Botequim et al., 2015 ). The biodiversity score ranges from 0 (indicating minimal biodiversity or barren land) to 8 (representing the highest level of biodiversity). The reader is referred to Ferreira et al. (2015) , Rodrigues et al. (2021) , and Botequim et al. (2015) for further detail about these indicators.

The stand and landscape level values of the aforementioned ecosystem services indicators were estimated for a 50-year planning horizon, subdivided into five planning periods of 10 years each.

2.3 The optimization model

This research considered a Model I ( Johnson and Scheurman, 1977 ) integer problem formulation, with an integer decision variable X jkp (which takes the value 1 if prescription p ( 1, 2, …, P ) is assigned to species k ( 1, 2, …, K ) in stand j (1,2, …, J) and 0 otherwise). The equations that characterize the optimization problem:

J : Set of stands ( j  = 1,2,3, …, 686 stands).

K : Set of species ( k  = 1,2, …, 6 tree species).

T : Set of periods in the planning horizon ( t  = 1, 2, …, 5).

P : Set of management schedules (prescriptions).

X jkp : binary decision variable which takes the value 1 if prescription p ( 1, 2, …, P ) is assigned to species k ( 1, 2, …, K ) in stand j (1,2, …, J) and 0 otherwise.

TWOOD : the total wood production over the planning horizon.

VTHIN kt : Volume of wood from thinning of species k in period t.

VHARV kt : Volume of wood from harvesting (clearcutting) of species k in period t.

Thin jkpt : Volume of thinning of species k in stand j in period t where prescription p is applied.

H jkpt : Volume of wood from harvesting species k in stand j in period t where prescription p is applied.

CARB : Average carbon stock over the planning horizon.

C kt : Carbon stock of each species k in period t.

C jk p t : Carbon stock in period t that results from applying prescription p on species k in stand j.

CORK : Total amount of cork produced over the planning horizon.

Cork t : Cork produced in period t.

Z jk p t : Cork produced in period t that results from applying prescription p on species k (in this case Cork species) in stand j.

EROSION : Total soil erosion (in ton) over the planning horizon.

erosion kt : total soil loss in period t from stands covered by species k.

F jk p t : soil loss in period t that results from applying prescription p on species k in stand j.

FIRE : The average fire resistance indicator in the planning horizon.

Rait kt : The total fire resistance indicator from species k in period t.

R jkpt : Fire resistance indicator in period t that results from assigning prescription p to species k in stand j . Values range from 1 (less resistance) to 5 (highest resistance).

BIOD : The average biodiversity score in the planning horizon.

Bio kt : The total biodiversity score from species k in period t.

B jkpt : Biodiversity indicator in period t that results from assigning prescription p to species k in stand j . Values range from 0 (bare land or no biodiversity) to 8 (highest level of biodiversity).

a jk : area (in ha) covered by each species k in stand j.

A : Total area of the landscape (ha).

Equation 1 represents the total wood production from all species over the planning horizon. This is computed by adding Equation 2 (volume from thinning) and Equation 3 (volume from clear-cuts). The last equation ( Equation 14 ) is used to ensure that a stand (and any species in a stand) is assigned only to one prescription over the planning horizon. The remaining equations represent the provision of other ecosystem services: carbon ( Equations 4 , 5 ), cork ( Equations 6 , 7 ), erosion ( Equations 8 , 9 ), fire resistance ( Equations 10 , 11 ), and biodiversity ( Equations 12 , 13 ).

The equations above define the integer program resource capability model used to generate the Pareto frontier of the forested landscape. The latter depicts trade-offs among ecosystem services such as wood ( TWOOD ), cork ( CORK ), biodiversity ( BIOD ), carbon stock ( CARB ), fire resistance ( FIRE ), and erosion (EROSION). The provision of the first five is to be maximized while erosion is to be minimized.

2.3.1 Wood flow constraints

The total wood production across consecutive periods was regulated by constraining the model

where TWOOD t is the total wood production in period t , and σ is the allowable fluctuation in percentage (20–25% was considered for the current case study).

2.3.2 Formulation of the adjacency constraints

The adjacency constraint limits the size of clear-cut areas resulting from the harvesting of contiguous (adjacent) stands. We limit the maximum clear-cut area to not exceed 50 ha (as declared by the Portuguese law for the Integrated Management System for Rural Lands). The path algorithm proposed by McDill et al. (2002) was used to generate the corresponding Area Restriction Model ( Murray, 1999 ). The algorithm starts by defining a binary variable Y jt , for each stand which takes a value 1 if it is to be harvested in period t and a value 0 if not. In order to apply the algorithm to our problem, this binary variable was created as a function of the original decision variable X jkp using Equation ( Equation 17 ) for pure stands and Equations ( Equations 18 , 19 ) for mixed stands:

where h jpt is a parameter that takes the value one if the assignment of prescription p to stand j involves a clear-cut in period t . Equations 18 , 19 stipulate that clear-cutting is considered only to stand j if all its species are subject to clear-cutting in the same period.

Afterwards, the path algorithm proceeds with the enumeration of minimal infeasible clusters C ∈ A + ( A + is a set of all minimal infeasible clusters, i.e., infeasible clusters that would become feasible if one stand is excluded from it) and prohibits cutting of contiguous stands exceeding the harvest limit, i.e., 50 ha:

Where|C| is the number of stands in the cluster.

Python code (Python version 3.11) was developed to enumerate minimally infeasible clusters ( Appendix I ). Respective equations (constraints) were generated for the whole case study area.

2.4 Decomposition approach and the generation of Pareto frontier

The large number of adjacency constraints (176,955) complicates the process of generating the Pareto frontier. Initial attempts aimed at solving a single objective problem (e.g., wood) did not produce an optimal solution even after 24 h. To address computational complexity issues, a strategy was implemented that involved subdividing the problem. A first try involving just two sub-problems had negligible impact on the computational complexity. Hence, the problem was partitioned into four sub-areas ( Figure 2 ), named East Paiva_1, East Paiva_2, West Paiva_1 and West Paiva_2.

Figure 2 . The four sub-areas and the border stands (stands bordering the sub-areas).

The sub-areas were created using ArcGIS, ensuring that the number of stands in each sub-area was roughly equal. Besides, efforts were made to minimize the number of stands bordering the sub-areas. This was done by selecting a boundary line that touched as few stands as possible. Nevertheless, to prevent the violation of the adjacency constraint along the border between the sub-areas, stands adjacent to this border were first removed from the sub-area problem and included in the set of border stands ( Figure 2 ).

Two different models were used for generating the Pareto frontier for each sub-problem. The first only considered Equations 1 – 16 while the second added the adjacency constraints, Equations 17 – 20 . The frontier was generated using the approach outlined in Borges et al. (2017) and Marques S, et al. (2021) . Each Pareto frontier provided information about the trade-offs between the criteria, which corresponds to the levels of provision of ecosystem services, e.g., wood, cork, carbon stock, biodiversity, fire resistance, and soil erosion, in the corresponding sub-problem. Afterward, we proceeded with the selection of points in each frontier, i.e., the selection of ecosystem service values to be provided by each sub-problem that included adjacency constraints. Points representing the Pareto frontier for each sub-problem were selected purposively to maintain consistency among sub-problems. These points aimed to approximate the average between the maximum and minimum values of the ecosystem services indicators. Achieving this consistency involved leveraging the tool used to generate the Pareto frontier, which provided minimum and maximum achievement levels for the optimized criteria. For each sub-problem, the tool retrieved these minimum and maximum values of the optimized criteria. From this range, a point positioned at (Max – Min) /2 was selected. The corresponding management plans were then used to constrain the models representing the border sub-problem. Specifically, we eliminated from the latter the stand-level prescriptions that had an adjacency conflict with the prescriptions in those management plans. We then developed a Pareto frontier for the border sub-problem ( Equations 1 – 20 ). Within all four sub-problems, the wood flow constraint allowed a 20% variation between consecutive periods (refer to Equations 15 , 16 ). However, to maintain the feasibility specifically for the border sub-problem, adjustments were made to the wood flow constraint.

2.5 The Edgeworth–Pareto hull (EPH) and its approximation

The approach we followed to generate the Pareto frontier involved approximating the actual Edgeworth–Pareto hull (EPH). The EPH is the envelope or boundary formed by the set of solutions that are not outperformed by other solutions. In integer optimization problems, it is important to note that the non-dominated points forming the EPH may not necessarily form a convex hull ( Marques S, et al., 2021 ). As a result, there is a need to approximate the EPH with a surrogate Edgeworth–Pareto hull (cEPH; see the visual illustration in Figure 3 ). The cEPH serves as an approximation of the non-convex EPH, allowing for a more tractable representation. In our research, we conducted an assessment of the accuracy of this approximation technique, evaluating how well the cEPH represents the original EPH. For this purpose, the retrieval and comparison of the values was done for six randomly selected points (just for the sake of illustration) representing different levels of the optimized criteria. Moreover, we also analyzed the impact of problem size (e.g., number of stands and decision variables) and complexity (e.g., with and without adjacency constraints) on the accuracy of the generation of the Pareto frontier.

Figure 3 . Visual illustration of the actual Pareto frontier (EPH), indicated in solid line, and the approximated surrogate frontier (cEPH), indicated in dashed line when two objectives are being optimized. The points (Z1–Z5) represent Pareto optimal integer solutions (Modified from Marques S, et al., 2021 ).

The computations were performed on a personal computer with an Intel ® Core ™ i7-4790 processor with a 3.6 GHz frequency and 20 GB memory, using the CPLEX(R) Interactive Optimizer 12.6.3.0.

3.1 Pareto frontier for sub-problems

By dividing the larger problem into sub-problems, it was possible to generate the Pareto frontier of each of the four sub-problems even for the case where they included adjacency constraints (i.e., the maximum harvest patch size). The frontiers depicted trade-offs among the optimized objectives: Total wood ( TWOOD ), Cork ( CORK ) carbon stock ( CARB ), erosion ( EROSION ), fire resistance ( FIRE ) and biodiversity ( BIOD ). The mean generation time for sub problems with adjacency constraints extended over 1,271 s, while the mean generation time was about 340 s if no adjacency constraints were considered ( Table 1 ). This is a significant improvement given that it was not even possible to generate Pareto frontier for the whole landscape without subdivision. The effect of constraints on generation time was more pronounced for problems with more decision variables ( Table 1 ).

Table 1 . Problem size and Pareto frontier generation time for the four sub-areas and border problem.

The tool we have used to build the Pareto frontier is capable of generating a variety of decision maps, depending on the number of criteria (ecosystem services indicators) under optimization. The challenge arises when trying to effectively convey these maps to readers, especially when dealing with more than three criteria. In our current study, we created a six-dimensional set of decision maps for a specific sub-problem, illustrating trade-offs among all six criteria (i.e., levels of provision of the ecosystem services; Figure 4 ). Within the six-dimensional map, each segment or section reflects varying values of the fire resistance indicator (displayed horizontally) and biodiversity score (displayed vertically). A specific segment or set of decision maps, based on a combination of fire and biodiversity values, highlights the trade-offs between carbon and timber at different levels of soil erosion (represented by different colors, each associated with a decision map). These decision maps show that an increase in timber production is associated with a reduction in carbon stock, particularly at higher levels, illustrating the trade-offs involved.

Figure 4 . Six dimensional set of decision maps, Pareto frontier, showing trade-off among ecosystem services, for the West Paiva_2 sub-area. TWOOD: total amount of wood harvested and thinned (10 6  m 3 ); CARB: carbon stock (10 4 ton); EROSION: the total soil erosion (10 6 ton); FIRE: the average fires resistance indicator (value range from 1 to 5); BIOD: the average biodiversity score; CORK: the total cork production (10 6 arrobas. Arroba = 14.7 kg).

To enhance readability and comprehension, subsequent interpretation and discussion of results for each sub-problem were conducted using three-dimensional decision maps, focusing on three ecosystem services ( Figures 5A – D ). The Pareto frontier, along with the associated decision maps for the four sub-problems, highlight the trade-offs between ecosystem services in each sub-problem ( Figures 5A – D ). The optimized criteria present a range of minimum and maximum values that vary across these sub-problems, likely attributable to differences in the total land area. Despite an overall similarity in trade-off patterns among the sub-problems, some disparities are noticeable between the East and West Paiva sub-problems ( Figures 5A – D ). Notably, the Eastern sub-problems (5A and 5B) exhibit a relatively steeper slope in the trade-off compared to their Western counterparts (5C and 5D), particularly at a higher level of the optimized criteria.

Figure 5 . Pareto frontier showing trade-offs between three ecosystem services in the case of East Paiva_1 (A) , East Paiva_2 (B) , West Paiva_1 (C) and West Paiva_2 (D) . TWOOD: total amount of wood harvested and thinned (106 m 3 ); CARB: carbon stock (10 4 ton); EROSION: the total soil erosion (10 6 ton). NOTE: the levels of other ecosystem services (e.g., BIOD, FIRE) are fixed.

3.2 Pareto frontier for the border problem: addressing the adjacency conflicts between sub-problems

Selection of a single point from the Pareto front of each sub-problem was undertaken, with these points indicated by a ‘+’ sign in Figures 5A – D . These points represent approximate average (of maximum and minimum) values of each optimized criterion ( Table 2 ). From these points, solutions, i.e., management plans were derived and used to generate the Pareto frontier for the border problem. The latter encompasses all stands in the landscape and yet considers only decisions to be made in the stands along the border ( Figure 6 ). All other stands are to be managed according to the solutions to the four earlier sub problems.

Table 2 . Values of the optimized criteria in each of the solutions selected from the four sub-problems.

Figure 6 . Pareto frontier showing trade-offs between ecosystem services in the case of the East Paiva_2 sub-area, without (left) and with (right) adjacency constraint. TWOOD-total amount of wood harvested and thinned (10 6  m 3 ); CARB-carbon stock (10 4 ton); EROSION-the total soil erosion (10 6 ton). The values of fire resistance and biodiversity score were fixed at 3.6 and 2.6 in both decision maps.

Using this process, the decisions to be made in the stands along the border are constrained by the management plans selected for each sub-problem. As a result, out of the 4,665 alternatives available for these stands ( Table 1 ), 883 were eliminated. The border Pareto frontier highlights thus the trade-offs among ecosystem services that result from the integration of the four management plans with the decisions to be made in the stands over the border ( Figure 6 ).

3.3 Approximation of the EPH and its accuracy

Results show that a relatively larger discrepancy (larger difference-in the values of the optimized criteria-between the actual EPH and the surrogate cEPH) was observed when constraints were added to the larger sub-problem (East Paiva_2) compared to the no-constraint counterpart ( Table 3 ). In the latter, the minimum and maximum percentages of discrepancy were 0 and 0.03 in the case of the EROSION criteria in point 1 and the case of the CARBON criteria in point four, respectively. On the other hand, when adjacency constraints were added to the problem, the minimum and maximum discrepancy percentages were 0.001 and 0.19, respectively, in the case of the value of the EROSION criteria in point one and the value of the CARBON criteria in point six. In both constrained and unconstrained problems, a higher discrepancy was observed in the case of the CARBON criteria, indicating the higher sensitive of carbon stock to changes in the number of decision variables or in the number of constraints as compared to other criteria such as wood production.

Table 3 . Solution of EPH and cEPH retrieved from six random points for East Paiva_2.

To examine how sensitive the approximation is with respect to problem size, the discrepancy was also evaluated for the smallest sub-problem, East Paiva_1 ( Table 4 ). It can be hypothesized that as the number of decision variables increases, the optimization problem becomes more complex, and it may be more difficult for the optimization solver to find the optimal solutions. With a higher number of decision variables, the number of possible combinations of the decision variables increases exponentially, making it more difficult to accurately generate the Pareto frontier curve. However, in this study, we did not find a significant difference in the discrepancies among solutions to the small and large problems.

Table 4 . Solution of EPH and cEPH retrieved from six random points for East Paiva_1.

This was also observed when we evaluated the discrepancy between the EPH and the cEPH solution for the border sub-problem, whose Pareto frontier was generated by retrieving solutions from the sub-problems. The result shows that the discrepancy between the actual feasible solution (EPH) and the one approximated by the Pareto frontier tool was very low ( Table 5 ).

Table 5 . Solution of EPH and cEPH retrieved from six randomly chosen points for the border sub-problem.

3.4 Impact of spatial constraint on ecosystem service trade-offs

In order to assess the potential influence of spatial constraints on trade-off curves and patterns, an in-depth analysis was conducted to scrutinize variations. This was done by taking the East Paiva_2 sub-area as an example and fixing the values of the fire resistance and biodiversity score at 3.6 and 2.6, respectively (basically the median values shown in the decision map) for both scenarios, i.e., with and without the adjacency constraints. Upon examining the resulting trade-off maps (depicted in Figure 7 ), a noteworthy observation emerged: the spatial constraint showed limited influence on trade-offs. Across both representations, the trade-off between carbon and wood quantity remained prominent, especially evident at higher levels of annual soil loss. This persistent trade-off signifies that the impact of the spatial constraint appeared to be minimal in altering this relationship.

Figure 7 . Pareto frontier showing trade-offs between ecosystem services in the case of the border sub-problem. TWOOD-total amount of wood harvested and thinned (10 6  m 3 ); CARB-carbon stock (10 4 ton); EROSION-the total soil erosion (10 6 ton).

However, a clear consequence of the spatial constraint was identified: it impacted the ecosystem services provision possibilities. As expected, the constraint visibly restricted the range of attainable wood quantities. While the spatial constraint impacted negatively the wood production, it did not influence the broader trade-off pattern between carbon and wood quantity at any level of soil loss. Consequently, this analysis suggests that decision-makers retain the flexibility to set specific targets for ecosystem service achievements while remaining coherent with harvesting area constraints imposed by the spatial considerations.

4 Discussion

Decomposing large problems into some sub-problems has been a common approach for dealing with the computational difficulties of solving large optimization problems (e.g., Hoganson and Rose, 1984 ; Borges et al., 1999 ). The application of this approach to generate Pareto frontiers is, however, limited to a few studies; e.g., see Riffo (2020) and Marques S, et al. (2021) . By following the approach proposed in Lotov (2015) , the study of Marques S, et al. (2021) has shown the potential application of the decomposition approach for generating Pareto frontiers of multiple ecosystem services of a forest landscape. Our study extends these findings. It proposes an approach to address the fact that it is not computationally feasible to build the Pareto frontier of large landscape-level problems with adjacency constraints and that the decomposition approach proposed by Marques S, et al. (2021) is not capable of addressing adjacency across sub problems. The main success of this research is the demonstration that it is feasible to generate Pareto frontiers displaying the trade-offs between ecosystem services in the case of very large forest management problems that include adjacency constraints.

We opt for a comprehensive subdivision of the landscape-level problem, followed by a systematic workflow to generate the Pareto frontier for the entire landscape. This is achieved by incorporating the plans selected for each sub-problem and considering a restricted decision space for border stands. Specifically, this restriction entails the removal of management alternatives for border stands that are in conflict with the plans selected for the sub-areas. Though this approach may result in sub-optimal solutions, it effectively integrates spatial constraints into a Pareto frontier method. Despite sub-optimality (“sub-optimality” in our context refers to the compromise made in achieving the global optimal solution; given that our approach hinges on solving sub-problems individually, the final solution represents a compromise based on these sub-problem solutions), the study has illustrated how one can incorporate spatial constraints into a Pareto frontier method. Our approach may thus provide useful information on the trade-offs among different management objectives when adjacency conflicts are a concern. This in turn can be used to inform forest management decisions. By understanding the different trade-off patterns that emerge based on different management decisions, forest managers can make more informed choices about managing forest resources while complying with harvest regulations.

Previously, to the best of our knowledge, there are no results on the generation of Pareto frontiers when spatial constraints are included. Adjacency constraints pose a computational challenge to the analysis of trade-offs between ecosystem services. The approach implemented in the current study suggests that while ecosystem service supply possibilities may decrease as a consequence of the adjacency constraints, the trade-offs pattern themselves remain largely unaffected. This insight by our innovative approach underscores the importance of understanding how spatial considerations may impact those supply possibilities, while affirming the underlying trade-off patterns in multi-objective optimization scenarios. This insight may be useful to forest managers. It suggests that they might combine information provided by Pareto frontier approaches that ignore spatial constraints with information about the impact of the latter on supply possibilities provided by standard spatial optimization approaches (e.g., exact and heuristic (genetic algorithms, simulated annealing approaches) Baskent et al., 2020 ).

An important aspect that merits discussion is what are the advantages and disadvantages associated with our approach. On the one hand, our approach offers distinct advantages in cases where solving the entire landscape problem as a whole is computationally infeasible. For instance, even in the context of single-objective optimization, obtaining a solution for the entire landscape was often beyond the computational limits, requiring extensive computation times that exceeded 24 h. A vast body of literature has highlighted the large computational burden required to solve the resulting combinatorial optimization problems (e.g., Weintraub and Murray, 2006 ). Our study reaffirms this, shedding light on the computational complexity of the resulting mixed-integer problems, especially when one has multiple objectives.

To address this computational bottleneck, we proposed to break down the master problem into more manageable sub-problems. However, grappling with spatial constraints complicates this straightforward decomposition. Merely segmenting the problem and solving them independently poses challenges, primarily because these sub-problems share units or variables, potentially intertwining their solutions. There is no guarantee that solving one sub-problem adheres to the global spatial constraint, complicating the aggregation of solutions. Recently, Meselhi et al. (2022) delved into optimization strategies, proposing a decomposition approach involving overlapping sub-problems sharing certain variables. Their methodology tackled these sub-problems independently, employing three strategies-information sharing, mean value adaptation, and random selection-for handling overlapping variables. However, their approach does not seamlessly align with multiple objective optimizations, particularly in scenarios encompassing spatial constraints where units are interconnected across adjacent stands and clusters. While this avenue could merit exploration in future research, our approach of removing stands that share borders between sub-problems has shown to be a practical method of adhering to spatial constraints. This approach aims to navigate the spatial intricacies by eliminating stands that straddle the borders between sub-problems, mitigating the challenges posed by spatial constraints in multi-objective optimizations.

However, there are inherent disadvantages and limitations that we need to acknowledge. First, the removal of management alternatives from border stands due to adjacency conflicts may inadvertently introduce bias and impact the optimization of the master problem objective function. Second, quantifying the exact impact of these removed alternatives can be a complex undertaking, warranting further research. Lastly, the approach’s sensitivity to different sub-divisions may lead to divergent solutions, potentially undermining its robustness in different scenarios. It is crucial to recognize the potential biases introduced by the removal of management alternatives due to adjacency conflicts and to further investigate the exact implications of these removals on the optimization process.

Regardless of the problem size and whether or not there is a need to decompose a large problem, generating the Pareto frontier for the integer-type optimization problem is further complicated by the fact that the feasible domains (integer solutions) are disconnected, making it nonconvex. As a result, Pareto frontier generations are based on the approximation of the EPH ( Lotov et al., 2004 ; Lotov, 2015 ). A study by Burachik et al. (2021) applied for a small problem found insignificant differences between the approximated and real optimal solution, and by Marques S, et al. (2021) applied for a larger forest management problem also found acceptable discrepancies. In the current study, even though the discrepancies were found to be relatively higher for some ecosystem services than the previous studies (might be related to the nature of the problem or of sensitivity of the criteria being optimized), the approach was still able to provide a reasonable approximation.

An interesting finding in this regard is the fact that the accuracy of the approximation varies depending on the characteristics of the problem, such as the presence of constraints. For larger problems with many decision variables, adding constraints led to a larger discrepancy between the surrogate solution and the Pareto frontier solution. We assume that adding constraints reduces the feasible region and could make the optimization problem more complex and may make it more difficult for the solver to find the optimal solution. Furthermore, the study also found that the level of discrepancy did not vary significantly between small and large problems, which suggests that our approach is able to handle problems of different sizes reasonably well ( Marques S, et al., 2021 ). The fact that the accuracy of the approximation is influenced by problem characteristics, particularly the presence of constraints, underscores the need for robust optimization techniques capable of handling diverse problem sizes and complexities.

Our study highlights further that the impact of spatial constraint in forest management planning optimization problems is more pronounced when the latter has a larger number of decision variables. Nevertheless, the complexity of the solution process may vary with the algorithm used to formulate the spatial constraints (path algorithm was used in our study). Future research should explore the potential for using different algorithms such as the bucket algorithm, the clique approach, branch and cut algorithm etc. ( Constantino et al., 2008 ; Könnyu and Tóth, 2013 ; Constantino and Martins, 2018 ) to enhance the efficiency and effectiveness of landscape-level optimization in forest management planning.

5 Conclusion and future research directions

In conclusion, our study sheds light on the critical issue of spatial constraints in forest management and optimization. Spatial constraints pose a significant challenge in effectively balancing multiple objectives in forest management planning, and our research tackles this challenge head-on. The contribution of our study lies in our approach to decomposing large forest management optimization problems into smaller, more manageable sub-problems, and depict trade-offs among multiple ecosystem services. The information about these trade-offs is important to stakeholders (e.g., Tóth et al., 2006 ; Borges et al., 2017 ; Marques S, et al., 2021 ), namely in the case of forested landscapes that involve several decision-makers. As highlighted by these authors, it supports the development of participatory negotiation processes to come up with consensual ecosystem services target levels.

This partitioning not only ensures the adherence to harvest patch size constraint but also effectively addresses the complexities of spatial constraints. Moreover, our research successfully approximates the EPH with remarkable accuracy, although it is worth noting that spatial constraints can slightly increase the discrepancy between approximated and actual Pareto optimal solutions. While we acknowledge the limitations and challenges associated with our approach, from a management perspective, our study provides practical solutions and valuable insights for forest planners to design effective strategies tailored to meet both ecological and economic objectives while addressing spatial harvest regulations. Moreover, the practicability of the use of the Pareto frontier tool by AFVS and relevant stakeholders has been demonstrated by several authors (e.g., Borges et al., 2017 ; Marques S, et al., 2021 ). This research highlights thus the potential for practical use of this tool to address emerging forest ecosystem management problems that include spatial constraints. Its effectiveness will rely on outreach strategies as outlined by Borges et al. (2017) and Marques S, et al. (2021) . Future work will focus on its use to address similar problems in other contexts.

An important point for future improvement of the proposed approach is that the partitioning of the problem into sub-problems may not be straightforward, as it can be difficult to determine how to partition the landscape in a way that is both meaningful and effective for the optimization process. Moreover, as the optimal solution for the border stands depends on the specific solutions generated for the sub-problems, the final solution is not robust. Therefore, new approaches need to be developed that do not need partitioning or where the partitioning is optimal. Neural network-based technique and reinforcement learning approaches that have recently been applied to the solution of large integer problems (e.g., Tang et al., 2020 ; Huang et al., 2022 ) could be possible avenues for future research. Finally, our study, while providing valuable insights, does not consider climate change scenarios. When process-based models are available to project forest growth under climate change in the study area’s forested landscape, research may explore these scenarios for a more comprehensive understanding of their potential influence on trade-off patterns and the respective computational complexities. Nevertheless, our approach to generate Pareto frontiers can be as useful and applicable in this context as it is independent of the models used to make projections.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

DA: Conceptualization, Formal analysis, Investigation, Methodology, Software, Writing – original draft, Writing – review & editing. SM: Methodology, Software, Supervision, Writing – review & editing. VB: Methodology, Software, Visualization, Writing – review & editing. JR: Conceptualization, Methodology, Writing – review & editing. AW: Supervision, Writing – review & editing. MC: Methodology, Software, Supervision, Writing – review & editing. CL: Methodology, Writing – review & editing. JB: Conceptualization, Formal analysis, Funding acquisition, Methodology, Software, Supervision, Writing – review & editing, Writing – original draft.

The author(s) declare financial support was received for the research, authorship, and/or publication of this article. This study was partially funded by the Forest Research Centre, a research unit funded by Fundação para a Ciência e a Tecnologia I.P. (FCT) by project reference UIDB/00239/2020 (DOI identifier 10.54499/UIDB/00239/2020) and the Ph.D. grant of Dagm Abate (UI/BD/151525/2021); in the scope of Norma Transitória—DL57/2016/CP1382/CT15 (UIDB/00239/2020); as well as by the projects ref. H2020-MSCA-RISE-2020/101007950, with the title “DecisionES - Decision Support for the Supply of Ecosystem Services under Global Change,” funded by the Marie Curie International Staff Exchange Scheme and ref. H2020-LC-GD-2020-3/101037419, with the title “FIRE-RES—Innovative technologies and socio-ecological-economic solutions for fire resilient territories in Europe,” funded by the EU Horizon 2020—Research and Innovation Framework Program,” and the project MODFIRE—A multiple criteria approach to integrate wildfire behavior in forest management planning with the reference PCIF/MOS/0217/2017.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The author(s) declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision.

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Supplementary material

The Supplementary material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/ffgc.2024.1368608/full#supplementary-material

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Keywords: spatial-optimization, integer-programming, forest management, Pareto frontier, ecosystem services

Citation: Abate D, Marques S, Bushenkov V, Riffo J, Weintraub A, Constantino M, Lagoa C and Borges JG (2024) Assessment of tradeoffs between ecosystem services in large spatially constrained forest management planning problems. Front. For. Glob. Change . 7:1368608. doi: 10.3389/ffgc.2024.1368608

Received: 10 January 2024; Accepted: 25 March 2024; Published: 11 April 2024.

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Copyright © 2024 Abate, Marques, Bushenkov, Riffo, Weintraub, Constantino, Lagoa and Borges. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Dagm Abate, [email protected]