Which of the following best explains the spatial patterns illustrated in von thünen’s model?

5.1 Von Thünen and d’Alonso’s monocentric and polycentric models

D’Alonso’s model, derived from the von Thünen model and applied to a city rather than to the countryside, has been programmed in Mathematica by R.J. Brown [BRO 05a, BRO 05b]. Its graphic result shows the structure of a concentric system within a monocentric city. The author identifies five kinds of land uses. At the center, in the Central Business District, commercial activities and banking are predominant. Then, after a belt of small industries, we can find a residential pocket, encircled in turn by industries before the beginning of a rural section. We would only have to change the names and some of the parameters, and then add a sixth concentric area, in order to adapt this program to von Thünen’s initial model and, therefore, analyze the distribution of farmland around a market.

Figure 5.1 shows the initial situation. If we click on the “Show table” box, the program can even show us the area and income corresponding to each of the five activities. With the instruction Manipulate[], geographers can modify several parameters. They can change the initial conditions by dragging one or more sliders. For example, they can make the residential sector or the first industrial belt more or less significant. According to these inputs, they obtain a new diagram of the urban structure. This dynamic contribution makes it much easier to understand these geographical phenomena. Besides this representation of the city, the program yields the areas and income for each belt.

The author of the previous model, R.J. Brown [BRO 05a, BRO 05b], has also developed another equally interesting Wolfram Demonstrations Project program that simulates the formation of multiple centers, the appearance of edge cities, around a metropolis. As in the previous case, this small program allows us to display the dynamics of a city which this time, however, is polycentric. The urban fabric is represented in three dimensions. Users of this program can create one to three new edge cities. Moreover, this program allows us to vary the distance between the main center and these secondary centers, to locate the latter by modifying a direction parameter, and even to link them within a conurbation that would appear if a circular transport corridor, like a railway network or a road system similar to the ring road in Paris, were built. In spite of its simplicity, this little program is quite instructive. Figure 5.2 illustrates a stage of this appearance of edge towns around a city represented by an urban peak.

As with the previous program, if we drag certain sliders, a conurbation can form or break apart according to the values considered.

Water

Spatial management of water resources involves both surface water and groundwater.

Surface water flows through river, canal, and irrigation systems across landscapes, often with considerable variation in flow within and across years. Spatial management of water flows in river and canal systems include decisions about the amount and location of water diverted or withdrawn from the system and control over the amount of water lost as it travels through these systems. In these spatially networked systems with water flowing unidirectionally, water extraction upstream reduces instream flows and reduces water availability for downstream users. The shadow value of water in a canal system varies over location, which implies that crop choices will also vary across location on a canal irrigation system in a similar manner to crop choices in von Thunen models. Spatial management of water resources involves determining and enforcing rules about the location and quantities of water withdrawal. The development and implementation of water infrastructure systems requires characterizing the spatial flows of water in addition to the spatial distribution of water demand. The spatial characteristics of the infrastructure system are important due to the high costs of the infrastructure to move water across space and store it in locations on the landscape.

Groundwater also requires spatial management. Groundwater can flow in specific directions similar to the flow of surface water in river systems, although much more slowly. The spatial movement of groundwater should inform the location of wells. In a spatial externality, the wells to pump groundwater cause localized depressions in the water table. That lower water table implies longer pumping distances for nearby wells. The optimal spatial allocation of groundwater pumps reflects this spatial externality, which itself is a function of the transmissivity of the rock and the speed and quantity of the pumping. This spatial management interacts with the dynamic issues of timing of water demand and rates of groundwater recharge.

5.5.4 Modeling of Land Use

The planning for land use in cities is a complex multiparameter challenge. As land use decisions critically impact on environmental issues, it is important to control land use in order to mitigate air, water, and land pollution, provide enough land for green and open spaces, and conserve/restore wetlands and coastal resources. Several models of urban land use have been developed, which are characterized by different level of complexity and include among others [12] (Fig. 5.16):

Von Thunen's model (Fig. 5.16A): It is the oldest land use model and was developed by Von Thunen in 1826. It considers a central place, which is the central market, and its concentric impacts on surrounding land uses. The relative cost for the transport of agricultural products to the central market is the one that determines the use of agricultural land around the city. As a result, the most productive activities will compete for the land that is located closer to central market, while the activities which are not so productive will be located further away from the market center. Consequently, intensive farming will be located closer to the city center than forests. The main assumption of Von Thunen's model is that agricultural land use is formed as concentric circles around the central market; the latter consumes all the surplus production, which must be transported from the rural areas to the market. The model was developed in 1826 and was first applied to analyze the agricultural land use patterns in Germany of the 19th century. The main drawback of the model is that it does not consider differences in local, physical conditions since it has been developed in an isolated state.

The concentric zone model or Burgess model (Fig. 5.16B): This model was one of the first attempts to explain the distribution of social groups in urban areas. The model considers that there is a correlation between the socioeconomic status (mainly income) of households and the distance from the Central Business District (CBD). The further away the household is from the CBD, the better the quality of housing, but the longer is the time taken to commute. This way concentric circles (zones) are developed around the CBD which is Zone A. Zone B is adjacent to the CBD, is known as zone of transition, and includes industrial activities that are located there in order to take advantage of nearby labor and markets as well as transport facilities such as ports and railways. Zone C is close to the industrial areas and includes the poorest housings which are usually occupied by first-generation immigrants. Zone D is a residential zone that is dominated by the middle class. It has the advantage that it is located relatively close to the industrial zones of employment (ie, zones A and B). Zone E consists of high class and expensive housing in a rural, suburbanized setting. This model was first applied to explain the land use of the city of Chicago in 1925 and can still be reflective of the land uses of a city. The main criticisms against this model is that it is too simplistic, reflecting the urban characteristics which were observed 50–100 years ago. It was developed at a time when the American cities were growing very fast. Furthermore, the model was developed for American cities and has limited transferability. It assumes a spatial separation of place of work and residence, which was not generalized until the 20th century.

The Hoyt model (Fig. 5.16C): It was developed by the economist Homer Hoyt in 1939 and is a modification of the Burgess model. Although the Hoyt model accepts the notion of a CBD, it considers that all the zones expand outward from the CBD rather than in concentric zones; the zones are supposed to follow the routes of highways, railways, underground tube, and other transport means. Consequently, the effect of direction and time was also added to the impact of distance, which was overlooked by the concentric models. The land use often follow transport arteries, such as railway lines, resulting in the development of sectors. Thus, cities will grow along major transport axis. The model assumes that cities tend to grow in a pattern that resembles a wedge, starting from the CBD and growing outward. The low-income households will be concentrated close to industrial zones, while the middle and high income will be located further away. This model recognizes the tight connection between transportation arteries and land uses and is applicable to several cities in the United Kingdom. Its main limitation is that it is does not consider private cars, which allow the transport from land that is further outside and is not well connected to the public transportation means.

The multiple nuclei model (Fig. 5.16E): It was developed by Harris and Ullman in 1945, and, as its name implies, it assumes that cities grow through the gradual integration of several separate nuclei in the urban spatial structure. Although the city may have initially developed with a CBD, other smaller CBDs develop in the outskirts of the city. As a result, nuclei are formed in other parts of the city apart from the main CBD. The model is suitable for application in large cities and also takes into account the increased mobility given by private vehicles. The multiple nuclei may develop and expand for several reasons which include (1) the need to have suitable transport means (eg, ports, railways) for certain industrial activities, (2) the need to move to locations where land and house rents are cheaper, (3) the clustering of certain activities for mutual benefits and convenience for the inhabitants such as hospitals with pharmacies and Universities with bookstores, (4) the need for certain activities to be placed in different locations such as industrial activities and hospitals, and (5) benefits resulting from activities placed close to each other such as factories and residents. The model has some limitations since it makes assumptions of land being flat, even distribution of resources, transport costs, and distribution of people in residential areas which are simplifications.

Hybrid models (Fig. 5.16D): These models attempt to consider concentric, sector, and nuclei arrangements of different processes in order to account for land use in cities. Consequently, hybrid models integrate the concentric arrangement for CBDs and sub-centers with the sector arrangement for transportation in order to develop the land use pattern. Using hybrid models it is possible to account for the change of the urban spatial structure; hybrid models integrate the various spatial effects of transportation on land use giving also the time dimension. The city can develop as nuclei in certain locations due to specific conditions, but also along the transportation routes.

The land market model: It is a pure land economics-based approach, where the cost of land, supply, and demand are the drivers for land use. The higher the demand for the land, the higher will be its cost. The principle that is followed is that towards the center of the city, less land is available (ie, limited supply) and at a higher cost. As one moves toward the suburbs more land becomes available (ie, more supply) and the cost reduces. The accessibility and the ease of transportation are factors that significantly impact on the land rent and thus on its use. Within each city there are different categories of activities, and each one wants to occupy land and is willing to pay a specific price to acquire it (or rent it). However, this market-based approach on land use is challenged by the structural modification of modern large cities.

Cellular automata models for land use: They consist of dynamic models for land use applications. In these models space is divided into finite cell grids. Each cell grid represents a finite land unit. Certain land uses are defined for the different cells; when the use of one cell (ie, piece of land) is about to change, transition rules are applied. These models can dynamically and realistically simulate land use with a high level of detail. However, adequate and reliable data are required to apply them. The models can be integrated with Geographic Information Systems (GIS) for user friendly representation.

Regardless of the model that is used to guide decision making for land, it is recognized that this decision needs to be balanced and results from the trade-off of several, often conflicting, parameters. Land is finite but there are many different potential options for activities that can take place on each piece of land. Land is an open space that needs to integrate territorial cohesion, spatial planning, urban/rural diversity, housing, and transport. Land use needs to be productive, in the sense, that it must be used to extract minerals, to produce crops and feed the population, and produce crops that are used to produce bioenergy. Land has several functions including the protection of nature and ecosystems, for recreation, and flood mitigation. Proper land use can decrease greenhouse gas (GHG) emissions and can be used as a carbon storage tank mitigating the adverse impacts of climate change. It can also serve for adaptation measures to climate change [1].

Theory

Taking this approach, initial developments, during the 1950s and 1960s, can be viewed in one of two ways: either as introducing geography into hitherto aspatial economic theory or else using economic theory to provide a deductive framework for a hitherto atheoretical, essentially inductive, economic geography. A considerable amount of energy has been expended discussing the appropriate characterization of this process. However, the outcome does not appear to be in dispute. The resulting spatial theory was, and continues to be, strongly associated with formal mathematical models. This approach to the treatment of spatial economies traces its roots back to von Thunen's model of the isolated state. von Thunen was concerned with the role that yield and transport costs played in determining patterns of agricultural land use around cities. His approach to modeling determinants of this land use was to start with a number of simplifying assumptions. A city in an isolated state surrounded by wilderness removes the need to think about links to other places. A flat featureless plain means that farmers involved in the same activity would be equally productive wherever they are located, removing any role for first nature geography (i.e., differences in the physical environment). Farmers ship their produce straight to market (literally – no transport network here) but incur transport costs to do so. Finally, farmers locate so as to maximize their profits. This simple and highly stylized model leads to the well-known von Thunen rings with different activities occupying clearly defined rings around the city. The exact detail of what is produced, where, is less interesting than the fact that this ordered pattern is consistent with observed patterns of land use. From a theoretical point of view, the key point is that this ordered pattern emerges from the operation of competitive land markets without any coordination on the part of farmers. More than 100 years later, in the 1960s, the Alonso–Mills–Muth model (re)formalized these ideas to explain why, within a city, land values and population densities decline as one moves away from a central business district.

Of course, as with any stylized model, these theories of land use can be subject to criticism. Three issues in particular prove key in understanding further developments. First is the problematic assumption of the existence of a single center. Second is the fact that accessibility to this center is the only factor that explains urban structure, leaving no role for spatial interactions between individuals and firms. Third is the empirical observation that the theories may work quite well as models of land use, but they do not function so well as explanations of changes in land use. The reaction to these criticisms by different groups from the 1970s onward is informative. Geographers turned increasingly toward other social sciences and away from the quantitative geography that had hitherto overlapped extensively with regional science. The reaction from regional scientists was also to look to other disciplines, but in the sciences and not the social sciences. Drawing on social physics, the interaction between individuals was modeled mathematically using behavioral assumptions constructed from analogies with the laws governing the behavior of particles in physics. Alternatively, individual interactions were modeled using theories of mathematical ecology with animals and plants replacing particles as the basis for human behavior. A third group of urban and regional economists took the middle road, continuing to develop formal mathematical models which incorporated interaction between individuals but drew on economic and social theories of individual behavior. A similar story played out in another key area: that of location theory.

Alfred Weber (formalizing and publicizing ideas from Laundhart) provided an early model of industrial location. In the spirit of von Thunen, a number of simplifying assumptions make the problem tractable. In the simplest case, firms combine two inputs in fixed proportions to produce a final good. The two inputs are available in locations A and B, while the final good must be sold in the market at C. Transporting inputs or outputs between locations is costly. The assumption that firms face perfect competition (so prices do not depend on firm decisions) combined with the other assumptions on fixed inputs and transport costs reduces the firm's profit maximization problem to finding the location where total transport costs are minimized. The model can be complicated to allow for transhipment costs, new source of supply, etc., and (depending on the degree of complexity) algebra or algorithms solve for the firm's location decision allowing an understanding of the influence of factor prices, changes to transport costs, etc., on location. Extensions, by Moses, drop the assumption of fixed-proportion technologies allowing firms to substitute away from expensive inputs. This approach to the industrial location decision has had some success as an empirical model for explaining the location decision of particular firms, but it is less satisfactory as a broad theory of location for two key reasons. First, the simplifying assumption of perfect competition ignores questions of increasing returns to scale and of imperfect competition which give firms spatial monopoly power. Second, the theory is only partial. It can explain the location of particular industries given the location of the market, but, as with land-use theory, it cannot explain the location and existence of that market. Parallel developments in models of spatial competition, notably the work of Hotelling, addressed the first criticism. The second was addressed by attempts to provide a general equilibrium theory of location. This search for a general equilibrium theory has been a key objective of regional science from its foundation.

Early models, centered around the idea of central places, attempted to explain the spatial distribution of economic activities within an urban hierarchy. Christaller provided the first formulation by asking how a hierarchy of activities (in terms of the size of their market area) could be distributed to ensure that an evenly distributed rural population had access to all goods. The answer involved a series of hierarchical cities with nested market areas such that a location where a particular good is available also supplies all goods with smaller market areas. Whereas Christaller's central place theory drew heavily on empirical observation and inductive reasoning, Losch provided microeconomic foundations with market areas derived from consideration of the behavior of individual firms. Losch recognized that space meant that these firms would exercise some monopoly power (contrast Weber) and that this monopoly power would be limited by entry of other competing firms. However, lacking the necessary mathematical model of imperfect competition, closing the model in the general equilibrium case required ad hoc assumptions on the distribution of population and the assumption that all firms chose to locate at a common metropolis. One problem is that the resulting spatial distribution generates many inconsistencies with the underlying behavioral assumptions and so is not a true general equilibrium of the model. More importantly, Losch derives the efficient pattern, not the pattern that emerges from a decentralized decision-making process. Isard, in his seminal book, introduced the work of these German scholars to an English language audience as well as formalizing the microeconomic foundations of these approaches to location.

That book, and subsequent volumes, one on the search for a general theory and the other on research methods essentially created the field of regional science. Fairly quickly, however, this new field reached the crossroads already described above for the theory of land use. Economic geographers reacted against abstraction with increasing emphasis on context, contingency, and situation. Economists focused on issues of spatial competition and the importance of spatial interaction in determining location patterns, but restricted themselves to the problems that were amenable to analysis based on behavioral assumptions drawn from mainstream economics (eventually, via Krugman's new economic geography – NEG – this would lead to the first general equilibrium economic theory of location). Regional scientists either turned to increasingly complicated partial equilibrium theories of firm location or worked on developing a mixture of abstract, mathematical, and general equilibrium models. The latter drew increasingly on analogies from the hard sciences. This story, of initial engagement with other social scientists (particular geographers and economists) followed by a period of increasing abstraction and progressive disengagement is repeated across other theoretical areas such as transport modeling or migration analysis. Some might argue that a nascent reengagement with economics (on location theory) and geography (on geographic information systems – GISs – and spatial data analysis) is underway. Before considering this, attention is turned to the other key plank of work in regional science – the development of a methodological toolbox for regional and urban analysis.

Space matters: from regional spaces (e.g. peri-urban) to polarization in landscapes

Notwithstanding advances, the spatial dynamics of SI/EI are overlooked to a significant extent. General formulations tend to focus solely on site-based SI/EI, ignoring spatial considerations. Indeed SI/EI can appear to occur a-spatially, thereby obscuring broader, and meaningful, spatial patterns of land use. Recent studies have begun to emphasize the local variation of SI/EI as generally context-specific and location-specific [5••] and as place-dependent [18••,19••]. In rethinking the scope of this approach, new research is used to argue that intensification must be conceptualized spatially. This rethinking involves considering not only its place-level spatial characteristics but also, and importantly, the spatial relations of distinctive interactions integral to intensification with land use and food systems at a meso-scale (see also Ref [20]). Emphasis is on the ways that spatial interactions contribute to differentiated spaces of intensification at regional and landscape scales (Figure 1). The discussion highlights the spatial dynamics integral to current and future intensification, as well as its inverse process, disintensification, which is linked to de-agrarianization and land abandonment [21]. In our determination the spatial interactions of intensification/disintensification are central to globally consequential changes involving land use and agri-food systems (see also Ref [22]).

We first draw attention to both region-scale processes in spaces that extend from peri-urban to intermediate-distance and remote rural (Figure 1: areas H, M, and L) along with the polarization trend evident within regional landscapes that is described below. Our first emphasis is the intensification and disintensification occurring within and among these differentiated region-scale spaces (H, M, L) driven through: (i) distance-related factors that extend from urbanization and the role of peri-urban spaces to distintensification in remote rural locales; (ii) interactions of key factors (e.g. labor, capital, knowledge systems) within and among these spaces; and (iii) smallholder livelihood strategies, including gendered links to migration (a focus of the next section). Our conceptual framework highlights the role of regionally differentiated spaces but does not indicate spatial regularities that are structured solely as a function of distance. The latter would suggest comparison to the distance-related, concentric rings of the von Thünen model, which overlooks uneven development occurring through social dynamics, lowered transportation costs, and highly mobile capital investment among other factors.

Urban and peri-urban spaces of land use and agri-food systems — within H in Figure 1 — are expanding significantly in a world of continuing rapid urbanization and increasing urban-majority populations. Globally urbanization exerts powerful influences on land-use and resource-use spaces. This occurs in both proximate peri-urban locales and more distantly through the effects of long-distance connections, known as telecoupling, that preclude any assumption of simple or linear gradients per se [23–26]. Urbanization shapes land use and agri-food systems through agricultural prices, trade, markets, policies, and sociocultural changes. It generates expanding networks of consumption through agri-food systems that rely on both relatively proximate spaces and long-distance telecoupling to remote land use sectors [26,27]. Urbanization and other drivers of landscape change at the regional scale thus exert a pivotal influence while reinforcing the consideration that ‘space matters’ in the social–ecological processes and patterns affecting SI/EI prospects.

Peri-urban spaces in particular are characterized by pronounced transitions, which may involve a shift to non-agricultural use [28] or significant agricultural intensification including plot-level spaces as small as home gardens (in the H area of Figure 1). Expanding peri-urban areas, together with corresponding urban spaces, need to be integrated into global SI/EI analysis. So do the intermediate-distance spaces from a city, which are often the sites of intensification in more exclusively agricultural economies (M in Figure 1). Agricultural intensification tends to concentrate in prime growing areas at certain intermediate distances, as illustrated by the Central Valley of California, China's Xi or Pearl River valley, and the western South American valleys between Colombia and Chile. This region-level patterning is often reinforced through the role of institutions such as growers’ advocacy groups and development associations. For example, intensification influences of non-governmental organizations (NGOs) and government agencies, whose political affiliations range from neoliberal to neocollective, are often concentrated in these intermediate zones (e.g. in Bolivia; [29]). In such intermediate-distance spaces of intensification, agriculture plays a greater role in household and community livelihoods.

Many remote rural locations (L in Figure 1) show notable agricultural disintensification, albeit with potential for pockets of local intensification including agrobiodiversity that can contribute to food security [30]. The trend of remote-rural spaces toward disintensification is evident in Latin America, Asia, North America, and Europe. It is less so in African countries even though they share characteristics of dynamically changing livelihood strategies, increased migration, and the re-gendering of land and agri-food systems amid a new rurality — see next section.

We draw attention additionally to the polarization of land use within regional landscapes (i.e. within H, M, or L as shown in Figure 1). This spatial dynamic encompasses changes over time (T0 and T1 in Figure 2) combining local intensification with local disintensification in a single landscape. Neoliberal economic reforms from the mid-1980s have deepened smallholder integration into global markets, inducing the transformation in smallholder land use described as the new rurality. In a generalized pattern, local intensification occurs in areas conducive to mechanization or otherwise capitalized agri-food locales. Adjoining areas that are less productive for food cropping (e.g. steep slopes, rocky soils) simultaneously undergo active disintensification. Local disintensification typically occurs in areas characterized as marginal, on land that produces products of limited market demand, or set aside as conservation areas or reserves. The pattern of within-landscape polarization involving both intensification and disintensification is increasingly characteristic of countries of Latin America [22] and Europe [31••].

While such polarizing landscapes hold considerable potential for SI/EI objectives, disintensification may not strengthen ecosystem sustainability. For example, an increase in an area's vegetative cover can enhance biodiversity or conversely, reduce it, if disintensification favors expansion of non-diverse invasive species. The associated reduction or loss of cultural funds of knowledge linked to local land use and agri-food systems can also lead to negative environmental consequences, notwithstanding vegetative regrowth [32]. Other social–ecological processes, such as soil erosion, may improve or decline. One pertinent negative example is the cessation of soil conservation measures, such as farm terraces, when disintensification results in the abandonment of labor-demanding management systems on marginal lands [33]. Another example of deterioration amid disintensification concerns the reduction or loss of common property institutions and resource management. In such instances disintensification can also fundamentally rupture the interconnected spatial complexity of the agrarian landscape mosaics. Resulting landscape configurations become ecologically simplified and less resilient, thereby undermining the benefits otherwise derived from ‘land-sparing’ and ‘land-saving’ strategies [34,35].

Summarizing the above, our findings highlight the importance of non-linearities and thresholds in intensification and disintensification at the scales of regional spaces and landscapes. Globally important spatial patterns of the region-scale differentiation and landscape-scale polarization of intensification/disintensification are rooted in the changing livelihood strategies of individual households and communities [36,37•]. Of particular significance is the identification of potential tipping-points in these processes. We therefore extend our general conclusion to the non-linearities and thresholds of potentially influential tipping-point effects at the household-level and community-level as shown in Figure 3. Here we distinguish basic contrasts in the trajectories of both intensification-related and distintensification-related changes in land systems. Bifurcated trajectories of the intensification of land systems, for instance, can result from pathways that diverge between trends toward sustainable agri-food systems including agrobiodiversity (upper branch) versus deteriorating quality of agri-food systems (lower branch).