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INTERNATIONAL REGIONAL SCIENCE REVIEW 27, 3: 247–270 (July 2004) 10.1177/0160017604266026 Walker / THEORIZING LAND-COVER INTERNATIONAL AND LAND-USE REGIONAL CHANGE SCIENCE REVIEW (Vol. 27, No. 3, 2004)

ARTICLE

THEORIZING LAND-COVER AND LAND-USE CHANGE: THE CASE OF TROPICAL DEFORESTATION ROBERT WALKER

Department of Geography, Michigan State University, East Lansing, MI, [email protected]

This article addresses land-cover and land-use dynamics from the perspective of regional science and economic geography. It first provides an account of the so-called spatially explicit model, which has emerged in recent years as a key empirical approach to the issue. The article uses this discussion as a springboard to evaluate the potential utility of von Thünen to the discourse on land-cover and land-use change. After identifying shortcomings of current theoretical approaches to land use in mainly urban models, the article filters a discussion of deforestation through the lens of bid-rent and assesses its effectiveness in helping us comprehend the destruction of tropical forest in the Amazon basin. The article considers the adjustments that would have to be made to existing theory to make it more useful to the empirical issues. Keywords: deforestation; Amazon; von Thünen; land cover; land use

1. INTRODUCTION Land-cover and land-use changes generate many environmental problems at both global and local scales. Release of greenhouse gases, loss of biodiversity, and sedimentation of lakes and streams are but a sampling of the sorts of impacts that arise by virtue of modifications in vegetative cover due to changes in land use. Although land covers shift from one form to another throughout the world, independently of climate, topography, and level of economic development, most present-day concern focuses on tropical deforestation, which typically results when activities such as commercial farming, logging, mining, and even the residential use of space encroach on old-growth forest or replace long-fallow shiftingcultivation. Early commentators on tropical deforestation often drew a Malthusian alarm and worried that rapid population growth in less developed countries would soon destroy much of our biodiversity (Myers 1980). Social scientists began researching this topic in earnest in the 1980s, and throughout the 1990s a very large, statistical literature bloomed. The econometric work moved quickly past simplistic notions DOI: 10.1177/0160017604266026 © 2004 Sage Publications

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regarding population impacts on tropical forests and the environment more generally (Hardin 1968; Ehrlich 1968) to consider a wide variety of factors. Despite these advances, the Malthusian preoccupations of some in the environmental community are as strident as ever, with population bombs exploding in the tropical forest biome through the agency of fire (Nepstad et al. 1999) and the development of highway networks and infrastructure (Laurance et al. 2001). This article attempts to organize several strands of research on land-cover and land-use change, with a particular focus on tropical deforestation, a daunting task given the recent expansion of the literature on these topics. A number of authors have already provided useful reviews on the subject and summarized most of the work to date (European Space Agency 1994; Kaimowitz and Angelsen 1998; Geist and Lambin 2001; Lambin et al. 2001; Irwin and Geoghegan 2001; Geist and Lambin 2002). The present effort has its own specific interest, however, which stems from the recognition that land cover reflects land use and that land use has a significant theoretical foundation originating with the bid-rent concept of von Thünen.1 Be this as it may, the theoreticians of land use—à la Alonso, Mills, Muth, Fujita, Krugman, and others—have had little to say about land-cover and land-use change despite the relevance of their conceptual frameworks. For its part, landcover and land-use change research often addresses highly empirical questions using statistical methods and case studies, and it has generally avoided abstract theoretical formulations. Statistical modelers have a clear understanding of location rent and its importance to patterns of land use but have shown little interest in the theoretical underpinnings of the bid-rent concept and possible implications for the empirical phenomena in question. Indeed, Bockstael (1996) has called the von Thünen model increasingly “irrelevant” and “annoying” to noneconomists working on land-cover and land-use change. One goal of this article is to bridge this apparent intellectual divide between the theoreticians working in mathematical abstractions and the land-cover and landuse change researchers whose work is theoretically informed but empirically focused. This is accomplished by filtering a discussion of tropical deforestation through the prism of traditional land-use theory, namely, the bid-rent paradigm stemming from von Thünen and contemporary applications by urban economists and regional scientists. It will be seen that there are good reasons for, if not “annoyance,” then lack of interest on the part of the land-cover and land-use change community. Be this as it may, classical theory could be adapted and made more immediately relevant to the issue. Recently, Irwin and Geoghegan (2001) have pointed to the need to extend traditional theory on urban land use into the realm of land-cover change scholarship. Another goal of the article is to consider tropical deforestation in a particular region, namely, the Amazon basin, home to the world’s largest rainforest, much of which has vanished since the late 1960s. About 590,000 km2 of closed forest in the Brazilian portion of the basin have been converted to human-dominated land cover, much of it pasture (Alves forthcoming). This represents more than 14 percent of the

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original forest cover (Skole and Tucker 1993). What happens in the Amazon region may well have global impact, given the importance of its ecosystem to the global carbon cycle and biodiversity. It is not surprising that many are concerned about the destruction of its forest, which shows no sign of abating and averages between 10,000 and 20,000 km2 per year (see the World Resources Institute Web site: http:// www.wri-org/powerpoints/trends/sld04l.htm). The article is organized as follows. First, the so-called spatially explicit model is discussed, a legacy of “first-wave” statistical assessments of land-cover and landuse change processes that used aggregate data in regression analysis (Barbier 2001). As will be seen, a substantial convergence across the social and life sciences has occurred in stating and implementing these models. Following this, the article considers the bid-rent paradigm stemming from the seminal contribution by von Thünen and draws special attention to limitations of resulting analytical models. Although many approaches have been taken in addressing land-cover and land-use change, the focus here is on (1) statistical versions of the spatially explicit model and (2) analytical bid-rent models that have been advanced to theoretically describe urban and rural land use. 2 The article then describes deforestation processes in the Amazon basin and the adaptations that would be necessary to make analytical models more applicable to the issue. It also considers the long-run economic development context of emergent patterns of land cover and land use in the Brazilian Amazon. Addressed, if briefly, is the theory of the “forest transition” and the related notion of an environmental Kuznets curve. The article concludes by noting that bid-rent functions well as a metaphor for describing land-cover and land-use dynamics in large regions and, as such, meets the epistemological standard of the so-called “cultural turn” in economic geography, which is critical of traditional models like von Thünen’s (Barnes 2001). Here, economic geography is taken to be the social theory version associated with the discipline of geography and not its spatial reincarnation by regional scientists and economists (Fujita, Krugman, and Venables 1999).

2. THE SPATIALLY EXPLICIT MODEL Representation of land-cover change is an inherently spatial task, since land possesses aerial extent and parts of it may change while others may not, thus rendering a spatially explicit outcome. For the purposes of the present discussion, a spatially explicit model is taken to be an attempt to either statistically explain or predict such a spatial outcome. Attempts at explanation as through regression analysis may be not appear spatial when the analyst focuses on estimating an aspatial vector of regression coefficients. However, if observations on disaggregated spatial units are used in estimation, and if spatial information is contained in the independent variables, then regression results can indeed be used to describe the spatial outcome.

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SOCIAL SCIENCE EFFORTS AT EXPLANATION The spatially explicit model has roots in landscape ecology and in early statistical work on tropical deforestation by social scientists. Landscape ecologists were primarily interested in developing simulation models for predictive purposes (Baker 1989), while social scientists focused on explanation through the use of inferential statistics. In this early statistical work, the amount of forest loss, Y, occurring over some time period was estimated as a function of socioeconomic and physical variables, X, or Y = f(X). Data were collected for highly aggregated jurisdictional units, even nation-states, using forest inventories and government censuses (Barbier 2001). Although geographers and sociologists implemented the first regression models addressing the issue (Allen and Barnes 1985; Rudel 1989; Ludeke et al. 1990), behavioral theory awaited the involvement of economists, who provided a rationale for linking agent objectives, such as profit maximization, to variable selection for the statistical models. This had the conceptual effect of transforming deforestation—first viewed as a somewhat mysterious and irrational social phenomenon— into a derived demand for agricultural land (Panayotou and Sungsuwan 1994; Reis and Guzmán 1994). The derived demand concept fits neatly within the theory of the firm (Varian 1993), but current analysis posits deforestation as a discrete event affecting individual land parcels, whose potential uses are evaluated economically. A parcel is deforested if the land use generating the highest value requires that it be cleared. The availability of remotely sensed information, typically from satellites, and the functionality of geographic information systems have greatly facilitated this type of analysis. Estimation for highly disaggregated parcels is now possible, given satellite pixel dimensions. Landsat satellite imagery, for example, possesses pixel sizes of 30 m2. The conceptualization of land-cover and land-use change as a discrete outcome shifts specification from a focus on derived demand equations to the behavior of individual agents with effective control over land parcels, which they utilize in maximizing profits or utility (McFadden 1974; McFadden and Reid 1975; BenAkiva and Lerman 1985). Bockstael (1996); Chomitz and Gray (1996); Nelson and Hellerstein (1997); and Nelson, Harris, and Stone (2001) have provided similar rationales in this regard. For example, Bockstael noted that the probability of developing some parcel j may be written as Prob[develop] = prob[VjDt + εjDt > VjUt + εjUt],

(1)

where V is a “systematic” value component (net profit) for land cover in a developed (D) or undeveloped (U) state at time t, and ε is a random variable capturing unobserved effects. Similarly, Chomitz and Gray (1996); Nelson and Hellerstein

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(1997); and Nelson, Harris, and Stone (2001) hypothesized that a set of J land uses, alternative to undeveloped forest, generate rents, or net present values, Rh, where h ∈ J and rents are defined on prices for inputs and outputs and production magnitudes. The observed land use on some arbitrary parcel is given as j, when Rj > Ri, for all i ≠ j. These rentals can be stated as functions of distance, which leads to a common specification for the spatially explicit model. Following Nelson, Harris, and Stone (2001), define the net present value for land use h at location l and time period T as ∞

R hlT = max ∫ ( p hlT + t QhlT + 1 − W hlT + t X hlT + t )e − it dt X hlT + t

t=0

where p is output price, Q is output quantity, W is a vector of input prices, X is a vector of inputs that the land manager controls, and i is a discount rate. Time invariance in prices converts this to a static maximization problem, or ∞

R hl = max( p hlQhl − W hl X hl ) ∫ e − it dt X hl

t=0

Since the integral is a constant, it does not affect optimization, and one can proceed treating this as a yearly rental.3 Consequently, first solve the cost minimization problem associated with max( p hl Qhl − Wl X hl ), or X hl

min Wl X hl subject to fixed Qhl ( X jl ) = G hl ∏ x ia hi , i = 1 . . . , n for n production inputs. X hl

where production is governed by a Cobb-Douglas technology, with a coefficient Ghl reflecting resource quality at site l relative to land use h. The land use subscript (h) for input prices is suppressed, since these do not vary across land uses. Upon solution (see the appendix), rents can be written as a function of input (w) and output prices (p), 1

R hl ( p, w ) = F (G hl )( p hl ∏ wl−, ai hl a ahihi ) β h n

where β h = 1 − ∑ i a i , and F(Ghl) is a monotone increasing function in resource quality (see the appendix). To reflect transportation costs, write input and output prices as functions of distance, phl = exp[γh0 + γh1Dl], wl,i = exp[δ0i + δ1iDl], and substitute into the rental function, taking logarithms to find ln R hl ( p, w ) = Θ + ln F (G hl ) +

n  1   γ h 1 − ∑ a hiδ 1 i  Dl  βh  i

(2)

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where θ is a constant term including parameters γh0 and δ0i. Note that the transportation cost parameters, δ1i, are taken to be functions of input type, i. Under conventional hypotheses on the price parameters, γhl (0), the term associated n with distance, 1 / β h ( γ hl − ∑ i a hi δ 1 i ), is negative (Nelson, Harris, and Stone 2001). Although the model as derived considers only one distance associated with location, l, most applications use a set of distances as independent variables and not just one. This is accommodated by observing that market locations may differ for inputs and outputs as well as for inputs. Consider the case of three market locations, one for output and two for inputs. The distance-dependent prices are then phl = exp[γh0 + γhlDl,1]; wli = exp[δ20i + δ21iDl,2] for inputs i from market location 2; and wli = exp[δ30i + δ31iDl,3] for inputs i from market location 3; the transportation costs are taken as functions of market location. Equation 2 becomes

∑ a hiδ 21i ∑ a hiδ li3 γ h1 i ∈n 2 i ∈n 3 ln R hl ( p, w ) = Θ + ln F (G hl ) + Dl , 1 − Dl , 2 − Dl , 3 βh βh βh

(3)

where Θ is a constant distinct from θ including location specific price parameters, and n2 and n3 are the sets of inputs purchased from locations 2 and 3, respectively. In regression format and generalizing to k locations, equation 3 is ln R hl ( p, w ) = β 0 + β GG hl + D␤D

(4)

where β0 and βG are scalars, and D and ␤D are k element vectors. Specification for logistic regression may be illustrated as follows for the case of deforestation. Let there be two land-use/land-cover states, agriculture (a) and forest (f). The probability that deforestation occurs at some arbitrary location, l, is given as Prob [deforestation] = Prob [ln Ral (p, w) + εal > ln Rfl (p, w) + εfl]

(5)

where the εs are random variables covering unobserved effects as in equation 1. Assuming the εs to possess the appropriate extreme value distribution, equation 5 yields logistic probabilities parameterized by the coefficients of equation 4, which may be estimated through the method of maximum likelihood (Maddala 1983). Equations 4 and 5 constitute a conceptual backdrop for spatially explicit estimation when used to specify the probability of land-cover changes on parcels of land or individual pixels. Many have implemented versions of this model, but without formal behavioral statements (e.g., Ludeke, Magio, and Reid 1990; Wear, Turner, and Flamm 1996; Wear, Turner, and Naiman 1998; Wear and Bolstad 1998; Mertens and Lambin 1997, 2000; Geoghegan et al. 2001). It is important to emphasize that although distance, or “accessibility,” is a prime operational variable in

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such models, it functions as a proxy for the behavioral drivers represented by input and output prices (Nelson, Harris, and Stone 2001). ECOLOGY AND THE STOCHASTIC LANDSCAPE For landscape ecologists, initial motivations for constructing spatially explicit models sprang from difficulties in conducting experimental research on ecological impacts associated with land-cover change. Although many types of models have been advanced by ecological researchers to meet this challenge (Baker 1989), of special interest to this discussion are spatial landscape models and in particular those of a stochastic nature.4 The key concept is that land covers can be viewed as belonging to a set of discrete states and that land-cover change is simply a transition from one to another. When changes are nondeterministic, the basic model is Markovian, and following Baker (1989), nt+1 = Pnt,

(6)

where n is a vector (superscripted in time) containing magnitudes of j land-cover types for some land parcel; and P is a j × j matrix of transition probabilities between covers over the period, t to t + 1. Strictly speaking, the matrix P in equation 6 is actually the transpose of the matrix of transition probabilities, as usually defined (e.g., Çinlar 1975). In particular, a square matrix, P, with elements P(i, j), is a Markov matrix for i and j belonging to state space E if P(i, j) ≥ 0 and if for each i, ∑ j ∈E P(i, j) = 1 (Çinlar 1975, 108). The elements P(i, j) give the probability of transitioning over a finite time interval from state i to state j, which could be states of land use, for example. By the structure of equation 6 in which elements of the n vector at time t necessarily map into the same elements at time t + 1, the rows of P in equation 6 are the columns of the Markov matrix, P, as can be seen by considering an arbitrary element in n: nvt+1 = P(v, 1) n1t + P(v, 2) n2t + . . . + P(v, j)njt = P(1, v)n1t + P(2, v)n2t + . . . +P(j, v)njt.

Hence, P = P′. Early statements of the Markovian model met with criticism because of perceptions that the framework was unduly restrictive (Turner 1987).5 Analysts responded by noting that the transition matrix, P, could be parameterized, an observation leading to the basic formulation now serving as the estimation format for ecologists, economists, and geographers alike (Baker 1989). In particular, nt+1 = P(t, x)nt,

(7)

where n is as before but P is now a time-varying function of a vector of physical and social attributes, x, affecting land-cover change. Equation 7 can be made spatially

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explicit by including a locational marker, l (Browder, Bartley, and Davis 1985; Franklin and Forman 1987; Wilkie and Finn 1988). In particular, nlt+1 = Pl(t, xl)nlt.

(8)

In general, the probabilities estimated in spatially explicit models of land-cover and land-use change are given on the right hand side of equation 8, namely, the Markovian probabilities of the transition matrix (Bockstael 1996, 1171). The comparability of equation 8 to equations 4 and 5 is apparent on disaggregating x into physical and “distance” variables, or x = [G; D]. Time steps are rarely specified, however, which raises conceptual issues about the nature of the estimated probabilities. If the land-cover and land-use systems are taken to be in equilibrium, then they are not the transition probabilities of equation 8, which is defined for a finite time interval (Nelson and Hellerstein 1997; Nelson, Harris, and Stone 2001; Barbier 2001). In such a situation, they are interpretable as elements of the limiting distribution, π( j ) = lim P n (i, j ), n→ ∞

where i and j represent possible land covers in the state space of P, and Pn = PP . . . P is the product of n transition matrices (Çinlar 1975).6

3. RELEVANT LAND-USE THEORY: SPATIALLY EXPLICIT MODELS AND BID-RENT The early interests of social scientists in explanation and ecologists in prediction are evidently convergent in the spatially explicit model. Ecologists have provided strong motivation with their focus on the landscape as a biogeographic unit of analysis subject to fragmentation processes. For their part, social scientists have filled the explanation gaps on the human side of the equation. Now, social scientists and ecologists are even found to publish jointly on the topic (Turner, Wear, and Flamm 1996; Wear and Bolstad 1998). The spatially explicit model is increasingly used to predict landscape change and is often evaluated both in terms of conventional inference on variable coefficients and goodness-of-fit and with respect to ability to predict actual landscape change (Nelson and Hellerstein 1997; Wear and Bolstad 1998; Mertens and Lambin 2000). It is not the intention of this article to review these various applications. Instead, the spatially explicit model has been considered to provide a point of departure for broader discussion. The point of departure is established by noting that (1) this approach represents a unified statement about land-cover and land-use change across the social and life sciences; and that (2) similar sets of variables are surfacing in specification and estimation, independently of discipline. Of special interest in

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this regard is the family of variables that can be placed under the category “accessibility,” typically taken as some measure of distance from a parcel of land to a road, a market, a city, or a region.7 A robust result in the statistical work to date is that accessibility is strongly linked to the likelihood of land-cover and land-use change. This has a decidedly Thünenesque ring to it. The theory of land use—if not land-cover and land-use change—has been well articulated for both agricultural and urban settings. This theory, and in particular the concept of bid-rent stemming from von Thünen and its link to transportation costs, are well known to statistical modelers of land-cover and land-use change (Bockstael 1996; Chomitz and Gray 1996; Nelson and Hellerstein 1997; Nelson, Harris, and Stone 2001; Wear and Bolstad 1998). Analytical applications have been especially notable in attempts to explain urban form (Alonso 1964; Muth 1969; Casetti 1971; Mills 1972a, 1972b; Beckman 1973, 1974; Solow 1973; Wheaton 1978; Fujita and Krugman 1995). For example, Fujita (1989, 322) solved a utility optimization problem to define the bid-rent function, Ψ(u, r), which gives the maximum amount consumers of residential space are willing to pay under utility, u, and at distance, r, from the city center. In particular, Ψ(u, r) = αα/ββ[Y – t(r)]–1/βe–u/β,

where Y is per capita income; t(r) is the cost of commuting to the city center, which increases with distance; and α and β are parameters of the utility function of city residents. Land-use and spatial information are contained in the so-called fringe distance, the extent of the city given increasing transportation costs and optimal lot size, s(u, r), which is the reciprocal of residential density (Fujita 1989, 322), s(u, r) = α–α/β[Y – t(r)]–α/βeu/β.

Similarly for the agricultural case, Nerlove and Sadka (1991, 109; also see Fujita, Krugman, and Venables 1999) derived a rent function, R(r), for agricultural land use as a function of distance from a market center, R(r) = (1 – η)p(r)γ[l(r)]η,

where γ[l(r)]η is the agricultural production function with coefficients γ and η; l(r) is labor application per unit land at distance, r; and p(r) is the price received for the agricultural commodity at distance, r, which is diminishing in distance due to transportation costs. As in Fujita (1989), the formulation by Nerlove and Sadka (1991) yields fringe distance (the maximum extent of farming) and the intensity of labor applications in agriculture, l(r), a population density measure that declines with distance from the market.

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While bid-rent—and in particular the role of transportation costs—is useful in comprehending the forces driving land-cover and land-use changes, abstract formulations by urban economists and regional scientists rely on simplifying assumptions necessary to achieve analytical solutions. Mathematical model statements have focused on equilibrium states, asserted independent urban and rural land-use systems, considered highly disaggregate settings focused on a single city or hinterland, and made strong assumptions about the behavior and social composition of the land using agents (Walker and Solecki 2004). Anyone who has conducted research on a phenomenon such as tropical deforestation understands that the process is highly complex and occurs in a world quite different from that of the abstract models. Thus, the question that needs to be answered is this: do the simplifications necessary for analytical solution lead to a representation of reality so at odds with its empirical content that analytical model building is, as Bockstael (1996) suggested, irrelevant to the land-cover and land-use change community? In an effort to answer this question, these various model-building simplifications are now considered in light of the land-cover changes presently occurring in the Amazon basin.

4. LIMITATIONS OF THE BID-RENT FORMULATION EQUILIBRIUM LAND USE Theoretical bid-rent models have been criticized by social theorists and economists alike for their inability to account for both historical and short-run change due to the equilibrium assumption made in the interest of model tractability (Page and Walker 1994; Bockstael 1996). Since land-cover and land-use changes are inherently dynamic, they necessarily reflect underlying disequilibria conditions, typically neglected by theoretical modelers. It would therefore seem that a formal statement of bid-rent is not equipped to describe the transformative forces unleashed by economic development. This criticism may not be as problematic as it first appears. In particular, one of the variables critical to the description of spatial form in theoretical models, namely, the extent of human land use (or fringe distance), can be parameterized in system characteristics such as population, income levels, and—perhaps most important from the land-cover and land-use change perspective—transportation costs (Fujita 1989). The functional relationships that result depict land-cover change, or the advance of the agricultural or urban fringe against an outlying landcover, when equilibrium adjusts to new parameter values (Walker, Solecki, and Harwell 1997; Walker 2001). Indeed, von Thünen has been applied heuristically to explain the advance of the Brazilian frontier into the central and western parts of that country during the early twentieth century (Katzman 1977). Development and extension of the coffee economy in the state of São Paulo raised bid-rents, pushing cattle ranching and small-scale diversified agriculture into unutilized land. Bid-rent

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has also been used to describe similar processes in the American west, with the advance of cattle ranching and intensive forms of agriculture into the ecosystem of the Great Plains, with its prairie grasses, bison herds, and Native Americans (Cronon 1991). ECONOMIC STRUCTURE AND EXTERNAL LINKAGES A second and potentially more serious shortcoming in analytical models is lack of attention to structural linkages between city and hinterland. Also neglected are trade and factor movements between cities and regions. Admittedly, specific model applications cannot be expected to reflect the myriad of spatial relationships in which a city or agricultural area is embedded, but the general failure to consider them raises issues in analytical modeling efforts. It must also be kept in mind that when extrasystem linkages are not addressed, individual model solutions represent only a partial spatial equilibrium. As might be expected, urban models consider urban land use only, while agricultural models focus on farming (exceptions include Sinclair 1967; Muth 1969; Walker 2001). For the agricultural model, the city is a dimensionless point, whereas in urban models agricultural land use may cease altogether or extend without bounds (Walker 2001). In addition, independent model statements neglect linkages between city and hinterland that affect regional land cover and land use. These include demographic interactions between city and hinterland such as rural-tourban migration and the movement of commodities both to meet local urban demands and to provide inputs for the processing of exports (Cronon 1991; Walker 2001). Although neglected in most analytical models, city-hinterland relationships and external linkages to the rest of Brazil have played important roles in land-use and land-cover changes in the Amazon region. In-migration from other parts of the country was a primary deforestation driver during the 1970s and 1980s. Technological change in soybean production in the south and drought in the northeast inspired many to seek better fortune in the Amazonian frontier (Hecht and Cockburn 1989). This push on migration was complemented by the pull factors of government land grants for the purposes of colonization and economic development (Hecht 1985; Simmons 2002). Subsequently, the dramatic rise of regional cities such as Belém and Manuas, arising in part by out-migration from farm holdings (Browder and Godfrey 1997; Perz 2000), altered this early dynamic by contributing a considerable component of forest regrowth through farm abandonment (Perz 2000). Although deforestation continues at a rapid, aggregate rate, secondary vegetation has also appeared throughout the basin due partly to rural out-migration (Moran et al. 1996; Perz and Skole 2003). Be this as it may, urban demand for beef from within the region is now contributing to countervailing processes of pasture conversion observed among small and large holdings alike, a major factor in current forest loss (Walker, Moran, and

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Anselin 2000). Faminow (1998) argued that population growth in regional cities, resulting from rural-to-urban migration, together with rising incomes, have created this demand against a background of transportation cost advantages favoring Amazonian producers despite more efficient ranches in the south.8 This is consistent with observed shifts in the cropping systems of small-holders, in particular (Walker and Homma 1996). Although many continue with diversified portfolios including both annual and perennial crops, the vast majority possess livestock and are engaged in pasture formation (Walker et al. 2002). AGENTS AND BEHAVIOR Both city-hinterland relationships and interregional processes, generally not treated in analytical models, have affected land-cover and land-use changes in the Amazon basin. Also not addressed in formal modeling approaches is agent complexity in behaviors and interactions, which affects landscape processes as well. The bid-renter is typically a farmer or a residential land user who makes competitive bids prior to either engaging in agriculture or consuming residential amenities. From the perspective of tropical deforestation, this is a limited list of agents and behaviors. The types of individuals taking down tropical forest vary by continental region and include government bureaucrats, loggers, shifting cultivators, commercial farmers, ranchers, fuel wood gatherers, and urban developers (Myers 1980; Hecht 1985; Geist and Lambin 2002). They often act interdependently in so-called logical tandems, and deforestation results as much from their interactions as from agent-specific behaviors taken in isolation (Geist and Lambin 2001). Two such tandems have received substantial attention in the deforestation literature, one associated with the so-called hollow frontier, or the “colono system” (Rudel 2002), and the other with the model of invasive forest mobility (Walker 1993). Under the hollow frontier thesis, poor individuals move to forest frontiers and initiate land-cover change by farming, typically a low-intensity form of shifting cultivation. Deforestation runs its course as wealthy ranchers consolidate the smallholdings into pasture, pushing the initial wave of settlers deeper into untouched forest and thereby creating a hollow frontier of consolidated but “empty” holdings (Wood 1983). Invasive forest mobility is a relationship also involving poor farmers, in this case interacting with loggers. Here, loggers build roads to selectively harvest, opening the forest to the farmers, who follow the roads looking for land. The process of deforestation is completed when the trees left standing by the loggers are cleared to make way for farming (Leslie 1980; Myers 1980; Schmithusen 1980; Office of Technology Assessment 1984; Ross 1984; Walker 1987; Repetto and Gillis 1988; Walker and Smith 1993; Kummer and Turner 1994; Brookfield, Potter, and Byron 1995). Although statistical information on such tandems may be limited for the Amazon Basin, anecdotal evidence suggests their existence. The hollow frontier thesis is often invoked to explain the process of frontier occupation in Latin America, if

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not the land-cover changes that follow in its wake. As for links between loggers and colonists, many have observed mutually beneficial wood exchanges in the Brazilian frontier (e.g. Simmons, Walker, and Wood 2002). Interactions between agents, whether they be loggers, small-holders, or wealthy ranchers, are fundamentally dynamic when two different agents act on the landscape at two different time points, due to the nature of their social relationship. In such a situation, deforestation results from a sequence of logically connected behaviors, and not from individualized land clearance actions taken by specific agents. Assumed agent behaviors in the formal bid-rent paradigm are limited as well, focused as they are on the maximization of rents, profits, and utility. This may be reasonable for explaining land use under the implicit institutional environment of the bid-rent paradigm, where rents accrue to landowners whose property rights are never disputed, and the economy is free from catastrophic shocks. Of course, development frontiers such as in the Amazon basin are vastly different from the utopia of von Thünen and the urban modeler. Individuals may seek to minimize risks or take them as the case may be (Walker et al. 2002). Poorly defined property rights are not conducive of the competitive bidding process that leads to the equilibrium rent profile, so essential to both urban and agricultural models. Insecure land tenure leads to excessive rates of deforestation more akin to a liquidation and mining of resources than an agricultural activity (Mueller et al. 1994; Alston, Libecap, and Mueller 1997).9 In addition to overlooking important “on-the-ground” behaviors in the immediate vicinity of where land-cover and land-use change is occurring, analytical models do not consider the higher-order behaviors that precipitate changes in important system parameters such as transportation costs. Such behavior, largely bureaucratic and distal in that it occurs far from the impact areas, is what governs the infrastructure investments that have sparked tropical deforestation processes around the world. Clearly, land-cover and land-use changes follow from governmental decisions influenced, as they are, by the social and political context in which they are made. While formal bid-rent models can predict the impact of a reduction in transportation costs on the extensive margin of agriculture, they cannot predict when the reductions will occur or how large they will be. Yet this is perhaps the most critical part of the story (Cronon 1991; Walker and Solecki 2004). Indeed, during the late 1960s and 1970s, highway construction was a major objective of state-led development efforts in the Brazilian Amazon (Goodland and Irwin 1975; Mahar 1979; Smith 1982), and corridors were established connecting the region to other parts of the country.10 The impact of these investments on the region’s land cover is borne out by econometric work in which roads—and accessibility more generally—consistently emerge as an important explanatory factor in deforestation (Reis and Margulis 1991; Reis and Guzmán 1994; Anderson 1996; Anderson and Reis 1997; Pfaff 1999; Wood and Skole 1998). Tabular data based on geographic information systems (GIS) buffering functions along transportation corridors also show a preponderance of forest loss in close proximity to highways

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(Laurance et al. 2001; Alves 2002). Roads have provided the means of access for in-migration by poor farmers, capitalized ranchers, loggers, and miners, the primary agents of deforestation in the Amazon (e.g., Martine 1980; Moran 1981; Schmink and Wood 1984). In fact, this is an old story given that railroads performed a similar function at the turn of the twentieth century by opening the central part of Brazil to agricultural expansion (Katzman 1977). Just as with railroad construction during those early years, the decisions to build the roads to Amazonia and create bid-rents in the region were made by individuals far from the scene and in response to factors not strictly economic, but social and political (Hecht 1985).

5. THEORY OR CONVENTIONAL WISDOM FOR THE AMAZON? Loss of the Amazonian forest in the present day and age has been well documented in many Amazonian countries, and much of the story has already been told. In general, governments in the region desired to secure national borders, to exploit untapped natural resources, and to settle land-hungry populations (e.g., Hecht 1985). Pursuant to these national objectives, they constructed roads and by so doing paved the way for land-cover and land-use changes on a massive scale. That roads and transportation infrastructure more generally lead to extensive land-cover and land-use change in developing regions is now a conventional wisdom.11 Presumably, such impacts emerge from the masses of rent seekers who follow in their wake, chasing their fortunes in a quest for a better life. But does the bid-rent story for the Amazon end here? Has its utility been exhausted with the specification of distance variables in econometric models and the development of interesting historical points that only need the narrative version of von Thünen (e.g., Katzman 1977; Cronon 1991)? Or can an old theory be refurbished for new applications and insights? This article has focused attention on shortcomings of the analytical bid-rent model in explaining tropical deforestation. The most serious ones include structural separation between urban and agricultural statements, the partial equilibrium nature of spatial representation, and the incomplete depiction of land-cover change agents, including their behaviors and interactions. Consequently, a number of modifications would be necessary if the received framework is to serve the discourse on land-cover and land-use change. Important among these is the functional integration of agricultural and rural models to allow for the impact of urban-rural linkages on hinterland landscapes. Muth (1969) provided an early model along these lines, which was elaborated by Walker (2001) to specifically address land-cover and land-use change as a function of urban-rural commodity linkages. These may occur on the supply side, as when agricultural or extractive products provide input to regional exports, such as lumber, and on the demand-side, as when urban populations use regionally produced foods for home consumption, such as beef (Faminow 1998; Walker 2001). Of course, labor market interactions between urban and rural sectors have long been

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recognized in the development literature, particularly rural migration due to industrial job growth in cities (Fei and Ranis 1964). Such processes have been considered in purely agricultural formulations (Nerlove and Sadka 1991) and presumably could be built into integrated models to translate the impact of both labor and commodity market dynamics on regional landscapes. Also critical to adapting bid-rent models to land-cover change explanation is recognizing their partial equilibrium nature, in a spatial sense. Although von Thünen has been used somewhat heuristically to explain land-cover changes in large regions emanating from spatially diffuse urban demands (Katzman 1977; Cronon 1991), theoretical formulations mainly provide insight into points associated with individual cities (and hinterlands) for which key variables are taken as exogenous, such as population, income, and utility levels (Fujita 1989).12 As noted, economic relationships binding cities into systems of cities condition these variables and—by implication—the patterns of land use emerging at both micro and macro scale (Fujita, Krugman, and Venables 1999). Thus, to be useful to the landcover and land-use change discourse, bid-rent would have to be embedded in the structural relations between city and hinterland and be linked to trade relations among cities. An early suggestion along these lines may be found in Isard (1956, 17-18).13 Repairing certain of the structural shortcomings in analytical models appears feasible, and groundwork has already been broken in this regard. Less work has been accomplished addressing issues presented by the bid-rent paying, or appropriating, agent. The Amazon basin in particular offers numerous examples of complex interactions and behaviors, as well as types of agents not often observed in Thünenesque explanation. Although bid-rent has been formally applied both to forestry (Ledyard and Moses 1976) and shifting cultivation (Jones and O’Neill 1993a, 1993b), the foresters and farmers considered are rational profit maximizers engaged in long-run land use, not in resource exploitation made attractive by weak land tenure institutions and a risky economic environment. The bid-rent concept, inherently static and devoid of social complexity, cannot easily capture the land occupation sequences, involving loggers, poor farmers, and ranchers, which ultimately result in Amazonian deforestation. Nor can analytical models abstract from their own structure to the less tangible, political economy realm of bureaucrats and politicians, who play such significant roles in regional development activities and investment. But as has been argued and demonstrated by historical narrative, illuminating these roles is critical to understanding how Thünenesque forces shape the landscape (Cronon 1991). Equipping the old models with heterogeneous agents and interactions, not to mention non-profit-maximizing behaviors, presents obvious challenges. One approach for addressing the heterogeneity issue would be to develop a concept of successional frontiers based on specific agents, with transitions from one frontier to the next taken to represent agent interactions. For example, both logging and

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subsistence frontiers have been identified for the Brazilian case (Katzman 1977; Schneider, Verissimo, and Viana n.d.). Their sequence in time evidently reflects invasive forest mobility, with loggers advancing into lands beyond the extensive margin, followed by subsistence farmers. The rents captured by loggers are transitory, at least in the short run, given slow rates of forest regeneration. Moreover, they are directly appropriated and do not accrue to private landowners, who do not exist in the institutional setting as described. Be this as it may, a dynamic Thunian framework is at least conceivable given the distance dependency of the rents involved (Schneider, Verissimo, and Viana n.d.). Perhaps the greatest challenge in applying formal bid-rent theory to land-cover and land-use change processes in the Amazon and elsewhere resides in incorporating agent behaviors that do not conform to standard notions of profit and utility maximization. Key among these is the bureaucratic decision making so critical to infrastructure expansion. It is probably unfair to expect any analytical model to explain a phenomenon so messy, arcane, strategic, and idiosyncratic. Be this as it may, the bid-rent concept has been joined to structural and poststructural analysis to describe land-cover and land-use change processes resulting from the impact of social and political forces on the structure of urban and rural land markets (Walker and Solecki 2004). Such an approach is conceivably adaptable to the Amazonian case.

6. CONCLUSION This article has considered loss of the Amazonian forest in light of the classic bid-rent model and has specifically addressed its utility as an explanatory device. Clearly, accessibility, broadly defined, influences the use of land and, by implication, the cover of that land, be it natural vegetation or a completely human artifact. In addition, these uses and covers do show organization in space that is intelligible and capable of being theorized. To adapt the existing analytical framework to the issue of deforestation it would be necessary to (1) represent critical linkages in the space economy and (2) provide an adequate description of the true complexity of the agents involved and their interactions. Although some of this retooling could be accomplished, issues remain in describing agent behaviors, particularly those involving political decision making. For a region the size of the Amazon basin, it may not make much sense to work toward unified explanation, based on bid-rent or any other particular class of models, given the number of locality-specific deforestation processes. The concept of accessibility and site-specific economic potential can be established by considering transportation costs only, without reference to the elaborate machinery of analytical models. Indeed, specification of the spatially explicit model, as presented here and elsewhere (Nelson, Harris, and Stone 2001), needs to consider only transportation costs and market locations.

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Although analytical bid-rent models address some form of “long run” in that they assume an equilibrium outcome, empirical land-cover changes at the national scale last centuries. Such historical processes may well lie beyond the purview of analytical model explanation. Nevertheless, a discourse has emerged on precisely this issue under the shared banner of so-called forest transition theory and the environmental Kuznets curve. Forest transition theory posits an evolution in a nation’s land-use system, which parallels its development from an agricultural to a postindustrial economy. With agricultural modernization, industrial job creation, diminishing demand for fuel wood, and changing preferences for environmental amenities, farmlands—initially extensive under rudimentary forms of agricultural technology—are abandoned, allowing for forest regrowth and expansion over the long run. Such recoveries have been observed in many developed countries, whose forests have regained area at national scale following the deforestation associated with earlier agricultural development (Walker 1993; Mather 1990; Rudel 2002). The environmental Kuznets curve posits a similar process of change but is focused on rates of deforestation, primarily in developing tropical countries (Cropper and Griffiths 1994; Barbier 2001). The most recent cross-sectional econometric evidence suggests that Latin American countries should experience a downturn in rates of deforestation at per capita GDP exceeding about $6,300 (in 1996 U.S. dollars). That Brazil’s 2000 per capita GDP was on the order of $6,900 (in 1996 dollars) suggests that conditions in the aggregate economy should be reducing rates of forest clearance, if not entraining the process of ecosystem recovery envisioned by the forest transition.14 As it turns out, rates of deforestation in the Brazilian Amazon have shown little recent trending, and through the mid 1990s, they increased from an early decadal dip.15 Thus, deforestation in this part of the world is likely to remain a serious environmental concern for some time to come, and models that explain it will be valuable to policy makers. The bid-rent paradigm, whether in its econometric specification as “accessibly” or its representation in analytical models, remains a powerful conceptual tool despite funereal pronouncements by social theorists (Page and Walker 1994). Whether a new class of formal models will be developed to explain region-scale processes of land-cover and land-use changes in the Amazon or elsewhere remains to be seen. The present article remains agnostic on this account. At the very least, the bid-rent concept and von Thünen’s notion of land zonation can continue to serve as a powerful explanatory metaphor, as it already has on more than one occasion (Katzman 1977; Cronon 1991, 1994). As such, von Thünen and his urban followers, presumably, meet the nonpositivistic test of providing useful theory that has recently been advanced by proponents of the “cultural turn” in economic geography (Barnes 2001). Spatial theorists should not stop here, however, with vindication from economic geography. Efforts to adapt analytical models, if not producing “grand” theory, can only help us in our quest to understand tropical deforestation.

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APPENDIX The first-order conditions for minimization are, x hl , j =

λa hjQhl wj

for all j, j = 1, . . . , n, which can be substituted into the production function to solve for λ, yielding the factor demand equations 1

x hl , j

a hl

−1

a hj n  wl , i  ∑ a hi a a = Qhl∑ hl G hl∑ hl ∏  wl , j i  a hi 

These can be used to state the cost function as 1

−1

a a C hl ( w, Qhl ) = Qhl∑ hi G hl∑ hi

a hi

1

 wl , i  ∑ a hi a = KC *hl ( w )Qhl∑ hi ∑i a hi ∏  a hi  n

where −1

a K = G ∑ hi hl

a hi

 wl , i  ∑ a hi ∑i a hi and C*hl(w) = ∏i  a  . hi n

n

The rental and supply functions are now16 1

a R hl ( p, w ) = p hlQhl − KC *hl ( w ) Qhl∑ hi

∑ a hi n  1 − ∑ a hi   p hl ∑ a hi  i  and Qhl =  ,  KC *hl ( w )     

which can be written as

(

a − R hl ( p, w ) = F (G hl ) p hlC *hl ( w ) ∑ hi

)

1 βh

(

= F (G hl ) p hl ∏ wl−, ai hl a −hia hi

)

1 βh

∑ a hi  ∑ a hi  1 − ∑ a hi  where F(Ghl) ≡ (1 – K)  .   K 

NOTES 1. The land-cover changes considered here are those responsive to human manipulations of land use, such as when farmers decide to replace primary forest with agricultural fields. Of course, land covers

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change naturally for many reasons. Trees drop their leaves in temperate deciduous forests with the onset of winter, and entire ecosystems are altered with the advance, or retreat, of glaciers. 2. These models may be taken as one class of spatial economic models, as considered in Fujita, Krugman, and Venables (1999). Characteristic features include a market center (or centers), classes and spatial boundaries for land use (fringe distances), and distance decay functions for rents and density of land occupation. 3. An important potential issue in the present context concerns the time sequencing of returns from agriculture. It takes time to build a herd or realize output from perennials. By suppressing a time index on the production function, such dynamics are neglected. 4. Although stochastic representations of alterations in land cover have been widely used by ecologists, a number of early applications arose in the social sciences. Drewett (1969), Bourne (1971), Burnham (1973), Bell (1974), and Bell and Hinojosa (1977) laid the theoretical foundations for Markovian models of switches between land uses in several regional landscapes of North America. 5. Turner (1987) noted a number of “limitations” including nonstationarity of transition probabilities and the existence of spatial effects. Karlin and Taylor (1975) gave a general, nonstationary statement of the Markov formulation, while Haining (1990) discussed extension of the Markov property to spatial neighborhoods. 6. Existence of a limiting distribution can be an issue (Çinlar 1975, 152). A sufficient condition for existence is that the state space be finite and that all transition probabilities be positive. This is reasonable for a land-cover and land-use transition matrix, given reversible changes. 7. Although they are not spatially explicit in the sense of this article, the work by Reis and Guzmán (1994), Panayatou and Sungsuwan (1994), Andersen (1996), Pfaff (1999), and Walker and Solecki (1999) explicitly incorporate distance measures into their analysis. Pfaff considered the distance of individual counties to the main southern cities in the south of Brazil, while Walker and Solecki fit a spatial trend surface using the centroids of individual counties in New Jersey. 8. Faminow (1998) present a spatial pricing model to explain the supply areas of beef for Amazonian cities. 9. Nor should it be forgotten that land use can and does occur outside the extensive margin of commercial agriculture. Consequently, deforestation takes place in the absence of markets for products and labor, which are foundational to agricultural and urban bid-rent models, respectively (Boserup 1965; Walker 1999). Although the aggregate land-cover impact of such extramarginal activity is probably small, effects on the species composition of forest stands—and therefore forest type—can be quite dramatic. Balée and Gély (1989) estimated that up to 12 percent of the Amazon forest has been impacted by indigenous peoples, who deliberately concentrated species over millennia by opportunistic broadcasting the seeds of valuable trees. Concentrations of Brazil Nut and Babassu Palm are the most notable examples. 10. In particular, the federal government constructed north-south highway connections from the capital, Brasília, to Belém, the Amazon’s largest city (BR-010); from Cuiabá to Santarém (BR-163); and from Manaus to Boa Vista on the Venezuelan border (BR-174). East-west connections constructed included the highway from southern Brazil through Cuiabá to Porto Velho and Rio Branco (BR 364), now being extended to the Pacific coast; and the Transamazon Highway (BR-230), from Brazil’s northeast through the towns of Marabá and Altamira in the state of Pará westward into the state of Amazonas. Programs initiated by individual states have also been active, particularly in the state of Pará, where PA150 provides another north-south axis west of the Belém-Brasília highway. 11. A more nuanced view has emerged in this regard, involving possible endogenity of road construction to the process of deforestation (Anderson et al. 2002). 12. Fujita (1989) described endogenous processes, such as the adjustment in utility levels given fixed population in a closed system. Since the system is closed, there are no linkages with other cities. 13. Inclusion of global cities in the system would enable the introduction of globalization effects. 14. Barbier (2001, 164) reported the turnaround point for maximum deforestation in Latin America at $4,946 in 1987 U.S.$. This converts to $6,354 in 1996 U.S.$, using the price deflator from the U.S.

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Department of Commerce. In 2000, Brazilin GDP per capita was $7,400, which converts to $6,915 in 1996 U.S.$. 15. Perz and Skole (2003) showed that rates of deforestation can be regionalized in the Amazon and speculated that forest transition will occur there without extreme initial deforestation. 16. Note that the supply function is only defined if the sum of the Cobb-Douglas exponents is less than 1, indicating diminishing returns to scale and presumably a fixed production factor (Varian 1993, 17). Nelson, Harris, and Stone (2001, 204) assumed that the exponents on the Cobb-Douglas function sum to less than 1.

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