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THE STRUCTURE OF UNCULTIVATED WILDERNESS:LAND USE BEYOND THE EXTENSIVE MARGIN*

Robert WalkerDepartment of Geography, Florida State University, Tallahassee, FL 32306. E-mail:[email protected]

ABSTRACT. This paper presents an agent-based model of shifting cultivation thatexplains patterns of land use and forest structure beyond the extensive margin ofagriculture. The anthropological literature is first examined in order to specify key aspectsof farming group preferences vis-à-vis food requirements. Two existing theories of shiftingcultivation are then addressed to motivate the present formulation, which integrateshousehold production theory and the concept of optimal rotation originating in the forestryliterature. It is argued that the cycling of secondary vegetation by shifting cultivatorsrepresents a form of rotation analogous to the foresters’ case.The model developed explainsthe empirical observation that individual agents use multiple rotation ages, and it does sofor the nonmarket case, which is consistent with the institutional environment of manyindigenous peoples and colonists. The paper concludes with an application to the problemof rural violence in Brazil and with suggestions for extending the framework to the policyarena of global change.

1. INTRODUCTION

Many view tropical deforestation as an irreversible process leading topermanent landscape change (e.g., Gomez-Pompa, Vazquez-Yanes, and Guevara,1972) despite the accumulating evidence to the contrary that succession oftenoccurs in the wake of human disturbance (Moran, et al., 1996).The anthropological

JOURNAL OF REGIONAL SCIENCE, VOL. 39, NO. 2, 1999, pp. 387–410

*This research was supported by the International Institute of Tropical Forestry, U.S. ForestService,and the National Science Foundation,Geography and Regional Science Program,under NSFgrant number SBR-95-11965 (Charles Wood, Principal Investigator). Support was also provided bythe U.S. Fulbright Commission and by Resources for the Future.A version of the paper was presentedat the Workshop on the Social Meaning of Secondary Forest,Tropical Conservation and DevelopmentProgram, University of Florida, in Gainesville, October 21, 1996. It was also presented in a workshopat Resources for the Future on June 9, 1998. The seminal insight of multiple rotations associatedwith individual farming groups belongs to Arnaldo Jose de Conta; the idea to apply Faustmann tothe problem of shifting cultivation arose in conversation with Fred Scatena. To them I am gratefulfor the model concept. I would also like to thank Tony Smith for providing mathematical critique,and William Balee and Oliver Coomes for sharing with me their field insights and data. WilliamDenevan and Jan Salick generously allowed me to reproduce data they had previously published.Finally, I am indebted to Alfredo Homma, J. Daniel Khazzoom, Emilio Moran, Wallace Oates, andCynthia Simmons for useful and highly germane discussions, as well as to April Rubens, R.D., forproviding the nutritional information used in constructing Table 2b. I remain solely responsible forany remaining errors.

Received January 1997; revised January 1998 and June 1998; accepted August 1998.

© Blackwell Publishers 1999.Blackwell Publishers, 350 Main Street, Malden, MA 02148, USA and 108 Cowley Road, Oxford, OX4 1JF, UK.

record documents longstanding use of tropical forest resources despite the highlabor-costs associated with tree-felling under traditional technology (Denevan,1992b). Disturbance indicator species are widely scattered throughout the newworld tropics suggesting that pristine areas conceal evidence of human use.Forests with concentrations of Brazil nuts, lianas, and bamboo— accounting fornearly 12 percent of terra firme in the Brazilian Amazon—may be anthropogenicin origin (Balee, 1989). Local studies of modern hunter/ gatherers show depend-ence on artifactual forests including many fruit trees reflecting fallow improve-ments of pre-Columbian peoples (Balee, 1992). It has been estimated that about40 percent of the New World tropical forest represents some form of succession(Brown and Lugo, 1990), while most of the Congo Basin is in secondary forestcover (Allan, 1965).

Boserup has criticized the economists’ notion of empty land, examining thehistoric record to show that forest stands thought to be pristine have oftenconstituted fallow area under long rotation. Ironically, land use models based onnotions of bid-rent do not require the existence of a finite extensive margin, inwhich case agricultural activity (and residential land use) need not be confinedby an encircling perimeter of natural land. In at least one theoretical application(Jones and O’Neill, 1993b), rotation times decrease with distance from the city;a sufficiently long rotation would ultimately meet Boserup’s definition of forestfallow, in which case a theoretical model based on neoclassical principlesdescribes the empirical case Boserup uses to criticize an economic notion.Nevertheless, many formal applications of the bid-rent apparatus (e.g., Nerloveand Sadka, 1991) assert a finite boundary to urban and agricultural activities.Presumably, the domain of nature begins where human action ends.

The purpose of this paper is to provide a theoretical description of extra-marginal decision-making that includes, but is not limited to, market context.In particular, I state a model based on the notion of peasantry, for whom marketattachments are sporadic and incomplete (Ellis, 1993). My specific goal is toaccount for land allocation beyond the extensive margin of permanent agricul-ture in what von Thünen referred to as uncultivated wilderness. Current theoryexplains the allocation of land among residential uses and crop types in termsof decision-making based on known prices for products and transportation. Itdoes not address allocation in the absence of market signals or explain thepattern of natural land cover resulting from human activity under such condi-tions. These shortcomings are important omissions for both social and ecologicalreasons.

Much conflict in developing countries occurs in frontier areas on lands thatare marginal or extra-marginal (Alston, Libecap, and Mueller, 1997). Suchconflict probably has some basis in the activities of the parties involved, namelyagriculture. From an environmental perspective, the distribution of forest agecohorts beyond the areas of cash cropping is of great importance given variationin species composition and carbon sequestration potential across different agesof secondary regrowth. Indeed, secondary forest dynamics in tropical countries

© Blackwell Publishers 1999.

388 JOURNAL OF REGIONAL SCIENCE, VOL. 39, NO. 2, 1999

may prove of critical importance to the carbon balance, but they are not wellunderstood (Alves and Skole, 1996).

The paper is organized as follows. In Section 2 I consider the globalimportance of small-scale farming, address secondary forest succession, andconsider the influence of crop complementarity in food consumption on thepattern of natural landscapes. In Section 3 I discuss previous models of slash-and-burn farming and in Section 4 present a new model overcoming certainempirical limitations of these earlier approaches. In addition, this model pro-vides a description of natural vegetative cover and crop types beyond theextensive margin of market-based agriculture. In Section 5 I discuss the results,calibrate them with field data, and consider the model in an application to landscarcity and rural violence. In Section 6 I summarize my conclusions.

2. SUCCESSION AND COMPLEMENTARY FOOD REQUIREMENTS

The effects of small-scale farmers on land-cover represent a globally signifi-cant phenomenon. For tropical rainforest areas alone the 1990 resident worldpopulation is estimated at 402,200,000, with a population density of 44 inhabi-tants per square kilometer, and the annual growth rate of forest residents overthe decade was 2.4 percent (Food and Agricultural Organization, 1992). Thetropical lowland forests of Latin America have long been used by people.Denevan (1992a) estimates a pre-Colombian lowland population of 8.6 millionin South America, yielding a density of 0.62 persons per square kilometer, basedon a lowland expanse of 13,305,000 square kilometers (Food and AgriculturalOrganization, 1992).1 At present, the tropical rainforest zones of Latin America(and the Caribbean) show a population of 52,900,000, or 10 persons per squarekilometer. Evidently, human population pressure on the land has increased bymore than an order of magnitude as the density estimate of Denevan (1992a)covers all forest biome types including those more densely settled than tropicalrainforest such as tropical deciduous forest (See Food and Agricultural Organi-zation, 1992). In any event, in Latin America and in other parts of the tropicalworld forest dwellers and their land use systems are primary agents of forestdynamics and environmental change.

It is important to draw a distinction between land uses of indigenouscultivators and those of colonists to agricultural frontiers (Walker and Homma,1996). Many have argued that indigenous farmers practice sustainable forest-use in contrast to the exploitative activities of colonists (Vayda, 1979; Hamesand Vickers, 1983; Dove, 1986; Posey and Balee, 1989; Moran, 1990). Neverthe-less, Beaumont and Walker (1996) demonstrated that degradation outcomesunder common property (the indigenous case) and private property or open access(the colonist case) are highly dependent on external economic circumstances.

1Such an aggregate calculation masks considerable site variation associated with particulargroups. For example, Clastres (1973) has estimated a population density of 4 persons per squarekilometer for 1,500,000 Guarani, at the time of contact. However, for Greater Amazonia the densityfigure is closer to 0.58 persons per square kilometer (Denevan, 1998).


WALKER: UNCULTIVATED WILDERNESS 389

Simmons (1997) found no differences between tribal groups and colonists withrespect to forest management in a settlement frontier in Panama.

Although the degree to which environmental impact varies between indige-nous and colonist households is a subject of controversy, their farming systemsshow important differences, possibly as a function of degree of access to trans-portation systems and markets (Simmons, 1997). Indigenous systems oftenpossess high crop diversity particularly when fallows are directly incorporatedinto farm management (Unruh,1988 and 1990; Salick,1990). On the other hand,colonists show diversity in field components. Although the number of crops maybe restricted, the farming system comprises diverse structural elements suchas pasturage, plantations of perennials, and fields with consortiums of annualvegetation (Nair, 1987).

The purpose of this paper is not to provide a typology of farming systems inorder to comprehend cultural distinctions in resource management, but todevelop a context for the discussion of subsistence agriculture in tropicalfrontiers. The conceptual model presented is a hybridization of indigenous andcolonist agriculture in which annuals production occurs in monospecific fieldsthat are rotated. All nutritional sustenance is assumed to be so provided; fallowproducts are neglected despite the abundant anthropological record of theirimportance. In the following discussion I refer to forest occupants practicingsmall-scale agriculture, whether indigenous or colonist, as subsistence farminggroups, except when developing a culturally specific point.2

The rotation of fields (and fallows) involves a repetitive return to old plots,in which case the used and temporarily abandoned land constituting a stock ofswidden and secondary vegetation represents a form of equilibrium land use. Inthe sequel, I refer to the stymied successional processes within the group’s activeland use system as cyclic succession; that occurring on permanently abandonedland I define as terminal succession. The distinction between cyclic and terminalsuccession is a theoretical construct. In the absence of technological change, ifgroup characteristics remain constant through time and the group practicesrotational agriculture quantities of land are distributed over fixed age cohorts.In such a situation the cohorts may be said to be in equilibrium. On the otherhand, if the group abandons a field or farm in principle land may return toold-growth vegetation indistinguishable from primary forest. Of course, demo-graphic characteristics change and land abandonment does not preclude reoc-cupation by other parties.

Subsistence farmers require a wide selection of natural commodities tosurvive and pursue cultural activities. In the absence of markets such commoditiesare taken directly from the forest environment or through agricultural activitiesof limited scope. Typically, forest ecosystems consist of numerous floral andfaunal components and they are capable of dynamic responses to environmental

2In the present context the subsistence group is a nuclear family, a clan, or a kin group.Members of clans all trace their ancestry to a single individual whereas kin groups are more flexiblyorganized systems of blood relatives (Keesing, 1975).



change through succession. Succession may be of fundamental importance tosubsistence groups because species composition is in large part a function ofsuccessional stage. Many of the plants and animals found in recently clearedfields are different from those found later in old fallows, which may be virtuallyindistinguishable from the primary forest.

Certain stages in the successional process maximize the probability ofencountering particular species given changing densities of encountered indi-viduals. An appropriate choice of fallow would presumably improve labor pro-ductivity in searching for useful plants and animals, an important householdobjective (Staver, 1989). The efficient expenditure of labor, together with func-tional links between species distribution and successional stage, provide behav-ioral and technical bases for indigenous fallow management across varying ageclasses of secondary vegetation.

Tables 1a and 1b show the distribution of plant species grouped by usecategory for various age classes of fallows and secondary forest. Table 1a revealswhat may be referred to as inter-fallow complementarity in the provision ofcarbohydrates and protein, derived from game.3 Twenty-seven food plants arefound in house garden clearings whereas 21 are found in fallows aged two yearsor younger. Although a substantial number of food plants show up in fallowsaged 2 to 40 years, this successional stage also includes 46 types of plants thatattract game. In addition, Table 1a shows distributions of essential, nonsubsti-tutable items across fallow ages including food, medicinals, and constructionmaterials (the technology class). These distributions suggest some redundancygiven similar frequency counts for uses in certain of the fallows. Nevertheless,as presented the data conceal important items necessary to the fulfillment ofbasic needs. For example, the best firewood trees, a technological species in theclassifications given, are more readily found in older fallows (Balee and Gely,1989). Table 1b shows changing species composition of food plants by age offallow for a second indigenous group.

Although strong arguments have been made that fields of subsistencefarmers mimic the diversity of their environs in tropical areas (Geertz, 1966),colonists often reduce the number of plant species cultivated given hopes ofmarket sale and the economies of monoculture. In such circumstances the fieldsthemselves may be differentiated to produce food complements, particularly inproviding combinations of carbohydrates and protein (Scatena et al., 1996).Suchinter-field complementarity is not restricted to colonists; indigenous peoples mayalso focus cultivation efforts on fields. Table 2a gives field counts for two samplesof indigenous communities; the fields in question show the production of food

3I use the term complementarity here in the sense of food complements, or food items that arenecessary and not substitutable, such as carbohydrates and proteins (see National Academy ofSciences, 1992). In the model development, I consider food items supplying complementary aminoacids that together provide a full protein. The formal representation is given by a Leontief technology(Varian, 1978) which produces subsistence on the basis of complementary food inputs, namely riceand beans.



complements. In general, crops are differentiated by both colonists and indige-nous peoples to provide basic nutrition requirements, as indicated in Table 2b.Although these data do not give the age of secondary vegetation associated withthe indicated crops, they do show that crops are chosen to provide basic foodcomplements of carbohydrate, protein, and fat (Salick, 1989; Pennington, 1989).These sources may be associated with fallows or old-growth forest as with BrazilNut, with fields as with rice, or with orchards or fallows as with mango andbreadfruit (See also Unruh and Alcorn, 1987; Unruh and Paitan, 1987).

Nutritive requirements across basic food groups provide an explanation ofdiversity in crop selection but do not account for production magnitudes. In turn,these magnitudes determine the size of the swidden and by implication the areasof fallow, or the garden areas (Allan, 1965), in various age categories associatedwith particular rotation series. As such, the production decision leads directlyto the magnitude of land allocation in cleared parcels under particular crops andabandoned parcels undergoing cyclic succession.

The amount of land used by subsistence farmers and the associated produc-tion magnitudes are functions of both long-run and short-run phenomena,including patterns of historical accumulation, the wealth position of the group,and domestic cycle stages affecting the availability of labor (Walker and Homma,1996; Coomes and Burt, 1997). Greater wealth and increased stocks of labor,

TABLE 1a: Species Counts by Use in Successional VegetationKa’apor-Maranhao, Brazila

UseFallow Age 1 2 3 4 5 6 7 8 9

House Garden 27 9 5 12 3 7 7 8 40–2 years 21 23 17 15 2 1 0 4 32–40 years 30 46 15 18 1 1 0 4 2240–100 years 14 18 6 4 0 0 3 1 7

aAdapted from Balee and Gely (1989); use classes are: 1=food; 2=game food; 3=technology;4=remedy; 5=commerce; 6=spice/stimulant; 7=magic; 8=personal adornment; 9=other.

TABLE 1b: Species Types by Age of Successional VegetationBora-Brillo Nuevo, Perua

0–1 year corn, rice, cowpeas1–2 years manioc, banana, cocoa1–5 years manioc, pineapple, peanuts, coca, guaba, caimito, uvilla, avocado, cashew,

barbasco, peppers, game4–6 years peach palm, banana, uvilla, caimito, guaba, annatto, coca, game, pineapple6–12 years peach palm, uvilla, macambo, game12–30 years macambo, umari, breadfruit, copal≥ 30 years umari, macambo

aAdapted from Denevan and Treacy (1987).



reflecting increased demand for food, lead to larger land holdings. The wealtheffect may be diminished in pure subsistence economies; here, social differen-tiation is little pronounced to begin with and incentives to accumulate land arelinked to consumption demands, which in turn are correlated with farminggroup labor supply. Consequently, the amount of land allocated to swiddens andfallow will be largely a function of the demographic condition of the farminggroup. Data adapted from Salick and Lundberg (1990) presented in Table 3 areconsistent with this assertion for the case of individual households, althoughsample size is limited. Within the infertile soil category, early stage householdsshow smaller holdings on average than one at middle stage.4 Early and late

TABLE 2a: Fields Counts

Eastern Perua 3.33 fields per householdb

Colombia/Venezuelac 4.25 fields per householdd

a Salik and Lundberg (1990).b Average calculated on basis of 90 fields in community of 27 households.c Ruddle (1974).d Average calculated for 4 case study households.

TABLE 2b: Prime Nutrition Sources by Nutrient and Subsistence Groupa

(1) (2) (3)

Carbohydrate Mango Sour Sop MangoSour Sop Rice Sour SopRice Pigeon Pea Bread Fruit

Protein Pigeon Pea Pigeon Pea Brazil Nut (4)b

Hyacinth Bean Broad Bean Avocado (4)Lima Bean Cow Pea

Fat Cashew Cashew Brazil NutAvocado Peanut AvocadoPeanut Coconut

aAdapted from Salik’s appendix (Salik, 1989): (1) Peru—indigenous (Salik, 1989); (2) Brazil—Colonist (Moran,1981); (3) Brazil—Indigenous (Posey,1985).Three prime sources selected randomly;cultivation often provides more than three prime sources in the various sites. See Salik (1989,pp. 207–211). Prime source of carbohydrates defined as providing 25 grams or more in a “typicalserving”; prime source of protein defined as providing 10 grams or more in a “typical serving”; primesource of fat defined as providing 10 grams or more in a “typical serving.” (See Pennington, 1989.)The Brazil indigenous group shows relatively few English translations of crop names, necessary foruse of Pennington (1989). That only two crops are listed as prime sources of protein and fat mayresult from this.

b Grams protein provided by maximal source, as identified by English name, necessary forextraction of data from Pennington (1989).

4Table 3 is adapted from Table VI in Salick and Lundberg (1990, p. 210). The category earlyincludes a “poorly established” family and three “newly established” families. The category middle



stages reveal comparable holdings for fertile soils;a late stage would presumablyshow contracted labor and reduced consumption demands by the farming group(Bonnal et al., 1993). Soil quality is an important influence on the amount of landnecessary for achieving desired production levels (Salick and Lundberg, 1990).

3. LANDSCAPE MODELS

In this section I describe two models in order to establish a conceptualmotivation for the theoretical structure to be presented. Existing theory primar-ily presents macro-relations between human population and the environment,although the von Thünen–based approach, describing land use at macro-scale,is predicated on the behavior of decentralized agents. Empirical work has alsoaddressed relations at macro-scale (e.g., Turner, Hanham, and Portararo, 1977),although more recent research addresses the complexity of traditional systemsin describing site-level variations in farm system characteristics such as rotationtimes (Scatena et al., 1996; Coomes and Burt, 1997). Such work points totheoretical explanations based on demographic and economic characteristics offarming groups within a household economy framework (Ellis, 1993).

Boserup (1965) considers the long-run relationship between human popu-lations and the environment under traditional technology. Given natural in-crease of the population, pressure is brought to bear on land resources leadingto technological intensification. The initial phases of intensification involve areduction of rotation times. In essence, farming groups cultivate reduced areasby virtue of accelerated rotations, with the multiplication of such groups underpopulation growth. The landscape implication is that regions undergo ground-cover changes in the aggregate, from primary forest cover (or forest fallows) toever-younger associations of secondary vegetation (e.g., bush fallow) until per-manent agriculture is achieved with sedentary human populations.5

TABLE 3: Total Cultivation Areaa

Hectares Life Cycle Soil Quality

0.21 Early Fertile0.19 Late Fertile0.95 Middle Fertile and Infertile2.25 Middle Fertile and Infertile0.89b Early Infertile1.02 Middle Infertile

a Adapted from Salik and Lundberg (1990).b (n=3)

includes three “large” families, whereas the late category is represented only by one family unitconsisting of a widow.

5Strictly speaking, forest fallows represent a form of successional, or secondary, forest.Nevertheless, fallow lengths may be sufficiently long to allow the recovery of structure and speciescomposition similar to primary forest formations.



The von Thünen model has been adapted to the case of rotational agricultureby Jones and O’Neill (1993a, 1993b). Length of fallow (rotation time) is taken asan endogenous variable and shown to be sensitive to system parameters. Inparticular, the fallow period is inversely related to commodity prices, priceexpectations, nearness to the central market, the interest rate, population size,and expectations about future population levels. These results are consistentwith Boserup’s demographic contention about the link between populationdensity and degree of agricultural intensity, and extend Boserup’s argument tothe effects of the market economy including capital markets on intensity ofproduction, defined as length of fallow period. The results of Nerlove and Sadka(1991) are similar although they characterize production intensity by laborapplications per unit land. They also show that under this description agricul-tural intensity increases with nearness to the central market.

The model accounts suggest that rotation time is a function of economic,technological, and demographic conditions affecting subsistence groups. Byimplication, these variables explain the distribution of groundcover into cropsand various age cohorts of secondary forest through cyclic succession. VonThünen and urban-based models describe static landscapes with individualplots permanently dedicated to particular crops, technologies, or lot sizes.Equilibrium succession implicit in the described models allows that individualplots change groundcover, although systematically. Plots are successivelycleared and abandoned to fallow; with each passing year in fallow, secondaryvegetation ages until it is slashed upon reaching the maturity associated withrotation time. Although vegetative covers on individual plots are dynamic, in theabsence of economic, technological, and demographic change the quantity of landdedicated to particular forms of groundcover is fixed at regional scale.

Boserup (1965) captures an important regional phenomenon, namely thatpopulation density and rotation times in the aggregate are functionally linked.However, a great deal of site-level variation is observed within countries andindividual farming groups may use various ages of secondary forest whichimplies a component of variation independent of demographic characteristics.Jones and O’Neill (1993a, 1993b) address the market basis of rotation timevariation.Nevertheless, market attachments of many subsistence farmers aresporadic at best, and it is within this group that slash-and-burn agricultureflourishes.6 The conceptual framework presented in this paper allows fornon-uniqueness in rotation times implicit in the notion of inter-field complemen-tarity. It also accounts for technical choice (i.e., rotation times) in the absence ofmarket attachments, beyond the extensive margin of agriculture. Consequently,the model provides an agent-based description of forest structure and land usein the empty realm of von Thünen’s uncultivated wilderness.

6Jones and O’Neill (1993b, p. 132) note the loose attachment of shifting cultivators to capitalmarkets and are well aware of the marginalized situation of rotational systems. Nevertheless, theirmodel ascribes technical choice to economic behavior driven by market incentive, namely profitmaximization with perfect information about prices and transportation costs.



4. MODEL OF ROTATIONAL AGRICULTURE

The model presented combines household production theory with an adap-tation of the forestry rotation problem to shifting cultivation (Mitra and Wan,1985). The household or farming group chooses an optimal level of leisure andsubsistence, which is a food measure based on crop complementarity vis-à-visnutritive requirements. In the rotational component of the model subsistence isprovided by crops planted in the wake of secondary forest clearance, or a “slashand burn” operation. The production value of the forest is the crop output, afunction of soil fertility, which itself is a function of age of secondary forest(Barrett, 1991). These functional relationships vary with crop type becausedifferent crops possess different nutrient preferences. Soil fertility and henceproduction potential increase with time in a manner analogous to wood-valuegrowth functions typical in statements of forestry optimization problems (seeHirshleifer, 1970). The problem for the shifting cultivator is to optimize farminggroup welfare with respect to leisure and subsistence (Ellis, 1993) by selectingthe magnitude and timing of slash and burn operations in clearing secondaryforest. The formulation identifies the allocation of land to individual crop types(the crop allocation) and the total amount of land demanded by the group. Thus,the stock of land is endogenous to the model.

The model statement assumes monocultural fields and because more thanone crop is necessary for metabolic survival the farmer must make multiple fielddecisions; in the sequel, two crops involving two fields are considered. When thenecessary crops show differential responses to rates of fertility recovery afterfallow the farmers use different ages of secondary forest each year and followdifferent rotation cycles for the crops. I assume that the farmers follow cyclicrotations (see Spencer,1966) and that the cultivation period is one year,althoughmulti-year cultivation may be incorporated directly into the model.An importanttropical forest system not treated by the present formulation is that involvingrelay cropping of complementary crops. In this system nutritional subsistenceis attained through synchronizing multiple fields under the same rotation sothat complementary crops are simultaneously available (Allan, 1965).

The solution is given as follows: First, I fix the farming group’s consumptionof leisure and identify welfare-optimizing outputs for the two crops in question.By assumption, land is worked as a fixed coefficient of labor expenditures andindependently of crop type or field operation which implies an allocation ofavailable land between crops referred to as the crop allocation. This allocationyields an optimal subsistence level associated with the fixed leisure value. I thenintroduce the functional relationship between subsistence and leisure into thewelfare function and solve for the optimizing choice of leisure. Prior to statingthe solution, I develop an explicit statement of rotational agriculture andconsider the notion of a subsistence production function.



Rotational Agriculture and Stationary Programs

Following Mitra and Wan (1985), let crop i production potential of secondaryforest per unit area be represented by a function, fi, of forest age, a, or f(a) for a≥ 0. It is assumed that fi(a) = 0 for 0 ≤ a ≤ ai for some ai ≥ 1; fi is continuous fora ≥ ai, and there exists a positive integer Ni > ai such that fi(a) increases in a fora < Ni and decreases for a > Ni. The function fi refers to one crop only; differentfunctions are associated with different crops. As such, it should not be confusedwith the growth function of secondary vegetation, which relates time of recoveryto a biomass measure such as carbon. The function considered here representsplant nutrients specific to individual crops; consequently, soil fertility recoversat differential rates as a function of crop type even though the secondaryvegetation is the same.

Let d be the first unit vector and e the (N+1)th unit vector of N+1. Let µand v be the sum vectors in N and N+1. Let In be the N × N identity matrix.Define the (N+1) × (N+1) matrix

and the N × (N+1) matrix B as

[ 0 IN ]

Define the set Di=[xi in +N+1: vxi= γi, exi=0]; the set Ei = [(xi, yi) ∈ Di× +

N+1: yi

= Axi]; and the set Fi = [(xi, zi) in Di × Di = B(Axi – zi) ≥ 0]. Note that vyi = γi anddyi = 0, where γi is a fixed positive constant. Let xi

t = [xit(0), . . ., xi

t(Ni)] for a = 0,1, . . ., Ni be the amount of land occupied by the input of secondary forest of agea at the end of period t for crop i. There is a feasibility condition that secondaryforest will never be allowed to grow beyond Ni for any reasonable objectivefunction for the household economy. In this regard, feasible programs forsecondary forest management are restricted to those satisfying xi

t(Ni) = 0, or exit

= 0. For area γi, xit belongs to the set Di for each t given full utilization of land

under crop i, or vxit = γi.

Let yit+1 = [yi

t+1(0), . . . , yit+1(Ni)]; then for a = 0, 1, . . ., Ni, the amount of land

occupied by the output of secondary forest of age a at the end of time period (t+1)associated with crop i is yi

t+1(a). Hence yit+1(1) = xi

t(0); . . .; yit+1(Ni) = xi

t(Ni – 1).By definition, yi

t+1(0) = 0 or dyit+1 = 0. It follows that yi

t+1 = Axit and (xi

t, yit+1) is

in Ei. At the end of time period t + 1 vegetative stands of different ages areslashed and burned and agricultural production takes place. Secondary forestand shrub clearance,and agricultural activities including harvests,are assumedto occur simultaneously. A field used during some arbitrary year will showsecondary forest aged one year at the end of that year. In this context the termsecondary forest is somewhat of a misnomer from an ecological perspective. Forterminological simplicity, I do not make a distinction between regrowth catego-ries on the basis of age and refer only to secondary forest or regrowth. Note that

RR R

0 10IN

LNM

OQP

R R



output in this context is not a production magnitude but the amount of landcontaining secondary forest of the specified age at the end of some time period.This is the terminology of a “point-input–point-output” framework (see Mitraand Wan, 1985, p. 266) and is not to be confused with the actual crop outputwhich is the product of the amount of land slashed and the latent productivityof the slashed vegetation, represented by the production potential function, f(a).

Given the relationship between x and y, it must be the case that yit+1(1) ≥

xit+1(1); . . .; yi

t+1(Ni) ≥ xit+1(Ni), which implies B(yi

t+1 – xit+1) ≥ 0. Let the

slash-and-burn routine be defined as Cit+1 = [Ci

t+1(1), . . ., Cit+1 (N)]; Ci

t+1(a) fora = 1, . . ., Ni is the yearly clearing for crop i made in secondary forest of age a,that is released to succession at the end of period t + 1.Note that Ci

t+1(a) = [yit+1(a)

– xit+1(a)] for a = 1, . . ., Ni; or, Ci

t+1 = B(yit+1 – xi

t+1); thus, it is an areal measure.The input of land to succession for purposes of production of crop i at the end ofperiod t + 1, or xi

t+1(0), is the sum of all clearings of secondary forest of thedifferent ages, or xi

t+1(0) = Cit+1(1) + . . . + Ci

t+1(Ni). Consequently, µCit+1 = dxi

t+1.A feasible program for the production of crop i, from xi in D, is a sequence

<xit, yi

t+1> satisfying xio = xi, (xi

t, yit+1) ∈ E, B(yi

y+1 – xit+1) ≥ 0 for t ≥ 0 (See Mitra

and Wan 1985, p. 267). A feasible program is stationary if xit = xi

t+1 for t ≥ 0. Inthe sequel, only stationary programs are considered in order to maintainconsistency with the statement of utility. In particular, strong variations in thetemporal pattern of consumption are not likely to be consistent with fixed groupsize so the dynamic optimization problem identifies an invariant level of suste-nance. Note that a feasible program is associated with a feasible slash-and-burnroutine because

Cit+1 = B(yi

t+1 – xit+1)

Consider the function gi(a) = δafi(a)/[1 – δa], for 1 ≤ a ≤ Ni, where δ is a discountfactor in (0,1). There exists an integer Mi such that 1 < Mi ≤ Ni and gi(Mi) ≥ gi(a)for a ∈ [1, . . . , Ni]; this is a Faustmann solution. Define βi = γifi(Mi)/Mi, whereγi/Mi is area under production of crop i utilizing secondary growth of age Mi.Then βi is the associated actual output, or production magnitude, of crop i whena field of size γi is rotated under Faustmann cycles. By implication the utilizedsecondary growth is aged Mi years.

Define the vector i = [γi/Mi, γi/Mi, . . . γi/Mi, 0 . . . 0] such that v i = γi. Thisvector belongs to Di and defines an output of land i, in the “point-input–point-output” framework. Together, < i, i> yield a feasible stationary program withyearly production of crop i fixed at βi, presumably measurable in some outputmagnitude, e.g., kilograms of rice. Note that any allocation of land acrosssame-sized age cohorts of secondary forest gives an xi belonging to Di. Considerall such vectors unequal to i for fixed γi; let x*

i represent an arbitrary vectorof this set. Then <x*

i, y*i> is a feasible stationary program with a fixed yearly

output of crop i. Let this output of crop i be zi, where zi = γifi(T)/T and T is the

$x $x$y

$x $y

$x



rotation time associated with the stationary program (or age of secondary forest).Note that zi = βi when T = Mi.

Subsistence as Metabolic Production

Consider a subsistence production function, S, from +2 to ; subsistence

is based on two crops consumed by the farming group. By the definition of theproduction potential function, fi , potential crop i output per unit area defines avector Qi = [fi(1), . . ., fi(Ni)] whose elements reflect the age of secondary growth.The actual production of crop i at time t is then given as the product of this vectorand the land utilized in each age cohort of secondary forest, or QiCi

t. Let afarming group subsistence program be represented as <Q1C1

t, Q2C2t> for two

subsistence crops, and a stationary subsistence program, as <z1, z2>, where zi,i = (1,2), is the fixed yearly total production of crop i. That is, in the stationarycase, zi = QiCi

t for all t. Let Q1C1t and Q2C2

t serve as inputs to a metabolic“technology” generating S, the level of farming group subsistence or the subsis-tence output, which then enters as an argument in the group welfare function.Following Varian (1978, p. 5) complementary food requirements may be repre-sented by a Leontief metabolic technology in which subsistence derives fromfood inputs as follows for the two-crop case

S(Q1C1t, Q2C2

t) = Min(Q1C1t,bQ2C2

t)

where b is a constant reflecting the relative quantities of the crops required tofulfill metabolic needs.7 Note that the inputs are not complementary to produc-tion in the conventional way because there are no factor prices that would enableexplicit statements of the appropriate cross-price elasticities. The notion ofcomplementarity in this setting reflects the nonsubstitutability of food comple-ments in yielding sustenance (see National Academy of Sciences, 1992). ALeontief formulation captures this meaning.

THEOREM: Age of secondary forest used by shifting cultivators is unique tocrop-type whereas the land quantity demanded is unique to the welfare require-ments and demographic structure of the farming group

Proof. The proof is achieved by showing the existence of a unique choice ofleisure (l) and subsistence (S), given some arbitrary farming group whosepreferences are reflected in an increasing, strictly concave, and twice-differen-tiable welfare function, U(l,S), and discount rate, δ. This choice is identified bysolving the problem

R R

Max{l S

t

t

U l S, }

,δ=

∞

∑0

b g

7For example, rice and beans each bring a complement of amino acids to a diet, and in fixedproportion they generate a complete protein. Excessive rice or beans do not add subsistence valueto a meal with respect to protein requirements.



The solution is given as follows: Fix l and solve for optimizing S in terms of l.Then, substitute the optimizing S in the utility function and select for l. With lfixed the choice of optimizing S is identified by solving for a monotone transfor-mation of the summation function given in the Lemma. The theorem is thenproved by solution of the utility-maximization problem.

LEMMA: Given fixed leisure and associated land constraint, the optimal sta-tionary subsistence program is given by production under Faustmann rotations,<β1, β2>

Proof. Let L be the farming group labor endowment. Work (w) and leisure(l) are related as w + l = L. Total land stock used (for both crops), γ, requires laborfor clearance and preparation; this relationship is taken as linear, or γ = qwwhere q is the land requirement per unit labor.8 Therefore, a unique amount ofland is available given fixed leisure because γ = q(L-l).Given this land constraint,household utility is optimized for subsistence by solving the monotone transfor-mation of utility as follows, through choice of two stationary outputs

=

=

=

= Min

By theorem 5.1 in Mitra and Wan (1985, p. 277), each maximizationargument in the minimum function is solved uniquely by Faustmann allocations,assuming unique values of Mi; hence

Max{z z

t

t

S z z1 2 0

1 2, }

,δ=

∞

∑ b g

Max Min{z z

t

t

z bz1 2 0

1 2, }

,δ=

∞

∑LNMM

OQPP

RS|T|

UV|W|

b g

Max Min{z z

t t

t

z bz1 2

1 20

, },δ δe j

=

∞

∑LNMM

OQPP

RS|T|

UV|W|

Max Min{z z

t

t

t

t

z bz1 2

10

20

, },δ δ

=

∞

=

∞

∑ ∑FHG

IKJ

L

NMM

O

QPP

Max Maxz

t

tz

t

t

z b z1 2

10

20

δ δ=

∞

=

∞

∑ ∑LNMM

OQPP

,

8Labor is expended across crops which may be cycled over various rotation times. A sufficientcondition that guarantees a unique labor expenditure for different rotation times and for fixed land,allocated arbitrarily between crops, is that the biomass regrowth function be linear. Although thismay appear to be a strong condition, it should be kept in mind that succession to old-growth forestis a lengthy process possibly taking hundreds of years in tropical rainforests. On the other hand,



S <β1, β2> = Min [β1, β2] > Min [z1, z2] = S < z1, z2>.9

Faustmann rotations are indicated here as optimal stationary solutions forarbitrary crop allocations, but the optimal Faustmann rotation remains to beidentified. Crop production under Faustmann rotation is a function of landallocation to the individual crops, or βi = γiθi , where θi = fi (Mi)/Mi and γi is landallocated to crop i. Subsistence in the two-crop case is maximized through anoptimizing allocation of land to the crops in question through choice of γ1 and γ2

given fixed land stock γ,where γ1 + γ2 = γ.Figure 1 identifies the optimal allocationby intersection, which then may be directly solved for individual crop allocationsby observing

β1 = γ1θ1 = bβ2 = bγ2θ2

Because γ1 + γ2 = γ, this implies an optimal crop allocation

γ1 = [bθ2/(bθ2 + θ1)]γ and γ2 = (θ1/(bθ2 + θ1))γ

Given the structure of the subsistence production function and the definition ofβi, the optimal subsistence associated with land quantity γ ( = qw) is

S = φγ,

where

φ = [bθ2θ1/(bθ2 + θ1)]

and the subsistence–leisure function is given by direct substitution as

S = φq(L – l)

The main result may now be stated. By the Lemma, the problem of the farminggroup is reformulated as

Max δ φt

t

U l q L l=

∞

∑ −0

,c h

rotation cycles are frequently short by comparison,presumably due to the structure of the productionpotential growth function, fi. Consequently, it is possible that the set of feasible times for slash andburn fall along linear or near linear segments of the biomass growth function, which would upholdthe sufficiency condition.

9The individual maximization arguments in the final minimization statement of the problemrepresent objective functions in Mitra and Wan’s development (1985, pp. 277–278). Recall that forstationary programs, zi = QiCi

t , where the x and y vectors defining C possess same-sized elementsand yield the same crop production, namely z. The Mitra and Wan theorem is applicable to linearfunctions such as those appearing in the arguments. The initial x vectors are taken as free initialconditions,given wide variation in age classes of trees at local level and small field sizes of subsistencefarmers (Salick and Lundberg, 1990); the household chooses its initial stationary forest, dedicatedto crop i, as per a Faustmann rule.



Given that the arguments of the utility function are time-independent, asingle-period problem may be solved through total differentiation in leisure,yielding the conventional condition for utility maximization

US/Ul= 1/φq

where US = ∂U/∂S and Ul = ∂U/∂l. The result is depicted in Figure 2.

5. DISCUSSION

Figure 2 shows the optimizing choice of leisure and subsistence for somearbitrary farming group as indicated by a point of tangency between an indiffer-ence curve and a line representing its ability to produce leisure and subsistence.This line may be interpreted as a production-possibilities frontier; as such, itimposes a budget constraint on welfare maximization. The optimal choice ofleisure is associated with an expenditure of labor which, in turn, is used with aunique quantity of land. Thus, the amount of land demanded by the group is

Note: This figure gives the β arguments, physical crop output, in the optimized subsistenceproduction function. These βis are functions of their respective land allocations, γi (see text, p. 401).Thus, in moving from left to right, the Faustmann-timed production of crop 1 increases linearly withγ1. Optimal subsistence for total land, γ, is given by the point of intersection which identifies themaxi-min value of S.

FIGURE 1: Identification of Optimal Crop Allocation.



given endogenously on the basis of preferences and the technical relations offood production.

The figure is calibrated for a subsistence farming group of twenty personswith eight children and one elderly individual, yielding a consumption to workerratio of 0.82; the group uses four hectares to produce 4,000 kilograms of rice andtwo hectares to produce 700 kilograms of beans.10 These are approximate datafrom a survey of 261 properties along the Transamazon Highway undertakenby the author and Charles Wood in the summer of 1996. Numbers are taken forthose groups consuming all their rice and bean production (N = 44). Given thatrice and beans each provide 0.75 calories per gram, that rice provides 0.03 gramsof protein per gram, and beans, .06 grams of protein per gram, this gives 328grams of protein from rice and 115 grams of protein from beans per day, for atotal of 443 grams of protein. The daily caloric production is about 10,000.

FIGURE 2: Farming Group Optimization in Leisure and Subsistence.

10Group size reported by the colonists is consistent with Ka’apor Indians in eastern Para. Forthem, the decision unit is often an extended family with between ten and twenty individuals,consisting of two or more related nuclear families (Balee, 1998). The land requirement of six hectaresyields 0.74 acres per person, a number comparable to the average observed in traditional rainforestsystems in the Congo Basin which is about 0.5 acres per person (Allan, 1965).



Clearly, other food sources are available given the group sizes involved. Leisureendowment is taken as the total number of hours available to 11 workers with2,000 hours of potential labor available each year. Observed leisure is given asendowment minus group hours worked over a six-month farming season, at sixhours per day, for both men and women (Balee, 1998).

The budget constraint embodies a given labor supply, L, reflecting thedemographic structure of the farming group. Growth presumably leads toincreased labor availability and a shift in the budget constraint to the right.Such growth also changes group preferences, presumably with greater interestin leisure activities if dependency in the household diminishes. In particular,decreased dependency, or a lower ratio of consumers to workers, increases the“subjective wage” rate as relatively more workers become available to feed thegroup. This changes the marginal rate of substitution between leisure and foodand hence the slopes of the indifference curves (Ellis, 1993; Thorner, Kerbley,and Smith, 1966). Additional group members also shift the subsistence con-straint (represented by the vertical segment of the indifference curves) becausemore food is required as a direct function of group size (see Ellis, 1993, p. 115).Figure 3 shows a new optimal choice of leisure and subsistence, as a function ofevolving group structure, leading to new land requirements. The utilization ofland increases so long as labor supply impacts dominate the effect of the growingdesirability of leisure, as depicted in Figure 3. Although land stock changes thecrop allocation remains constant, as do rotation times for the fields in question.

An important consideration among shifting cultivators is the land-extensivenature of production, especially in the presence of growing population density(Boserup, 1965). The model presented assumes unrestricted access to land, andlabor always finds its necessary production complement without overlappingthe land used by neighbors. Nevertheless, growing rural population clearlyrestricts cost-free access to land, and competition for land resources introducessocial responses of importance to policy makers. In particular, agriculturalintensification allows reduction in rotation times to accommodate expandingpopulations, presumably in response to land competition (Boserup, 1965). Whenintensification is unsuccessful or too slow,rural-to-urban migration is a potentialsolution for forest farmers threatened by declining food security. Figure 4presents a model adaptation for the case of land constraints and food deficit.Here, a growing land constraint truncates the budget line pushing it beyond thesubsistence requirements of the group, thereby undermining food security. Suchan event may lead to conflict among farming groups or between such groups andlarge landholders as they struggle to relax their land constraints to generateproduction beyond subsistence thresholds.

Figure 4 may shed light on conflictive social processes such as those in Viseu,one of counties of greatest violence in the Amazonian state, Para, where the mostintense rural struggles are presently occurring in Brazil. Viseu is located in thenortheastern corner of Para, an old settlement region where shifting cultivationhas long been practiced. During the 1980s Viseu experienced 44 land-conflict-



related mortalities, about eight percent of all such deaths in Para over the period(Barata, 1995). If rice is produced on a rotation of ten years, and beans, fouryears, and if farming groups of twenty require four hectare clearings for rice,and two hectare clearings for beans (see footnote 10), then the total amount ofland necessary is given as11

v rice + v beans = 48 hectares

This estimate, yielding 2.4 hectares per group member, includes all cohorts ofsecondary forest aged one through ten for rice production, and one through fourfor beans.12 With intercropping the necessary land is 2.0 hectares per individual.

$x $x

FIGURE 3: Variable Demographic Structure.

11Coomes (1998) reports an average (on a small number of fields) of 9.3 years, when rice isgrown in a pure rotation without fallow crops in the regrowth intervals. The assumed four-yearrotation for beans is based on the observation that beans are typically planted in fields cut fromyounger regrowth than rice.

12The notational convention used in stating the calculated value is that for optimized,stationary rotations. The vectors include the area under cultivation as well as the fallow areas undercyclic land use at different stages of recovery. Ka’apor Indians grow rice in monoculture when marketopportunities are available. In the absence of markets intercropping occurs but fields tend to be



On the other hand, changes in land availability indicate that with ruralpopulation growth between 1980 and 1990 (from 33,930 to 78,706), the averageamount of farm land in the aggregate dropped from six to four hectares perperson (IDESP, 1980, 1990). Evidently, there is little margin in these calculationsfor agronomic problems associated with land suitability. In the absence oftechnological change and agricultural intensification it seems that subsistenceconstraints may be affecting the rural populations, leading to violent outcomes.13

6. CONCLUSION

In this paper I present a model of land use and natural ground cover beyondthe extensive margin of agriculture and describe an important mode of humanimpact on the tropical forest biome. It may be applied in a variety of policysettings, and the example of rural violence due to increasing land scarcity has

FIGURE 4: The Presence of Land Constraints.

dominated by single crops (Balee, 1998). On the Transamazon Highway beans are intercropped withcorn but are generally kept separate from rice (Moran, 1981).

13The land per person is calculated by subtracting area in holdings greater than 100 hectaresfrom total land area in the municipio. I use the land in establishments greater than 10,000 hectaresreported by INCRA in Berno de Almeida (1993), which is 5,223 square kilometers, for 17 reportingestablishments. This number is considerably greater than the 243 square kilometers reported byIBGE (1985) in the agricultural census for two large establishments.



been discussed. Ecological extensions await further treatment. Given informa-tion on the recovery of soil fertility, crop selections, and demographic charac-teristics of forest dwellers, the model may be used to predict forest agecomponents, their areal extent, and the allocation of land by crop type. Suchinformation may be useful to current debates on greenhouse gas buildup andloss of biodiversity.

Current models of agricultural land use are market-based as is appropriatefrom the economic perspective of value creation. Most agricultural products andvalues flow from producers well-integrated into input, output, and capitalmarkets. Nevertheless, such models overlook important phenomena from anecological perspective. In particular, humans exert substantial effects on thetropical resource base beyond the extensive margin of agriculture,and they havedone so since prehistory. The tropical forest biome is not now and has never beenempty, but has long served as home to indigenous peoples and colonists practic-ing shifting cultivation.Many tropical forests show human imprints. Indeed,onebasic premise of the formulation presented in this paper is that the tropicalforest is subject to the impacts of purposeful economic activity despite itsremoteness and lack of market access.

Shifting cultivation remains a widespread agricultural technology despiteefforts by many governments to control the use of fire.14 Given rapid populationgrowth in parts of the world with active settlement frontiers and relatively lowpopulation densities, this type of farming can be expected to persist and probablyextend its domain over the short- to mid-run. Peasantries and their land usesystems have proven remarkably persistent in this century despite significantadvances in agricultural technologies (Ellis, 1993). Extensions of the presentmodel may yield meaningful ways of linking household production theory to therealms of uncultivated wilderness that constitute much of our tropical land base.

REFERENCESAllan, William. 1965. The African Husbandman. New York: Barnes and Noble.Alston, Lee J., Gary D. Libecap, and Bernardo Mueller. 1997. “Violence and the Development of

Property Rights to Land in the Brazilian Amazon,” in J.N. Drobak and J.V.C. Nye (eds.), TheFrontiers of the New Institutional Economics, San Diego: Academic Press, pp. 145–163.

Alves, Diogenes S. and David L. Skole. 1996. “Characterizing Land Cover Dynamics Using Multi-Temporal Imagery,” International Journal of Remote Sensing, 17, 835–839.

Balee, William. 1989. “The Culture of Amazonian Forests,” Advances in Economic Botany, 7, 1–21.———. 1992. “People of the Fallow: A Historical Ecology of Foraging in Lowland South America,” in

K.H. Redford and C. Padoch (eds.), Conservation of Neotropical Forests, New York: ColumbiaUniversity Press, pp. 35–57.

———. 1998. Personal Communication at Resources for the Future.Balee, William and Anne Gely. 1989. “Managed Forest Succession in Amazonia: The Ka’apor Case,”

Advances in Economic Botany, 7, 129–158.

14Panama requires farmers to obtain permission for fire use 15 days in advance of burning;fines may be imposed if the farmer stands in violation (Instituto Nacional de Recursos NaturalesRenovables -INRENARE, 1994, pp. 25–26). Cameroon, Central African Republic, Zaire, Ivory Coast,and Tanzania have national laws restricting fire use (Schmithusen, 1986, p. 336).



Barata, Ronaldo. 1995. Inventario da Violencia: Crime e Impunidade no Campo Paraense. Belem,Brazil: Cejup.

Barrett, Scott. 1991. “Optimal Soil Conservation and the Reform of Agricultural Pricing Policies,”Journal of Development Economics, 36, 167–187.

Beaumont, Paul and Robert T. Walker. 1996. “Land Degradation and Property Regimes,” EcologicalEconomics, 18, 55–66.

Berno de Almeida, Alfredo Wagner. 1994. Carajas: A Guerra dos Mapas. Belem, Brazil: Falangola.Bonnal, P. Clement, D. Gastal, M. Xavier, J. Souza, G. Pereira, E. Junior, and J. Souza. 1993. Os

Pequenos e Medios Produtores do Municipio de Silvania-Estado de Goias: Carateristicas Gerais eTopology day Exploracoes. Planaltina, DF, Brazil: EMBRAPA/CPAC.

Boserup, Ester. 1965. The Conditions of Agricultural Growth. London: Allen and Unwin.Brown, Sandra and Ariel Lugo. 1990. “Tropical Secondary Forests,” Journal of Tropical Ecology, 6,

1–32.Clastres, Pierre. 1973. “Elements de Demographie Amerindienne,” L’Homme , 13, 23–36.Coomes, Oliver. 1998. Personal Communication at Resoures for the Future.Coomes, Oliver T. and Graeme J. Burt. 1997. “Indigenous Market-Oriented Agroforestry: Dissecting

Local Diversity in Western Amazonia,” Agroforestry Systems, 37, 27–44.Denevan, William M. 1992a. “The Pristine Myth: The Landscape of the Americas in 1492,” Annals

of the Association of American Geographers, 82, 369–385.———. 1992b. “Stone Vs. Metal Axes: The Ambiguity of Shifting Cultivation in Prehistoric Ama-

zonia,” Journal of the Steward Anthropological Society, 20, 153–165.———. 1998. Personal Communication at Resources for the Future.Denevan, William M. and John M. Treacy. 1987. “Young Managed Fallows at Brillo Nuevo,” Advances

in Economic Botany, 5, 8–46.Dove, Michael R. 1986. “The Ideology of Agricultural Development in Indonesia,” in C. MacAndrews

(ed.), Central Government and Local Development in Indonesia. Singapore: Oxford UniversityPress, pp. 221–247.

Ellis, Frank. 1993. Peasant Economics. Cambridge: Cambridge University Press.Food and Agricultural Organization of the United Nations. 1992. The Forest Resources of the Tropical

Zone by Main Ecological Regions. Rome: Forest Resources Assessment 1990 Project.Geertz, Clifford. 1966. Agricultural Involution: The Process of Ecological Change in Indonesia.

Berkeley: University of California Press.Gomez-Pompa, A., C. Vazquez-Yanes, and S. Guevara. 1972. “The Tropical Rainforest: A Nonrenew-

able Resource,” Science, 177, 762–765.Hames, Raymond and William Vickers, eds., 1983. Adaptive Responses of Native Amazonians. New

York: Academic Press.Hirshleifer, J. 1970. Investment, Interest, and Capital. Englewood Cliffs, NJ: Prentice-Hall.IBGE (Instituto Brasileiro de Geografia e Estatistica). 1985. Censos Economicos—1985 (Censo

Agropecuario-Para). Rio de Janeiro: Secrataria de Planejamento, Orcamento e Coordinacao.IDESP (Instituto do Desenvolvimento Economico-Social do Para). 1980. Anuario Estatistico do

Estado do Para. Belem, Brazil: IDESP.IDESP (Instituto do Desenvolvimento Economico-Social do Para). 1990. Anuario Estatistico do

Estado do Para. Belem, Brazil: IDESP.INRENARE. 1994. Ley 1 de 3 de Febrero de 1994. Panama City: INRENAREJones, Donald W. and Robert V. O’Neill. 1993a. “Human–Environmental Influences and Interactions

in Shifting Agriculture,” in T.R. Lakshmanan and P. Nijkamp (eds.), Structure and Change in theSpace Economy, Berlin: Springer-Verlag, pp. 297–309.

———. 1993b. “Human–Environmental Influences and Interactions in Shifting Agriculture WhenFarmers Form Expectations Rationally,” Environment and Planning A, 25, 121–136.

Keesing, Roger M. 1975. Kin Groups and Social Structure. New York: Holt, Rinehart and Winston.Mitra, Tapan and Henry Y. Wan. 1985. “Some Theoretical Results on the Economics of Forestry,”

Review of Economic Studies, 52, 263–282.Moran, Emilio F. 1981. Developing the Amazon. Bloomington: Indiana University Press.



———. 1990. The Ecosystem Concept in Anthropology. Washington, DC: American Association forthe Advancement of Science.

Moran, Emilio F., Alissa Packer, Eduardo Brondizio, and Joanna Tucker. 1996. “Restoration ofVegetation Cover in the Eastern Amazon,” Ecological Economics, 18, 41–54.

Nair, P.K.R. 1987. “Agroforestry Systems Inventory,” Agroforestry Systems, 5, 301–317.National Academy of Sciences. 1992. Diet and Health: Implications for Reducing Chronic Disease

Risk. Washington, DC: National Academy Press.Nerlove, Marc and Efraim Sadka. 1991. “Von Thünen’s Model of the Dual Economy,” Journal of

Economics, 54, 97–123.Pennington, Jean. 1989. Bowes and Church’s Food Values of Portion Commonly Used. Philadelphia:

J.B. Lippincott.Posey, Darrell and William Balee, eds., 1989. “Resource Management in Amazonia: Indigenous and

Folk Strategies,” in Advances in Economic Botany Monographs 7. New York: New York BotanicalGarden.

Ruddle, Kenneth. 1974. The Yukpa Cultivation System: A Study of Shifting Cultivation in Colombiaand Venezuela. Berkeley: University of California Press.

Salick, Jan. 1989. “Ecological Basis of Amuesha Agriculture, Peruvian Upper Amazon,” Advances inEconomic Botany, 7, 189–212.

Salick, Jan and Mats Lundberg. 1990. “Variation and Change in Amuesha Agriculture, PeruvianUpper Amazon,” Advances in Economic Botany, 8, 199–223.

Scatena, Fred, Robert T. Walker, Alfredo Homma, Arnaldo Jose de Conto, Celio A.P. Ferreira, Rui deAmorim Carvalho, Antonio C.P. Neves da Rocha, Antonio I. Moreira dos Santos, and Pedro Mourãode Oliveira. 1996. “Cropping and Fallowing Sequences of Small Farms in the ‘Terra Firme’Landscape of the Brazilian Amazon: A Case Study from Santarem, Para,” Ecological Economics,18, 29–40.

Schmithusen, Franz. 1986. Forest Legislation in Selected African Countries. FAO Forestry Paper 65.Rome: Food and Agricultural Organization of the United Nations.

Simmons,Cynthia S.1997. “Forest Management Practices in the Bayano Region of Panama:CulturalVariations,” World Development, 25, 989–1000.

Spencer, Joseph E. 1966. Shifting Cultivation in Southeastern Asia. University Publications inGeography, 19. Berkeley: University of California Press.

Staver, Charles. 1989. “Why Farmers Rotate Fields in Maize-Cassava-Plantain Bush Fallow Agri-culture in the Wet Peruvian Amazon,” Human Ecology, 17, 401–426.

Thorner, Daniel, Basile Kerblay, and R.E.F. Smith. 1966. A.V. Chayanov on the Theory of the PeasantEconomy. Homewood, IL: Richard D. Irwin.

Turner, Billie L. II, Robert Q. Hanham, and Anthony V. Portararo. 1977. “Population Pressure andAgricultural Intensity,” Annals of the Association of American Geographers, 67, 384–396.

Unruh, Jon D. 1988. “Ecological Aspects of Site Recovery Under Swidden-Fallow Management inthe Peruvian Amazon,” Agroforestry Systems, 7, 161–184.

———. 1990. “Iterative Increase of Economic Tree Species in Managed Swidden-Fallows of theAmazon,” Agroforestry Systems, 11, 175–197.

Unruh, Jon D. and Janis B. Alcorn. 1987. “Relative Dominance of the Useful Component in YoungManaged Fallows at Brillo Nuevo,” Advances in Economic Botany, 5, 47–51.

Unruh, Jon D. and Salvador F. Paitan. 1987. “Relative Abundance of the Useful Component in OldManaged Fallows at Brillo Nuevo,” Advances in Economic Botany, 5, 67–73.

Varian, Hall R. 1978. Microeconomic Analysis. New York: W. W. Norton.Vayda, Andrew P. 1979. “Human Ecology and Economic Development in Kalimantan and Sumatra,”

Borneo Research Bulletin, 11, 23–32.Walker, Robert T. and Alfredo Homma. 1996. “Land Use and Land Cover Dynamics in the Brazilian

Amazon: An Overview,” Ecological Economics, 18, 67–80.



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