Malthusian assumptions, Boserupian response in models of the transitions to agriculture
MMalthusian assumptions, Boserupian response inmodels of the transitions to agriculture ∗ Carsten Lemmen
Institut f¨ur K¨ustenforschung, Helmholtz-Zentrum Geesthacht, Max-Planck Straße 1,21501 Geesthacht, Germany ([email protected])
Abstract.
In the many transitions from foraging to agropastoralism it is debated whether theprimary drivers are innovations in technology or increases of population. The driver discussiontraditionally separates Malthusian (technology driven) from Boserupian (population driven)theories. I present a numerical model of the transitions to agriculture and discuss this modelin the light of the population versus technology debate and in Boserup’s analytical frame-work in development theory. Although my model is based on ecological—Neomalthusian—principles, the coevolutionary positive feedback relationship between technology and popu-lation results in a seemingly Boserupian response: innovation is greatest when populationpressure is highest. This outcome is not only visible in the theory-driven reduced model, butis also present in a corresponding “real world” simulator which was tested against archaeolo-gical data, demonstrating the relevance and validity of the coevolutionary model. The lessonto be learned is that not all that acts Boserupian needs Boserup at its core.
The relationship between humans and their environment underwent a radical change duringthe last 10,000 years: from mobile and small groups of foraging people to sedentary extens-ive cultivators and on to high-density intensive agriculture modern society; these transitionsfundamentally turned the formerly predominantly passive human user of the environment intoan active component of the Earth system. The most striking global impact is only visible andmeasurable during the last 150 years (
Crutzen and Stoermer , 2000;
Crutzen , 2002); muchearlier, however, the use of forest resources for metal smelting from early Roman times andthe medieval extensive agricultural system had already changed the landscape (
Barker , 2011;
Kaplan et al. , 2009); global climate effects of these early extensive cultivation and harvestingpractices are yet under debate (
Ruddiman , 2003;
Lemmen , 2010;
Kaplan et al. , 2011;
Stockeret al. , 2011). ∗ To appear in: “Society, Nature and History: The Legacy of Ester Boserup”, Springer, Vienna a r X i v : . [ q - b i o . P E ] M a y ransitions to agriculture occurred in almost every region of the world, earliest in Chinaand the Near East over 9000 years ago ( Kuijt and Goring-morris , 2002;
Londo et al. , 2006),and latest in Australia and Oceania with the arrival of Polynesian and European immigrantsfew hundred years ago (
Diamond and Bellwood , 2003). While each local transition can beconsidered revolutionary, the many diverse mechanisms, environments, and cultural contextsof each agricultural transition make it difficult to speak of the one ’Neolithic revolution’,as the transition to farming and herding was termed by V. G. Childe almost a century ago(
Childe , 1925). The transitions from foraging to farming were not only one big step, but mayhave consisted of intermediary stages:
Bogaard (2005) looks at the transition in terms of theland use system: she sees first inadvertent cultivation then horticulture then simple and thenadvanced agriculture, while
Boserup (1965) discriminates these stages by the managementpractice ranging from forest, bush and short fallow to annual and multi cropping.In contemporary hunting-gathering societies much less time has to be devoted to procur-ing food from hunting and gathering opposed to agriculture and herding (e.g.,
Sahlins , 1972);less labor is required for long fallow systems compared to intensive multi-cropping agricul-ture(
Boserup , 1965). So why farm? Different responses from archaeology (
Barker , 2011),demography (
Turchin and Nefedov , 2009), historical economy (
Weisdorf , 2005), and ecosys-tem modeling (
Wirtz and Lemmen , 2003) call upon processes such as social reorganization,the value of leisure, changing resources, or coevolutionary thresholds.The probably simplest relationship was proposed by
Malthus (1798, p.11), namely thatmore production sustains larger population. With larger population, more production is pos-sible, thereby constituting a positive feedback loop, which ideally results in ever greater (geo-metric) growth and productivity. That this is not the case in a world with finite resources wasexpressed by
Malthus (1798, p. 4) by stating that “Population, when unchecked, increases ata geometrical ratio. Subsistence increases only in an arithmetical ratio. A slight acquaintancewith numbers will show the immensity of the first power in comparison with the second”.Malthus identified the need for positive and preventive checks to balance population increasewith the limited capacity of resources.How does an increase in productivity come about? First and foremost, the input of morelabor increases productivity (
Malthus , 1798, p. 11), subject to the constraints of finite re-sources and diminishing returns. Where Malthus, however, focused on extensive productivityincrease, the intensification component of productivity increase was highlighted by
Boserup (1965). Investments in a more intensive production system would, however, require large addi-tional labor, and the benefits of such investments were often small. To stimulate an investmentin more intensive agriculture, Boserup requires population pressure.Both
Malthus (1798, 1826) and
Boserup (1965, 1981) concentrate on the role of labor (andlater division of labor and social/family organization) and innovations which increase areaproductivity (like storage or tools, requiring relatively more labor for harvesting, building,and tool processing). Both authors neglect the role of labor-independent innovation, or innov-ations which increase both area and labor productivity; these are innovations in the resourcesthemselves, such as cultivation of higher-yielding grains or imported high yield varieties, ortheir management such as water rights; this distinction may not be unambiguous for all in-novations, it is used here conceptually. Labor-independent innovation can be stimulated bydiversity and density of a population, both of which are positively related to population size.2lready
Darwin (1859, p. 156) wrote “The more diversified [..], by so much will they be bet-ter enabled to seize on many and widely diversified places in the polity of nature”. Translatedinto the realm of innovativity, Darwin’s “seizing of places”, or niche occupation, would be therealization of technical and scientific opportunities. As for density as a stimulus of innovation,it is aggregation which constitutes a motor of technological and cultural change (
Smith , 1776;
Boyd and Richerson , 1995) . In 1996, E. Boserup reflected on the problems arising from the differences in terminology andmethodology when comparing different models of development theories (
Boserup , 1996). Shesuggested a common framework to facilitate interdisciplinary cooperation based on six struc-tures: Environment ( E ), Population ( P ), technology, occupational structure, family structureand culture. In this framework, she then interpreted the major works of Adam Smith, ThomasMalthus, Max Weber, Karl Marx, David Ricardo, and Neomalthusian thinking, as well as herown view on different stages of the developmental process.For many of the theories and models discussed by Boserup in this framework, the partition-ing in six structures can be simplified by (a) aggregating technology and occupational structureinto a single entity technology ( T ), and by (b) aggregating culture and family structure intoa single entity culture ( C ). Aggregating technology and occupational structure means that Iassume here that changes in technology are equivalent to changes in organization and that thelocation of technological change is the occupational sector. By aggregating family structureand culture I assume that values and social conventions penetrate from the society into thefamily and are governed by similar dynamics. The reduced framework then consists of thefour compartments population, environment, technology, and culture ( PETC , Figure 1).In this
PETC framework, the one referring to
Malthus (1798) involves only population andenvironment. Population growth exerts pressure on the environment, and failure to provideadequate resources from the environment acts as a positive check on population through highermortality (Figure 1a). Technology does not play a role in this simplest Malthusian model .Culture in the form of preventive checks—such as birth control—acts on population only inlater versions of his theory ( Malthus , 1826). At its core remains “the dependent role he assignsto population growth” (
Marquette , 1997). D.
Ricardo (1821) proposed that the incentive tointensify and develop technologies comes from a stimulus in population pressure. The demandfor more land ( E ), however, leads to declining marginal benefits of and a negative feedback oninnovation ( T ) due to high costs of renting the land (Figure 1b). In Ricardo’s work, populationis independent, and technology and environment are the dependent variables.Population is also the driving factor in Boserup’s (1965; 1981) works. Of the six trans-itions considered by Boserup (1996), five can be accommodated within my
PETC frameworkas a succession of population, environment, technology, and culture: foraging to crop produc-tion, village development, Eastern hemisphere pastoralism, urbanization, and industrialization This does not, however, give the reason for a particular choice of one innovation over another (
Sober , 1992). Malthus considered the increase of carrying capacity by autonomously occurring inventions (
Lee , 1986), how-ever, this was not discussed by
Boserup (1996) in her model intercomparison. . In all these transitions, population growth leads to pressure felt from the limitedenvironmental resources, which in turn stimulates technological and organizational change,and later results in cultural changes evident in cults, social hierarchies, women’s status, andstatus symbols. Within this group of five transitions, her model of village development, inaddition, has a direct population–technology link, and allows for a feedback of the land re-sources on occupational structure (dotted lines in Figure 1c). Furthermore, her model of theforaging to farming transition includes a feedback from culture to organizational structure (notshown). I suggest here a different model of population development taking the foraging to farmingtransition as an example (Figure 1d). This model is a reduced form of the Global Land Use andtechnological Evolution Simulator (GLUES, described below), which has been operationallyapplied to a number of problems in archaeology and climate research (
Kaplan et al. , 2011;
Lemmen , 2010;
Lemmen and Wirtz , 2012;
Lemmen et al. , 2011). The reduced model shares thefunctional characteristics of the full model, but it is not spatially explicit and the biogeographicand climate background is regarded as constant (see Appendix for equations).In terms of the
PETC framework, the dynamics between population, environment, techno-logy and culture is the following (Figure 1d, cmp.
Boserup → T → P Population growth stimulates innovation by aggregation and diversity. In-novations in, e.g., health care increase population;2. P → E → P Population growth uses ever more land for hunting and exerts pressure onthe game stock, higher population densities damage the environment, and food shortageleads to reduced fertility (preventive check) or higher mortality (positive check). Therising capacity of the environment supports higher population;3. T → E More intensive foraging or farming strategies damage the environment, whileefficiency gains lead to higher capacity of the environment;4. T → C Adoption of novel technologies induces changes in social structure where spe-cialists and leaders or cults emerge;5. C → P Family and social structure change reproduction rates.
Richerson and Boyd (1998) claim that basically all models which are rooted in ecology areNeomalthusian in essence, i.e., they can be characterized by a P → T → E loop in
Boserup ’s(1996) framework. This loop can be detected in my model, as well; in fact, historically itdeveloped from ecosystem models of tree stands or algal communities(
Wirtz and Eckhardt ,1996). Unlike many other models, however, GLUES is based on coevolutionary dynamics oftechnologies and population, and as such has no a priori information on whether there is a The sixth transition—Western European fertility decline—follows a different path as a succession of techno-logy, environment, culture, and last population; it is not considered here. ) Thomas Malthus b) David Ricardoc) Ester Boserup d) this paper P = Population T = Technological level and occupational structureE = Environment C = Culture and family structure
Figure 1: Four compartment framework for the interrelationship between population, environ-ment, technology, and culture. Four economic theories are contrasted: the essays onthe principles of population by T.
Malthus (1798, 1826) (panel a, dotted line indic-ates the revised essay including culture change); D.
Ricardo (1821)’s principles ofeconomy (panel b); E.
Boserup (1965, 1981)’s theories for five transitions explainedin
Boserup (1996) (panel c, 1981 refinements shown as dotted lines); and the eco-logical model proposed in this chapter. The framework is a simplification of the sixcompartment framework originally proposed by
Boserup (1996).5Malthusian) “invention-pull view of population history” (
Lee , 1986, p. 98), or whether popu-lation is the (Boserupian) driver of development . Applications of GLUES show that there isan emergent emancipation of population development from the environment with increasingpopulation and innovation ( Lemmen and Wirtz , 2010, 2012;
Lemmen et al. , 2011).GLUES mathematically resolves the dynamics of population density and three population-averaged characteristic sociocultural traits: technology T A , share of agropastoral activities C ,and economic diversity T B . These are defined for preindustrial societies as follows:1. Technology T A is a trait which describes the efficiency of food procurement—related toboth foraging and farming—and improvements in health care. In particular, technologyas a model describes the availability of tools, weapons, and transport or storage facilities.It aggregates over various relevant characteristics of early societies and also representssocial aspects related to work organization and knowledge management. It quantifiesimproved efficiency of subsistence, which is often connected to social and technologicalmodifications that run in parallel. An example is the technical and societal skill ofwriting as a means for cultural storage and administration, with the latter acting as aorganizational lubricant for food procurement and its optimal allocation in space andamong social groups. T A is labour dependent.2. A second model variable C represents the share of farming and herding activities, en-compassing both animal husbandry and plant cultivation. It describes the allocation ofenergy, time, or manpower to agropastoralism with respect to the total food sector.3. Economic diversity T B resolves the number of different agropastoral economies avail-able to a regional population. This trait is in the full model closely tied to regionalvegetation resources and climate constraints; in this reduced model, it denotes a labour-independent technology. A larger economic diversity offering different niches for agri-cultural or pastoral practices enhances the reliability of subsistence and the efficacy inexploiting heterogeneous landscapes.The temporal change of each of these characteristic traits follows the direction of increasedbenefit for success (i.e. growth) of its associated population (Appendix equation 2); thisconcept had been derived for genetic traits in the works of Fisher (1930), and was recentlymore stringently formulated by Metz and colleagues (
Metz et al. , 1992;
Kisdi and Geritz ,2010) as adaptive dynamics (AD). In AD, the population averaged value of a trait changes ata rate which is proportional to the gradient of the fitness function evaluated at the mean traitvalue. The AD approach was extended to functional traits of ecological communities (
Wirtzand Eckhardt , 1996;
Merico et al. , 2009), and was first applied to cultural traits of humancommunities by
Wirtz and Lemmen (2003).The adaptive coevolution of the food production system { T A , T B , C } and population P (Ap-pendix equations 1–4), which is at the heart of this model’s implementation, had also beenfound empirically by Boserup (1981, p. 15): “The close relationship which exists todaybetween population density and food production system is the result of two long-existing See also
Simon (1993) for a detailed discussion. ) PET trajectories b) Innovativity vs. pressure Figure 2: Trajectories of population P , environment E , and technologies T A , T B (panel a) andphase diagram of innovation rate versus population pressure (panel b) from a simu-lation with a simplified version of the Global Land Use and technological EvolutionSimulator. The trajectories describe the temporal evolution of population density,capacity denoted as environment, a labour dependent technology T A , and a labour-independent technology T B . Numbers identify the different stages of developmentin the both diagrams. In the phase diagram b), the innovation rate, derived as thecumulative change in T A + T B , is shown in relation to population pressure, calculatedas 1 − E + P .processes of adaptation. On the one hand, population density has adapted to the natural condi-tions for food production []; on the other hand, food supply systems have adapted to changesin population density.” The outcome of the coevolutionary model simulation with the reduced GLUES is shown inFigure 2. I divided both the trajectories (temporal evolution of state variables, panel a) and thethe phase space (panel b) into six stages, which I discuss below.1. Growth phase: Starting from a Malthusian perspective, and looking only at populationand environment (quantified here as the ecosystem capacity, i.e. the ratio of birth overmortality terms in the growth rate equation 3), population grows towards its capacitywith diminishing returns as P approaches E ; this first phase spans only a short period oftime but covers a large area in phase space;2. Persistent innovation in technology T A and associated investments in tool making andadministration allow sustained slow growth of population P and alleviates the built-up7opulation pressure; in contrast to the growth phase, the phase space coverage is verysmall while the temporal extent of this phase is large;3. Transition phase: rapid innovation in a labour-independent technology T B (e.g. domest-ication successes) leads to4. Pressure relief, but induces also a change in culture (not shown);5. Equilibration: Innovation slows but has led to a wider gap between P and E because ofthe investments made in manufacturing and organization during the transition: accord-ingly, population pressure increases more slowly and up to a lower value than in thegrowth phase (1.).6. Persistent innovation: corresponds to phase (2.) and is again characterized by persistentinnovation in technology T A and a slow population pressure relief.What can be learned about the relationship between population pressure and innovativityfrom Figure 2? (i) Innovation is greatest at high population pressure. (ii) In this model thereis always innovation, at no time is technology change negative. (iii) The relationship betweeninnovativity and population pressure changes profoundly during the foraging-farming trans-ition; three different regimes can be identified: (i) a positive relationship where acceleration ofinnovation corresponds to population pressure increases (phases 1., 2., 6.), (ii) a negative rela-tionship with pressure relief during accelerating innovation (phase 3., 4.), and (iii) a negativerelationship with deceleration of innovativity at increasing pressure (phase 5.).A superficial analysis would find that population pressure is the motor of innovation in thisexample: population increase seemingly precedes the stepwise technological change (Fig-ure 2a). Only a detailed look at the phase space (Figure 2b)—especially at the transitionphases 2. and 3.—shows that innovativity decelerates at very high population pressure andthat the largest innovation occurs slightly below the highest population pressure. In fact, thedriver in the transition depicted here is not population, but technology . Only the different co-evolutionary time scales of population growth (fast) and innovation (slow) yield the seeminglyBoserupian, i.e., population driven, response.The same mathematical model—plus spatial and biogeographic aspects—has been used tosuccessfully simulate the many transitions to agriculture in Neolithic Europe ( Lemmen et al. ,2011), with good agreement with the radiocarbon record. Also there, the transitions appearBoserupian with critical innovations occurring at high population pressure. If the numericalanalysis had not been available (and proved that this is in fact technology driven), such as it isin the discretely sampled data from observations of technological change, one would have tohave come to the erroneous conclusion that this type of innovation was population driven.
I presented a reduced version of the Global Land Use and technological Evolution Simu-lator, a numerical model which is capable of realistically simulating regional foraging-farming There would be no evolution of T without P due to the coevolutionary definition of the system. The dynamicsof T , however, leads the dynamics of P at the foraging farming transition. Boserup ’s (1996) framework in developmenttheory the model should be classified as Neomalthusian. I thus demonstrated that Boserupianappearance may be based on Malthusian assumptions; I caution not to infer too quickly aBoserupian mechanism for an observed real world system when its dynamics appears to bepopulation pressure driven.
Appendix: the reduced GLUES model
A coevolutionary system of population P and characteristic traits X ∈ { T A , T B , C } is definedby the evolution equations d P d t = P · r (1)d X d t = δ X · ∂ r ∂ X , (2)where r denotes the specific growth rate of population P , and the δ X are variability measuresfor each X . Growth rate r is defined as r = µ · ( − ω T A ) · ( − γ √ T A P ) · SI − ρ · T − A · P , (3)with coefficients µ , ρ , ω , γ . In this formulation, the positive term including food productionSI is modulated by labour loss for administration ( − ω T A ) and by overexploitation of theenvironment ( − γ √ T A P ) . Food production depends on the cultural system C and availabletechnologies as follows: SI = ( − C ) · (cid:112) ( T A ) + C · T A · T B , (4)where the left summand denotes foraging activities and the right summand agropastoral prac-tice.To produce the results for Figure 2, I assumed the following parameter values: µ = ρ = . ω = . γ = . δ T A = . δ T B = .
9; a variable δ C = C · ( − C ) ; and initialvalues for P = . T A , = . T B , = .
8, and C = . Acknowledgments.
This study was partly funded by the German National Science Found-ation (DFG priority project 1266 Interdynamik) and by the PACES program of the HelmholtzGemeinschaft. The paper received great stimulus from discussions during the Ester BoserupConference 2010—A Centennial Tribute: Long-term trajectories in population, gender rela-tions, land use, and the environment, November 15–17, 2010 in Vienna, Austria. I receivedhelpful comments from two anonymous reviewers. GLUES is free and open source softwareand can be obtained from http://glues.sourceforge.net/.9 eferences
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