DIFFERENCES IN THE MECHANISMS OF TRANSITION TO AGRICULTURE IN THE FOREST ZONE OF EUROPE AND NORTH AMERICA*

Despite the similar natural conditions of the forest zone, the emergence and spread of productive farming in eastern North America and Europe occurred in different ways. To explain the differences in the timing, speed, and mechanisms of transition, we use the modeling system of global land use and technological evolution - a numerical model for modeling demography, innovation, domestication, migration, and trade in a geoecological context. It is shown that the European population received a complex of cultivated plant and animal species from other territories and quickly moved to a productive economy. Unlike in Europe, in the eastern part of North America, hunting-gathering and farming-pastoralism co-existed for a long time, and agriculture was slowly integrated into the already existing life support system. From this, it is concluded that there is a qualitative economic difference in the transition to agriculture in these regions: limited human resources in Europe and limited natural resources in eastern North America.

Keywords: early agriculture, "Neolithic package", population of pre-Columbian America, adaptive dynamics, socio-technological model, human ecodynamics.

The emergence of agriculture in the forest zone

The first Neolithic revolution occurred in the Eastern Mediterranean and the Yangtze and Yellow River valleys of China between 10,000 and 8000 BC, when hunting and gathering were replaced by agriculture and cattle breeding as the main means of obtaining food (Willcox, 2005; Kuijt and Goring-Morris, 2002; Londo et al., 2006). Subsequently, almost every human community around the world moved to a productive economy at different times, at different speeds, and through different mechanisms. In some regions, this transition was not independent: management methods were adopted from the main agricultural and pastoral centers (see, for example, [Wen et al., 2004; Fuller, 2011; Lemmen, Gronenborn, Wirtz, 2011]). Examples include Europe and eastern North America (for the latter, see [Price et al., 2001; Zeder, 2008; Smith, 2011]).

In most of Europe, the transition to a productive economy occurred between 6000 and 4000 BC, with a gradual shift in timing from the southeast (at the earliest in Greece and the Balkans [Perles, 2001]) to the northwest (Southern Scandinavia [Price, 2003] and Britain [Whittle and Cummings, 2007]). The most striking example of a large homogeneous agricultural comp-

* This work was supported by the German National Science Foundation (priority project Interdynamik N 1266) and the RASGB program of the Helmholtz Association of German Research Centers. None of these organizations had any influence on the content of the manuscript or on the decision to accept the manuscript for publication. I would like to express my gratitude to K. Wirtz for his help in developing the Global Pand Use and Technological Bvolution Simulator (GPUBS) and valuable comments on the previous version of this study. I am also grateful to DG. Anderson for his invitation to present an earlier version of the paper at the 75th Annual Meeting of the American Archaeological Society (St. Louis, April 14-18, 2010) on "Moving to a More Complex Forest Environment: A Comparison of Eastern North America and the Subtropical Temperate Zone".

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Lexa is a culture of linear-ribbon ceramics in Central Europe (Ltining, 2005). Everywhere the emergence of a manufacturing economy was accompanied by the appearance of ceramic products. No plant species was cultivated in Europe; all the crops cultivated there were native to Western Asia, where they first appeared. The "Neolithic package" that entered Europe consisted of cultivated plant and animal species that originated in the Fertile Crescent region (Flannery, 1973) and included wheat, barley, rye, lentils, peas, cattle, sheep, goats, and pigs (Willcox, 2005; Luikart et al., 2001; Edwards et al., 2007; Larson et al., 2007; Zeder, 2008]. Although genetic analysis indicates migration processes that accompanied the emergence of the Neolithic pack [Haak et al., 2010], the study of cultural expansion models shows an equally high probability of the scenario of diffusion distribution of these plant and animal species in Europe [Ackland et al., 2007; Lemmen, Gronenborn, Wirtz, 2011].

The transition to a productive economy in North America occurred much later, between 1000 BC and 1000 AD. For its eastern part, this period is designated as the Woodland period. Local cultivated plants, such as amaranth and sunflower, were cultivated in parallel with hunting and gathering as the main forms of economic activity. Gradually, maize and beans penetrated eastern North America from Mexico, becoming the main crops; domesticated animals were absent [Piperno, 2011]. The Woodland period is characterized by the constant use of ceramics and a gradual increase in dependence on agriculture (Anderson and Mainfort, 2002). In contrast to Europe, cultivated plants were distributed in eastern North America through trade, rather than through migration from the regions of cultivation; cultivation was developed by the local population (Hart, 1999).

Successful crop cultivation requires suitable climatic conditions, as well as a sufficient amount of cultivated soil and water. With the exception of the arid plateaus along the Western Cordillera, North America and Europe share similar climates, vegetation types, topography, and landscape diversity, including large rivers, mountain ranges, plains, and hills. The natural vegetation type in most of their forest zones is represented by temperate forests (Williams et al., 2000; Thompson and Anderson, 2000; Cheddadi et al., 1997).

This paper uses a model of global land use and technological evolution, which can help solve problems of local innovation, migration, and the spread of cultural features [Wirtz and Lemmen, 2003; Lemmen, Gronenborn, and Wirtz, 2011]. This model provides a plausible explanation for the emergence of a productive economy in many regions of the world. In this study, the analysis is limited to North America and Western Eurasia. The differences in the processes that led to the emergence of productive farming in Europe and eastern North America will be discussed in more detail, and a rough estimate of the pre-Columbian population of the North American Woodland will also be given.

Materials and methods

The Global Land Use and Technological Evolution Simulator (GLUES) model [Wirtz and Lemmen, 2003; Lemmen, 2010; Lemmen, Gronenborn, Wirtz, 2011; Lemmen, Wirtz, 2012] describes the development of regional socio-cultural features while limiting the process to biogeographic conditions. The resources used by communities can be estimated based on the primary useful productivity of the region, which is calculated for past epochs using simulated temperature and precipitation anomalies (Climber-2 system model) [Claussen et al., 1999] using the IIASA climatological data base [Leemans and Cramer, 1991] and the bioclimatic model of vegetation limits [Lieth, 1975]. The concept of the model is described below (for more information about the algorithms used and the mathematical basis of the model, see [Wirtz and Lemmen, 2003; Lemmen, Gronenborn, Wirtz, 2011]).

Socio-cultural model. The socio-cultural sphere is characterized by three factors that describe the human population. The evolution of each factor over time tends to bring more and more benefits to the associated population and, consequently, contribute to its growth [Dieckmann and Law, 1996; Wirtz and Eckhardt, 1996]. In this paper, we model the evolution of the distribution of each factor at different moments, rather than its single value.

The socio-cultural factors of the model can be briefly described as follows.

1. Technology-a factor that describes the cost-effectiveness of obtaining food and the effectiveness of basic treatments. In particular, it includes the availability of tools and weapons, as well as the organization of labor and storage of the produced product. This includes writing as a tool for managing and transmitting cultural experience.

2. Share of agriculture and pastoralism (in terms of energy, time, and labor employed) in the total food sector.

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3. The number of agricultural and pastoral forms of management available to the population of the region. So, for example, there are four of them if there is pig breeding, barley, wheat cultivation, and goat breeding in one community. The analysis of this factor uses the work of S. Shennan (2001), in which population dynamics is directly linked to the process of cultural evolution.

The model parameters are limited by the requirement for successful modeling of the emergence of agricultural and pastoral centers in the five main regions during the corresponding periods. According to a study by B. D. Smith [Smith, 1998, p. 12], these are the "Fertile Crescent" (7500 BC), Central Mexico (7000 BC), Southern (8500 BC) and Northern (7800 BC) China, and the southern part of the Central Andes (7000 BC) and the eastern part of the United States (4500 BC)*. In each model with a random change in parameters, the estimate is calculated taking into account the space-time distance to the specified centers. In this paper, a set of parameters with the best indicators out of a million simulations was selected for a retrospective study.

The mathematical model was based on the following concept: for each biogeographically defined region (with an average size of 127x103 km), data corresponding to the Mesolithic hunter-gatherer population is entered at the beginning of the simulation. Its population is growing at a rate limited by socio-cultural factors; it is limited by natural resources. With the development of technology, resources are used more efficiently, and the first cases of cultivation of plants and animals occur. Population growth and technologically advanced use of natural resources leads to a decrease in the latter. The local transition to agriculture occurs only when the combination of technology and cultivation provides more material benefits than the hunter-gatherer lifestyle allows. As a rule, this process is completed in less than 200 years, which is in good agreement with empirical data (see, for example, [Zvelebil, 1996]).

The productive economy spreads from the centers of its origin to more remote regions through trade and migration, the mechanism of which is based on the concept of difference of influences [Renfrew and Level, 1979], which describes the direction of development and the vector of exchange. Migration occurs at a rate proportional to the length of the contact zone divided by the distance between two neighbors. The impact of trade exchange is proportional to the difference between the products of trade. It is assumed that it penetrates a distance 100 times greater than migration. The importance of trade and migration as vectors for the spread of cultural influences or the settlement of peoples with the subsequent adoption of new cultural forms was studied in a recent work [Lemmen, Gronenborn, Wirtz, 2011] using the GLUES model. Both processes were found to be consistent with radiocarbon dating for Europe.

To distinguish between empirically determined dates and those modeled in the mathematical model, a scale of simulated time BC was introduced [Ibid.Ideally, the simulated year BC should be numerically equal to the calendar year.

Biogeographic and bioclimatic factors. The socio-technological model was considered in a geographical context in combination with data on the flora of past epochs. In the GLUES model, vegetation is estimated using primary useful productivity, which is derived from the bioclimatic limit model (Lieth, 1975) based on average annual temperature and precipitation. To obtain data on vegetation of past epochs, we used the results of climate modeling of Holocene transition conditions of moderate complexity Climber-2 (Claussen et al., 1999) as anomalies of the HASA climatological database for monthly average values of temperature and precipitation (Leemans and Cramer, 1991).

Figure 1 shows the natural resources associated with the simulated transition to a productive economy. The highest plant productivity in 1000 BC is found in southeastern North America, the average in the eastern and central United States and Europe, and the lowest in northern Canada, the Rocky Mountains, and the Sahara (Fig. These data are representative of the entire simulation, since changes in climate parameters are so insignificant that the values of simulated productivity do not differ too much throughout the Holocene. In the forest zone of Europe and eastern North America, plant productivity is in an acceptable range (500-1500 g per 1 m2 per year), if converted to the relative potential productivity of agriculture and cattle breeding (Fig. With the function defined by [Wirtz and Lemmen, 2003, fig. 1] for the transition from primary useful productivity to potential productivity of agriculture and cattle breeding, this potential is quite high (above 75 %) for the whole of Western Europe, and for the eastern and central part of the USA.

The function of transition from primary useful productivity to local species diversity has a narrow optimal range of 400-600 g per 1 m2 per year, which indicates the most favorable conditions

* In this paper, I use modern names to indicate the approximate geographical location.

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open woodlands for cattle breeding and agriculture (annual grasses, grazing herbivores). The modeled species diversity shows very high rates throughout Europe, in the northeastern and central part of the USA, but only moderately high in the southeastern part (Fig. To correct for the expected higher species diversity in large areas compared to smaller areas (which was already indicated almost 200 years ago [Watson, 1835]), this study uses a concave relationship between species and area in assessing the local diversity of suitable species for cultivation on the continent [Connor and McCoy, 2001]. Potentially suitable for agriculture and cattle breeding, the diversity of species in Eurasia is 4 times higher than in North America.

Results

Agriculture and cattle breeding as the main forms of food production appear in the simulation model almost all over the world by the 1490 model AD. Hunting and gathering remain important in the boreal zone of Europe and North America (Figure 2), as well as on large islands such as Iceland (not shown) and Ireland. Figure 2 shows the simulated time of transition to agriculture and cattle breeding, when more than half of the region's population is provided with food using these forms of management. For most of continental Europe, this period is 7000-4000 model years BC, and for most parts of eastern North America - 2500 model years BC-1490 model years AD. This difference in the simulated transition time to a productive economy compared to Europe is a consequence of different biogeographic conditions on these subcontinents [Wirtz and Lemmen, 2003].

Population growth in Europe. The model shows the earliest increase in population density of about 8000 model years BCE in Greece, Italy, Anatolia, and the northwestern Iberian Peninsula (Figure 3). By 6000 model years, the entire population of the Iberian Peninsula was growing at the same time.

Figure 1. Biogeographic context for modeling socio-technological evolution in GLUES (biogeographic variables a-c are derived from the reconstructed temperature and precipitation in 1000 BC models), a - primary useful productivity (kilograms per square meter per year); b-relative potential productivity of agriculture and cattle breeding; b - the relative number of species suitable for cultivation.

Figure 2. Time of transition to agriculture or pastoralism as the predominant method of food production, modeled using the GLUES socio-technological system (white color means that the model does not predict the transition in this place before 1490 AD).

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Figure 3. Population density (per 1 km2) in Europe between 8000 and 1000 BC (GLUES data).

Figure 4. Population density (per 1 km2) in North America between 3000 BC and 1000 AD (GLUES data).

In Europe, this figure is approximately 1 person per 1 km2. The population density of up to 3 people per 1 km2 is localized in northern Greece and extends to the entire Balkans and Anatolia. By 5000 BC, it was increasing in these regions to 5 people per 1 km2. It was also increasing in Italy and the Iberian Peninsula. By 4000 BC, most of continental Europe had a population density of just over 2 people per 1 km2. Greece, the Balkans, Anatolia and the surrounding territories are densely populated (5-6 people per 1 km2). By 3000 BCE, the population density in Italy and the southern Iberian Peninsula rises to 5 people per 1 km2, while in most of Central Europe it reaches a level of just under 3 people per 1 km2. By 1000 BCE, along the entire Mediterranean coast, the density of the population of the Mediterranean Sea rises to 5 people per 1 km2. The population is 5-6 people per 1 km2, and in most of the European forest zone - almost 3 people per 1 km2.

Population growth in North America. Here, the simulated increase in population density occurs later and reaches only half of the maximum population density in Central Europe. The first increase from the background level of 0.3 persons per 1 km2 is evident by 3000 BC in the area of the coast of Virginia and North Carolina (Figure 4)*. The model shows the lowest population density along the Rocky Mountains (less than 0.1 people per 1 km2). By 2000 BC, the population density reaches 0.8 persons per 1 km2 in these states and slightly exceeds

* Note the difference in the scales shown in Figures 3 and 4. Population densities in Europe are calculated at 6 km2, while in North America they are calculated at 2 km2.

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background level in some areas of East Texas, Arkansas, Missouri, Tennessee, Mississippi, Alabama, and Georgia. By 1000 BC, it is 1 person per 1 km2 in the southern region of eastern North America and Texas, and the highest rate is observed in the Mississippi River region between Arkansas, Missouri, Kentucky and Tennessee.

Since 1 AD, the population centers of the southeastern United States have merged with East Texas, and a large area of increased population density has emerged from Mexico to the Atlantic coast. The coastal states of North Carolina and Virginia have the highest rates of 1.1 people per 1 km2. By 500 AD, the population density in the main area is still increasing, and in the coastal states to the south of this area, in the Midwest to the west of it, and in the north up to the fortieth parallel, it reaches 0.6 people per 1 km 2. By 1000 AD, in the eastern part of North America to the south At the fortieth parallel, the figure increases to 1.5 persons per 1 km2 on the Atlantic coast and in the center, and to 0.9 persons per 1 km2 on the rest of the territory. In areas north of the fortieth parallel, the simulation shows a low population density (up to 0.4 people). per 1 km2 south of the Great Lakes, up to 0.35 people per 1 km2 in Canada).

Transition to agricultural development of the forest zone. For both Europe and eastern North America, the model shows a 6,500-year interval covering the transition to a productive economy - 7,500 - 1,000 model years B.C. and 5,000 model years B.C. - 1,500 model years A.D., respectively (Figure 5). In most European territories, the transition to a productive economy is based on the same model years. to the producing economy occurs between 6500 and 4000 model years BC (Fig. 5, a). In America, this process begins after 4000 BC and does not reach its completion in the pre-Columbian period, i.e. it is more than 2 times longer than in Europe (Fig. 5, b), and at the level of not only sub-continents, but also individual regions (respectively, about 600 and 600 BC). about 250 years old).

There are significant differences in the diversity of economic activities between Europe (Figure 5, c) and eastern North America (Figure 5, d). For Europe, the model shows a gradual increase in their number, corresponding to an increase in the value of the producing economy. On average, since 4000 BC, European farmers and pastoralists have used five different forms of economic activity, and this number remained approximately the same until the end of the modeling period. Development in eastern North America began around 4000 BC and was much slower. The number of business forms used gradually increased, but did not exceed 1.5 during the entire simulated period. The slow rate of assimilation of new forms of management in the model is, in particular, a reflection of archaeobotanical processes, including the long time required for the adaptation of such a tropical plant as teosinte to subtropical and temperate conditions acceptable for maize growth [Smith, 2011].

Although it is clear from this work and from earlier studies that the difference in maximum values is due to different biogeographic conditions, it should be noted that there is a clear difference between the two subcontinents in the ratio of actually used and potentially available forms of management based on local or imported resources.-

Figure 5. Graph of socio-technological development in the forest zone of Europe and eastern North America (GLUES data are averaged over all regions of the subcontinents under consideration). a, b - the share of agriculture and cattle breeding in the life support system; c, d - the number of different forms of economic activity; e, e - the percentage of used forms of economic activity in relation to the natural potential

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5, d, f). The share of practised economic activities in Europe increases from 20% to 100 % by 4000 BC. e. A low initial figure shows that all natural wealth was practically not used and the system lacked human resources: in the Neolithic era, there were not enough farmers to develop the full economic potential. Only since the Eneolithic period, the entire diversity of resources begins to be effectively exploited in Europe. In North America, even at the beginning of the transition to a productive economy (c. 4000 BC), the full range of economic potential of the landscape was used. Here, the system was limited to natural resources, and the penetration of new forms of management from outside led to the diversification of economic activity. In the archaeozoological context, such resource constraints are primarily expressed in the absence of draft animals and fertilization of the soil (Piperno, 2011).

Population growth in the forest zone. The average population density in Europe (Figure 6) increases sharply between 7000 and 4000 BCE from 0.1 to 3 people per 1 km2. Between 4000 and 1000 BCE, it increases more slowly, increasing by another 1.3 people per 1 km2. On a total area of 3.1 million km2, this population density corresponds to the true population size of 13 million people by 1000 BC. Some European regions show divergent population growth trends: explosive growth is observed in some areas in the south-east (for example, in Anatolia, Greece, and the Balkans), moderate - in Central Europe, and very low population density - in the northern regions (see Figure 3).

The model shows that the pre-Columbian population in the North American Woodlands reached approximately 3.5 million (see Figure 6). One million of this number already existed in the Archaic period; in the Woodlands and subsequent periods, the population growth was 2.5 million. The transition to agriculture and pastoralism was not fully completed by the end of the pre-Columbian era, and during this time hunting and gathering remained important in half the area of the North American Woodland. This process proceeded at an accelerated rate between 4000 BC and 1 AD, and in the period 1 - 1490 AD, its development was linear. The main features of the transition to a productive economy on both sub-continents are summarized in the table.

Figure 6. Graph of demographic development in the forest zone of Europe and eastern North America (GLUES data are averaged over all regions of the subcontinents under consideration).

1 - population density; 2 - population size.

Key features of the simulated transition to agriculture in Europe and eastern North America

Indicator

Europe

Eastern North America

Beginning of the transition

6500 model BC

4000 model year BC.

Transition duration

2,500 years old

> 5,500 years

Potential for local resource diversity

2,8

1,0

Resource import options

2,5

0,5

Early period restrictions

Human resources

Natural resources

Peak population

1000 model years BC-13 million

1490 model year AD-3.5 million

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Discussion of the results

The "Neolithic package" and mixed forms of foraging. The almost instantaneous appearance of a number of different forms of economic activity in Europe may be associated with a large "Neolithic package", which, in particular, included spelt, single-grain wheat, barley, goats, sheep, and pigs (Willcox, 2005). A sharp increase in the number of people engaged in agriculture and cattle breeding indicates the emergence of not only cultivated plant and animal species in new territories, but also people familiar with the agricultural and cattle-breeding way of life. These processes can be interpreted as the displacement of the local hunter-gatherer population by agricultural settlers in accordance with the theory of the transfer of cultural forms through migration (Ammerman and Cavallisforza, 1973; Sokal, Oden, Wilson, 1991; Haak et al., 2010). An alternative explanation for the rapid transition to agriculture and pastoralism is the rapid assimilation of new forms of food production by the local population. This mechanism is confirmed by modeling in the GLUES system [Lemmen, Gronenborn, Wirtz, 2011]. The authors show that the transition to agriculture in South-Eastern and Central Europe corresponds to both a migration and cultural model; in both cases, the assimilation of new cultural forms by the local population plays a crucial role.

In the North American Woodlands, a small but diverse set of domesticated species consisted of native plants and allochthons, with no domesticated animals. Locally available were quinoa, pumpkin, and sunflower, which were part of the eastern agricultural complex (Delcourtetal., 1998; Smith, 2011). Gradually, local crops were supplemented with species whose origin is associated with the Mexican center of cultivation-corn, beans and another variety of pumpkin. These plants were often cultivated together as a single complex, called the "three sisters". The long transition time for all socio-technological development vectors in the North American Woodlands indicates cultural diffusion as the main mechanism of exchange between regions, as well as the slow assimilation of new ways of obtaining food [Hart, 1999; Piperno, 2011; Fuller, 2011].

World population and pre-Columbian American population. Data on the global population found in the scientific literature can be used as a basis for evaluating the effectiveness of the GLUES model in this regard. The values of the simulated population size are within a wide range of variations in data from prehistoric studies (for example, [Coale, 1974; McEvedy and Jones, 1978; Biraben, 2003]). At the subcontinent level, the GLUES estimate of 10 million inhabitants in Europe (see Figure 5 (a)) is in perfect agreement with the data collected by McEvedy and Jones (1978), or with the regional compilation of data by McEvedy and Jones (1978). Kaplan et al., 2011] for 1000 BC After that, in the Iron Age, the GLUES model may somewhat underestimate technological development and population density growth in Eurasia, since the cultural model does not yet take into account the increase in economic efficiency due to metalworking and increased social stratification. For the Americas, Africa, and Australia, the simulation shows reliable results up to the beginning of the colonial era, which is also not yet taken into account by the model.

Studies on the population of pre-Columbian America contain very different estimates, sometimes varying by more than an order of magnitude: from 10 million to 150 million people R. Nevl and D. Bird give a figure of about 60 million people. [Nevle, Bird, 2008]. Probably only 10 % of this number lived north of Mexico, while most of the population was concentrated in the Aztec and Inca empires, as well as in the Amazon basin (Denevan, 1992). Taking into account the above data, a very rough estimate of the population of the American Woodland at 4 million people seems quite convincing.

Only recently [Peros et al., 2010] the Canadian Archaeological Radiocarbon Database (CARD) [Morlan] was used to calculate the population growth rate in North America after the Ice Age and up to the time of contact with European civilization. According to these calculations, the maximum pre-Columbian population was 1.8-4.7 million people, most likely 2.5 million people. The GLUES model gives a value of 3.5 million people. by 1490 AD for eastern North America (see Figures 5, d) and 6.5 million people for the entire continent, which seems to be a realistic estimate.

Criticism of the model and prospects. The good consistency of the GLUES socio-cultural model data with previous studies is somewhat surprising, given its simplified approach and the uncertainty of many parameters. The fact is that the model deterministically translates the geographical location of a particular region and its plant resources into a potential for cultural evolution with universal settings for all regions of the world, after which the simulated processes of cultural development in each of them and the interaction of trade and migration give estimates of population size, food supply and technological progress. The success of modeling, most likely, is due to the fact that large-scale

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patterns of cultural evolution around the world are based on very similar functional dependencies on the biogeographic context and cultural interactions, despite the wide range of observed differences in the characteristics of cultures.

The model could be even more accurate if there were reliable chronologies for a large number of archaeological sites with their simultaneous clear interpretation. For Europe, Lemmen, Gronenborn, and Wirtz (2011) used 765 radiocarbon dates with Neolithic attribution (Pinhasi, Fort, and Ammerman, 2005); the model showed an average discrepancy of ± 500 years. For the American Woodland, the Canadian archaeological radiocarbon database (CARD) [Morlan] was used: 3,705 dates from it have the designation "Woodland", the central 95 % distribution of which refers to the period from 1000 model BC to 1500 model AD with the maximum frequency in the XI century AD. As a result of applying these statistics to GLUES model territories located in the region with radiocarbon dates of the Woodland period, 23 dates of the emergence of agriculture and cattle breeding were obtained in a wide range between 3500 model BC and 1490 model AD with a maximum frequency in the range from 2000 model BC to 1000 Model AD For the eastern part of North America, the modeled indicators are shifted to slightly earlier dates.

It should be noted that the compilation of radiocarbon dates is problematic due to differences in dated materials, calibration and quality control procedures, as well as analysis methods in different laboratories and subjective selection of monuments for inclusion in the database; calibration itself introduces errors (see, for example, [Stuiveretal., 1998]). However, an even more serious problem that needs to be overcome when comparing simulated and archaeological data is inconsistencies in determining the timing of the transition to a productive economy. The model uses a quantitative parameter defined as the time (model year BC) when more than half of the food was produced by farmers and pastoralists. It cannot be used for archaeological data where the remains of crops or domestic animals, agricultural implements, or images indicating the occupation of agriculture or cattle breeding indicate the existence of a producing farm, but not its scale. In cases where this farm is associated with the peculiarities of ceramics or stone tools, its presence can be established even without direct evidence. In the archaeological data, there is not a single parameter of agricultural and pastoral activity that can be directly compared with the results of modeling.

Quantitative comparisons can be made using regional patterns of cultural evolution based on radiocarbon dating and modeling, as well as indirect parameters such as population density or size. However, the most interesting thing is the deviation of retrospective modeling results from the historical path, which indicates the need to explain the discrepancy from a cultural point of view. One such example is the unusually low (relative to the natural capabilities of the natural environment) population density of hunter-gatherer communities in North America compared to Europe. This could force a model in which this indicator, determined by natural resources, is higher, to give an earlier date for the emergence of a productive economy in the North American Woodland economy than is observed in reality (see Figure 4).

The model presented in this paper works at the community level. Naturally, it does not address individual people and their cultural choices, i.e. active creation and change of the society in which they live (Dornan, 2002). Should such a model include the impact factor at the collective level, as suggested by M. Shanks and K. Tilley [Shanks and Tilley, 1987]? I don't think so. Modeling only that part of the socio-technological evolution that occurs without the direct influence of individuals, and comparing the results with historical data, allows us to identify those periods when this factor was significant. In other words, the forecast of the model should be perceived as a historical "null hypothesis"; the discrepancy between the simulated results and real data can serve as an indication of special rare events that had significant and long-term consequences [Acklandetal., 2007].

Conclusions

In this paper, we present a numerical model of the regional transition to a productive economy. It is able to plausibly model a potential history, which can then be compared with archaeological data. The reliability of modeling is confirmed, for example, by predicting the real population values: 10 million. in Europe by 1000 BC and 6.5 million in North America (3.5 million of them). in Woodland) on the 1490 model year AD.

Despite the similar natural conditions of the American and European forest zones and the general allochthonous nature of the main crops, the transition to land-based management is still very difficult.-

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agriculture and pastoralism occurred in these regions in different ways. The early and rapid adoption of a new way of life in Europe, modeled in the GLUES socio-technological system, is confirmed by archaeological evidence. The model shows the radial spread of agriculture and pastoralism from the Eastern Mediterranean at a rate comparable to the wave propagation model, with the entire European population moving to a productive economy by 4000 BC. e. The transition is completed in a fairly short period of time; it is characterized by a lack of human, not natural resources.

When using the same global set of parameters to model the transition to productive farming in the American forest zone, the model gives a different picture. Here, hunting and gathering coexist for a long time with agriculture and cattle breeding; cultivated species include both native plants and allochthons; the transition to a new way of life is carried out through the spread of cultural forms, rather than migration. This process can be described as limited by natural resources. The transition to a productive economy is carried out at a rather late period, from about 2000 B.C., and never reached its completion by 1490 A.D.

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The article was submitted to the Editorial Board on 23.12.11, in the final version-on 25.12.12.

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