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[http://dx.doi.org/10.17504/protocols.io.vpve5n6] Population density is estimated as population size divided by size of the area that population inhabits and is expressed in persons per sq. km. In our approach, literature was surveyed to obtain values of regional population density; these values were subsequently included in the analysis as they were estimated by the authors of the original studies (S1 Table). In doing so, we respect the individual approaches of the authors (see S1 Table) as representing some kind of regional expert knowledge. Within the scale of our analysis, variability that is due to the diversity of the individual methods is approximated, allowing the comparison of results, as it is recognized that the application of different methods is related to the qualities of archives in respective regions (Table 1). Further applications of the proposed methodology to significantly extended databases require critical analysis of initial palaeodemographic estimates. This will also include consideration of different estimates proposed for the same datasets. Furthermore, the increase in sample size that such an expanded study would bring decreases the estimated average values, resolving the issues of research bias and comparison of different methods of estimations, as suggested in studies of archaeological and ethnographical metapopulations [6–8].
Table data removed from full text. Table identifier and caption: 10.1371/journal.pone.0208739.t001 Methodologies applied for the estimations of population density. The sample collected for this paper includes 42 population densities from Southeastern Europe, 33 population densities from Central Europe and Southern Scandinavia, and 56 population densities from the Near East. All these cases refer to agricultural populations, although the mentioned areas were also inhabited by hunter-gatherers. The overall size of the areas in the latter populations decreased over time, which is taken into account in estimations. Changes in population density are traced at several spatial scales. Regional density, which is also labeled ‘global’ density in the related studies [2, 3], is estimated as population density in more densely settled core areas and the surrounding un- or less settled areas, e.g. mountains. Macro-regional population density is estimated for two larger territories, i.e. Southeastern Europe and Central Europe / Southern Scandinavia (Fig 1). The density of metapopulations is represented by the values obtained for the Near East and also for Southeastern and Central Europe, and Southern Scandinavia.
Figure data removed from full text. Figure identifier and caption: 10.1371/journal.pone.0208739.g001 Spatial arrangement of sites in Europe and the Near East (produced using the basemap Natural Earth data by Ines Reese and Karin Winter (Graphics department of the Institute of Pre- and Protohistoric Archaeology Kiel). The procedure of this research method considers several issues of data analysis. These can be summarized as follows: chronological resolution of changes;estimation of the weight of values for population density in order to transform the initial values included in the sample into the values that may be compared with each other at the regional scale;calibration of the transformed values into real population densities;estimation of the weight of values for population density at the scales of macro-regions and for the density of metapopulations.The subdivision of the analyzed time span depends on the chronological resolution of the regional estimates. Considering the temporal framework for the case studies included in our sample, we decided to subdivide the overall time range into periods of 500 years. As sample size and precision of the temporal resolution of sites increase in the future, the duration of the time periods used in further developments of this demographic survey will decrease. If the chronological framework of case studies exceeds the temporal limits considered, such case studies are included into estimations of averages for two or more time periods. For instance, LBK sites in Central Europe are placed into the chronological framework of 5500 to 4900 BCE [21, 22]. Therefore, the related population density is used in estimations twice: for the time periods of 5500–5000 BCE and 5000–4500 BCE. Case studies represent populations settling regions of different size, and for almost none of these regions were population densities estimated for the entire chronological framework of this study. Moreover, both the population size and size of the region influence the demographic averages at different spatial scales. For instance, consider a hypothetical situation in which the areas of regions A and B, which are settled by populations of different size, are estimated to make up 80% and 20% of the territory of macro-region AB respectively. The population density of the macro-region AB may then significantly deviate from the simple average value obtained as the sum of the population densities in regions A and B divided by two. Our study approaches these and other questions of economic demography by introducing correction coefficients which normalize the data used for palaeodemographic estimations dealing with macro-regions and metapopulations. With these coefficients, the following issues are questioned and addressed: To what extent does a small region that is inhabited by a large number of people, or a large area with a dispersed population contribute to the average population density at a macro-regional scale? If a certain innovation affects the increase in population density in a one region, then how does this innovation influence the population density of macro-regions and the density of metapopulations? In other words, we suggest weighting values in order to transform the initial population density data included in the sample into values that may be compared with each other at spatial scales of high orders. All macro-regions and metapopulations considered include both hunter-gatherers and agriculturalists, groups which are characterized by significantly different densities. Hence, the impact of the related values on macro-regional densities should be separated in the analysis. Since the set of regional values included in the sample represents the density of agricultural populations of different size and the size of their regions of occupation varies, the latter variable is weighted by the coefficient ‘p’ which represents the proportion of the total area of the macro-region contained in that region. Multiplication of the regional population densities by this coefficient produces the ‘transformed’ values that, on the one hand, allow comparison of population densities obtained for different areas, and, on the other hand, are used in estimation of the averages for macro-regions. The average obtained for a sample of the regions that make up a macro-region at a given period of time is projected to that macro-region. The coefficient representing the ‘weight’ of regions was estimated one time for each of regions, while the number of times a region was considered in different chronological periods is not taken into account. In other words, we propose to turn the overall occupied territory into a constant value and, hence, trace changes in population density via changes in population size. The relative sizes of the regions, as parts of the constant territory, are obtained as the result of the division of their real area by the total area of the macro-region. These contributions are then summed. Therefore, the related product of multiplication at this stage of the research does not represent the actual regional population density, but its ‘contribution’ to the macro-regional population density. The averages for agricultural populations in macro-regions are estimated as follows: DA=p1D1+p2D2…+pnDn∑i=1np;p=ACAM,(1) where DA is the average population density estimated for a certain time period, p1, p2, pn and D1, D2, Dn are, respectively, coefficients transforming the values obtained for the cases in sample and densities of the cases 1, 2 and n. AC is the size of the area in each particular case and AM is the size of the macro-region. Transformed values can be turned into real population densities with the introduction of the calibration coefficient ‘c’, represented by the ratio of the population density in any of the case studies to its transformed value. In the case of a sample that is as wide as possible, such as that which we plan to obtain in future investigations, the best solution for this purpose is the consideration of the most precise estimations possible in terms of original archaeological records, temporal resolution, etc. In this study, calibration coefficients for the macroregions Southeastern Europe and Central Europe and Scandinavia are equal to 1 when the initial population density values, i.e. the population densities for Thessaly from 6500–6000 BCE and for the LBK in Central Europe from 5500–5000 BCE, are considered. In the case of the Near East, the value of the calibration coefficient was estimated by random choice for the case of North Jazira in 6500 BCE in order to exemplify the application of the proposed methodology. An estimation of the population density for a macro-region must consider the regional densities calculated for both agriculturalists and hunter-gatherers. This linearization follows the logic of estimating the macro-regional population density from several differently sized regions as discussed above. This is made possible by an introduction of the coefficient ‘k’ that weights the size of areas that are inhabited by populations with these subsistence strategies. The averages, summarizing the densities of agricultural populations and hunter-gatherers living in the same macro-region (DS), are estimated as follows. DS=kHGDHG+kADA;kHG=AHGAM;kA=AAAM,(2) where kHG and kA are the coefficients representing the relation of the size of an area occupied by hunter-gatherers (AHG) and agriculturalists (AA) to the total size of the macro-region. The population density of hunter-gatherers in Europe, equal to 0.002 persons per sq. km, was borrowed from Maier et al. [7], who estimated the density of hunter-gatherers in Northern Europe in the range of 0.001–0.002 persons per 1 sq. km. These approximate values are based on the protocol, earlier proposed by Zimmermann [23], which is the closest to the procedure proposed here in terms of dealing with occupied areas and no-man’s land. Contrary, Bocquet-Appel and co-authors based their wide-scale study of Palaeolithic population dynamics in Europe on the assumption that the overall site distribution in well-researched areas is not going to change fundamentally in the future [9]. However, in areas of, for instance, high relief or extensive sediment cover, the reliability of gaps in the distribution of sites is limited [7]. Since new sites are usually discovered near known sites of the same age, the protocol of Zimmermann and co-authors, which relies on density-based delimitations of areas with intensive settlement activity, shows good results and is fairly robust with regard to the detection of new sites [23]. The population density of hunter-gatherers in the Near East, ca. 0.31 persons per sq. km, was borrowed from Hassan’s estimations [24]. Densities of metapopulations (DM) are estimated according to the same logic expressed in Formula (2). However, instead of densities estimated for agriculturalists and hunter-gatherers, the weighting of population densities for macro-regions (DS1 and DS2) is considered. This is expressed as follows: DM=kM1DS1+kM2DS2;kM1=AM1AT;kM2=AM2AT,(3) where kM1 and kM2 are, respectively, coefficients reflecting the relation of macro-regions AM1 and AM2 to the total size occupied by metapopulation (AT).
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