New formulae for estimating prehistoric populations for lowland South America and the Caribbean.

Curet, L. Antonio

Introduction

Many models in archaeology incorporate changes in population as critical elements to explain a wide variety of socio-cultural processes, including the evolution of social complexity and the development of agriculture. Population estimates have also been used in various studies to determine the degree of complexity of a polity, the extent of the power of a particular elite, and trade networks, among other issues. It is obvious, therefore, that the accuracy and precision of demographic methods to estimate prehistoric populations from the archaeological record are of vital importance for testing such models. In fact, the validity of the test is determined among other things by the accuracy of the population estimate.

Traditionally, demographics and change through time have often been used in the development of social models to explain many of the cultural phenomena in the archaeology of lowland South America and the Caribbean. Since the works of the early cultural ecologists such as Steward, Lathrap, Meggets and Evans, one of the main topics of debate has been the role of the resource/population relationship in cultural processes and how it affects (or, in some cases, determines) the structure of given cultures. Unfortunately, most of the discussions revolving around this topic have been limited to theoretical debates or estimates of environmental carrying capacity, while little has been done to estimate prehistoric populations empirically (see Meggers 1995). Few studies have attempted to estimate populations from the archaeological record. This article presents new, improved formulae to estimate prehistoric populations for lowland South America and the Caribbean islands at both the household and the community levels. In presenting these formulae the basic assumptions, methodology and premises are discussed in some detail. This work is a refinement of formulae developed for two of my previous projects: one dealing with prehistoric household structures (Curer 1992a) and the other with a demographic study of a small coastal valley in Puerto Rico (Curet 1992b; 1993). While these formulae are far from being perfect, they are an attempt to improve the study of prehistoric population trends in these culture areas.

General considerations

A discussion and review of several general points relevant to the study are presented here, but this is by no means exhaustive nor complete. More detailed reviews on this topic have been published elsewhere and the reader is referred to the works by Hassan (1981), Kolb (1985), Paine (1997) and Schacht (1981).

Several methods for estimating prehistoric populations in the archaeological record have been previously reported in the archaeological literature (Hassan 1981; Howels 1986; Kolb 1985). Most of these methods are based on one or more of the following types of archaeological or ethnohistoric data:

1 skeletal and other mortuary remains;

2 artefact assemblages and subassemblages related to food preparation, storage and consumption;

3 food remains;

4 surface refuse or ceramic densities;

5 architectural features such as roofed-over space; and/or

6 calculations of mean household size.

Although some of these data produce more accurate results than others (e.g. house area is better than site size), the source of information to be used is going to be determined mostly by the nature of the archaeological data at hand. Since most archaeological work consists of surveys and feature excavation, surface refuse and architectural features are two of the data-sets most widely used in most parts of the world for population estimation. In fact, surface refuse and architectural features are generally considered two of the most reliable archaeological indicators of prehistoric populations. For this reason, most of the work on estimating past populations has focused on determining the relationship between habitation area and number of people. This relationship has been used to estimate populations for both dwellings and communities, and is the most applicable approach for estimating prehistoric populations in lowland South America and the Caribbean. The following section concentrates solely on different aspects of estimating populations for these two contexts, dwellings and settlements. In general, most of the discussion is applicable to both levels of population estimation considered here (i.e. individual dwellings and settlements).

The 'universal' formula

Since the early work by Naroll (1962), many researchers have attempted to develop a 'universal' formula to estimate populations for houses and sites around the world. This approach has been criticized widely by many researchers [e.g. Casselberry 1974; Cook & Heizer 1968; Schreiber & Kintigh 1996; Wiessner 1974), because, among other reasons, the relationship between occupation area and number of people changes with the type of houses (e.g. extended vs nuclear family households) or sites (e.g. village vs hamlet vs camp site; political or religious centre vs village). Other researchers, however, have attempted to develop more accurate 'universal' formulae by controlling for the type of house or site and the geographic region (e.g. Casselberry 1974).

While studies concentrating on developing 'universal' formulae have made great contributions to the study of population estimates in archaeology, they tend to overlook some basic factors involved in the relationship between space and the number of people. In some instances these factors may be techno-environmental, while in others they may be determined by social and culture-specific practices. For example, in determining the relationship between house size and population it is important to consider the number and type of activities that take place in dwellings of different cultures. Cultures in tropical environments tend to do many of their daily activities (e.g. cooking) outside the house, while societies in temperate regions tend to perform many of these same tasks inside the house. This difference in the use of space produced by environmental conditions will result in different relationships between floor area and number of occupants, since the number and type of activity areas within the dwelling or the site will vary.

A similar situation may be created by different social and cultural practices. Differences in some of these practices may produce differences in the use of space, such as specialized ceremonial or public areas (e.g. temples, cemeteries, men's houses, etc.). In general, these practices will tend to increase the house or site area, reducing the total population density.

In sum, it is difficult to visualize the development of an accurate 'universal' formula that can be applied to any culture, under any set of circumstances. Even formulae that are confined to a certain type of house or site are of limited use since they tend to ignore social and culture-specific practices that affect the relationship between occupation space and number of occupants, such as cultural complexity, ethnic spacing standards or environmental conditions. Thus, it seems that a more accurate approach is to develop culture-specific or culture-area-specific formulae to estimate population size. The best way to accomplish this is through use of comparative data from groups that may be culturally related to the prehistoric group in question, and which inhabit a similar type of environment. In other words, the best methodology is the use of ethnographic analogy and the direct historic approach to archaeological interpretation.

Population estimates and ethnographic analogy

Regardless of which of the six methods mentioned above is used for estimating prehistoric population size, they all require the use of ethnographic analogy. The accuracy of the method used to estimate prehistoric populations, therefore, 'depends on the quality of the ethnographic analogies employed' (Schacht 1981: 128). The main underlying assumption in estimating populations from house or site size is that there is a correlation between occupation area and population size (Hassan 1981: 64; Kolb 1985: 582). However, in addition to population size, there are several other cultural, economic and social factors that can influence the final size of a house or a settlement (e.g. socio-cultural level of development, social organization, spatial patterning of activities, intra-site movement of households, architectural forms and duration of occupation) (Hassan 1981: 66; Sumner 1989). In most cases, it is expected that these factors can be compensated for by using ethnographic data for groups from the immediate cultural area that share similar cultural and subsistence traditions with the archaeological case.

Most of the studies using ethnographic analogy concentrate on estimating some measure of occupation area such as walled areas, roofed areas, floor plans, site size, etc. and correlating that with the number of occupants. In some cases the information can be obtained from ethnographies while in others archaeologists have collected their own data through ethno-archaeological research. Regardless of the source of the ethnographic data, however, researchers should consider several factors that can affect the 'quality' of the ethnographic analogy. First, as mentioned above, the ethnographic data are best obtained from groups related to the archaeological culture under consideration and that are adapted to similar environmental conditions.

Second, the researcher should attempt to control for dwelling or settlement type. In other words, the type of ethnographic dwelling or settlement should be comparable to that of the archaeological case. Sites and dwellings can be discriminated, for example, according to the duration of permanence (i.e. seasonal camp vs sedentary habitation sites; shelters vs permanent structures), size (i.e. hamlets vs villages vs cities; nuclear vs extended family dwellings), or function (i.e. religious or political centres, camps, habitation sites). Furthermore, studies should control for social factors such as status and social complexity. For example, chiefly dwellings tend to be large even though they might not house a population congruent with their size. One reason for this is that in many societies chiefly dwellings function as public and ceremonial structures as well as residences. Thus, in such circumstances, the size of the house is influenced more by its socio-political and religious function than by its domestic function. The same is true for sites where public, communal and/or ceremonial areas may affect the settlement area. Perhaps the best way to deal with these cases is to consider them as different types of houses or settlements and develop particular formulae for high-status dwellings or centralized settlements (Schreiber & Kintigh 1996). Ethnic spacing standards (i.e. proxemics) can affect also the size of sites or dwellings. Finally, Myers (1973) has cautioned that the relationship between site area and population may differ according to site shape (e.g. circular vs linear), type of dwellings included in the site (e.g. extended vs nuclear family houses), and the surrounding environment (e.g. grassland vs forest) (see also Meggers 1995).

A third factor that potentially affects the 'quality' or appropriateness of the ethnographic analogy is culture change and Western influence. For example, in many Amerindian societies, domestic units have changed from extended family dwellings to nuclear family households due to this type of influence (e.g. Siegel 1990). Needless to say, the more pristine the ethnographic culture, the greater the accuracy and quality of the ethnographic analogy. While it is almost impossible to obtain data from modern ethnographic groups without any substantial external influence, researchers should factor out this sort of problem. Cases where residential patterns have been strongly influenced by extraneous factors should be excluded from the analogy. The degree of influence where such an example should be omitted is difficult to measure and perhaps this is a dilemma that has to be solved on a case-by-case basis.

In conclusion, in using ethnographic analogy to estimate prehistoric populations on the basis of occupation area researchers have to control for several factors to ensure accuracy. These factors include, but are not restricted to, cultural and environmental similarity, house or site type, and something we might call the 'integrity' of the culture. In general, the closer in space, time and cultural practices the ethnographic and archaeological cultures are, the better.

Analytical methods used to develop the formula

Most early and some recent studies on developing mathematical models relating house or site area to population size make use of population densities. The main premise of this approach is that each person living in a house and/or a settlement needs a mean amount of area to be able to operate, and this 'mean' density is always constant. To obtain this mean, most researchers have collected data from a series of ethnographic cases, calculating the population density for each case. The mean is then derived from all of the population densities combined.

Although this approach has several Weaknesses (see Cook & Heizer 1968 for a more detailed discussion), perhaps the main problem resides in the assumption that population densities are constant for sites of all sizes, through time and cross-culturally. Recent studies have demonstrated that this is not always true and that population density varies across sites of the same culture and even within a settlement (Hassan 1981: 69; Norbeck 1971; Sumner 1989). In the majority of cases, population densities tend to be a function primarily of the total population within a house or settlement (Cook & Heizer 1968; Schacht 1981). Other factors that may affect population densities include age of the house or settlement, the presence of walls surrounding a site, subsistence strategies, the presence and size of communal areas, population growth rates and external as well as internal economic and political conditions.

In view of the inherent variation and fluidity in population densities, more rigorous analyses have been developed to determine the underlying relationship between occupation size and population, linear regression analysis being the most popular quantitative technique used by archaeologists. Simple linear regression assumes that the relationship between the two variables is not constant but that it changes linearly.

While this method tends to provide a more accurate and realistic mathematical model to determine the relationship between space and number of people, it can not be used indiscriminately. Two words of caution are in order. The first is that the relationship between the area of occupation and population is not necessarily linear. In fact, Naroll (1962) and Cook & Heizer (1968), among others, have argued that the relationship between these two variables is non-linear and allometric. Cook & Heizer (1968) in particular have demonstrated that the use of log-log transformations is a more accurate approach to derive mathematical formulae for population estimation. Although it is difficult to determine the relationship between the two variables a priori, I suggest that at least exponential, polynomial and logarithmic models should be tested in addition to the linear model (Curer 1992b; Hassan 1981: 64).

The second word of caution concerning regression analysis focuses on the misuse of the statistical technique as a predictive tool. A formula obtained from regression analysis is based on a mathematical model that is true only for any case within the limits of the ranges (i.e. the maximum and minimum points) of the dependent and independent variables used in the analysis. This range of values used in the analysis to obtain the regression equation is known as the scope of the model. When regression analysis is used as a predictive tool, it is very important that the value of the independent variable used for the prediction falls within the limits, or at least in the immediate vicinity of the scope of the model. Since we can not determine precisely the relationship between the two variables outside the original limits used to obtain the regression model, it is unreliable to extrapolate points outside its scope. In fact, this is one of the main criticisms that statisticians make against economic predictions based on regression analysis, and one of the reasons why these predictions tend to be so imprecise. Thus, to be of any utility in archaeology, regression formulae based on ethnographic data need to include house or settlement sizes comparable to the prehistoric cases. Failure to do so decreases the accuracy of the relationship between occupation area and population.

While most researchers recommend the use of regression analysis to develop more precise and realistic models, many of them have developed 'rules of thumb' to estimate prehistoric populations based on population densities. Most of these 'rules' or guides have been developed for enclosed areas or dwellings and are based on 'mean' population densities. Naroll (1962), for example, proposed a constant-density approximation, suggesting 10 sq. m of enclosed space per person, while Casselberry (1974) proposed the figure of 6 sq. m of floor area per person. Probably the only non-metric rule of thumb to estimate house populations was developed by Cook & Heizer (1968). They suggest allowances of 25 sq. ft (2.3 sq. m) for each of the first six people, and then 100 sq. ft (9.3 sq. m) for every additional person. However, this rule was developed for small settlements of hunter-gatherers and it might not be applicable to larger dwellings or groups with different subsistence systems and spatial patterns. For the Caribbean, Schinkel (1992) has suggested the use of a minimum of 3 and a maximum of 6 sq. m of floor area per person based on ethnographic data.

Few researchers have developed similar rules of thumb for estimating whole settlement populations. Perhaps one reason for this is the widespread recognition that such estimates are relatively inaccurate, since the relationship between site area and population varies widely in correlation with site size and type, cultural idiosyncrasies and other social factors. To the best of my knowledge, Roosevelt (1980) is the only researcher who has used population density to estimate populations of prehistoric sites in lowland South America or the Caribbean. She proposed a population density of 75 persons/hectare derived from ethnography to estimate populations of archaeological sites in the Parmana region of Venezuela (see note 1, however).

In conclusion, the use of ethnographic population densities to infer house and site populations tends to be unreliable as a predictor of prehistoric values, since population density is not constant in most circumstances. Regression analysis may be employed to enhance the accuracy of such models and better define the relationship between occupation area and actual population. However, to reiterate, this technique does not assume a priori that the relationship is linear and other models should be tested as well.

Archaeological considerations

The quality of the archaeological evidence is extremely important to the accuracy of any prehistoric population estimate. While the condition of the archaeological record is not emphasized in this work, four key aspects of the archaeological evidence need to be mentioned here: contemporaneity, formation and transformational processes, preservation and detection.

Despite the value of analogy various pro- and post-depositional processes may obscure the nature and form of the archaeological record. Particular factors of interest include

1 duration of occupation;

2 mobility within the site;

3 differential occupation of different intrasite areas across time;

4 reconstruction and enlargements of structures; and

5 natural and cultural transformational processes.

Thus, the final size and configuration era house or settlement will be a function of the aggregate of all these potential factors. Unfortunately, duration of occupation, mobility and horizontal stratigraphy are difficult to measure using survey data. While in some instances surface collections can help to distinguish intrasite chronological range and variability, more precise data from excavations are needed to tackle these problems in a precise manner (see Meggers 1995).

Since any population estimate is supposed to represent the number of people alive at a single point in time, the archaeological evidence on which the estimate is based must also be contemporary (Meggers 1995). Consequently, without chronological control the estimate of prehistoric populations obtained from the total site size in fact refers to the maximum number of people that could have lived in the site at one time. Under these circumstances it should be recognized that the site population might have never reached the estimated value, since it is possible that different areas of the settlement were occupied at different times. Although this problem is present in all kinds of settlements, it is more serious if we are dealing with multicomponent sites. To avoid or reduce the impact of this problem, researchers must tighten chronological control over the archaeological record by using refined chronometric techniques, whether relative (stratigraphic studies and seriation) and/or absolute (14C, thermoluminescence, etc.).

While it is difficult to determine the intensity and effects of post-depositional processes that may affect the overall size of a particular site, some effort can and should be made to minimize any source of error that will distort and obscure the original archaeological assemblage. For example, although it is theoretically possible to determine the overall site size and to distinguish intrasite temporal variation, in practice most of the time this variability is obscured by cultural and natural transformational processes.

In the case of tropical sites, several transformational processes can affect their integrity, cultivation being one of the major and most detrimental of these, both in past and present times. In general, ploughing tends to disperse surface materials, mix the upper stratigraphy and increase the breakage rate of surface or near surface archaeological materials (i.e. within the plough zone). Depending on the research approach, these effects can be a mixed blessing for archaeologists. While ploughing may mix and spread the artefacts over an area larger than the original site, destroy provenience information and affect the integrity of the archaeological material, it also brings material up to the surface, potentially increasing the variability of artefacts within and the size of surface collections. Since this widespread agricultural practice tends to increase the area covered by dispersed site materials, ploughing may produce an overestimation of prehistoric populations. Thus, this effect may need to be compensated for in estimation of population based on site size.

Roper (1976: table 1) determined that the amount of lateral displacement produced by ploughing averaged less than 5 metres. Other studies, however, have demonstrated that dispersion produced by ploughing depends on the size and form of the artefacts, as well as on the conditions of the ploughing process (see Lewarch & O'Brien 1981: 308-10). Following Roper's lead, it can be suggested that the total extent of sites that have been ploughed should be reduced by 5 m in all directions to ensure a more accurate population estimate.

The archaeological study of households and communities in the tropical areas of South America and the Caribbean has also been limited by problems of preservation and detection. The problem of preservation is posed by the perishability of the construction materials used. Although evidence of structures (i.e. post moulds and wall trenches) have been identified in archaeological excavations, for example, large areas of a site need to be excavated to be able to define and identify the totality of the dwelling unit. Until recently, extensive excavations providing such data were the exception rather than the rule in South America and the Caribbean (Chavez Mendoza & Puerta Retrepo 1988; Curet 1992b; Oliver 1997; Rivera & Rodriguez 1991; Schinkel 1992; Siegel 1989; Ziedler 1984). To date, aside from the presence of middens or mounds, no research has reported evidence of buildings observable on the surface.

On the other hand, the detection of archaeological settlements and features is made more difficult by the sedimentation produced by periodic floods and the lush vegetation that is characteristic in many areas of lowland South America and the Caribbean. This is more critical in surveys and regional studies, where population estimates are commonly made on the basis of the horizontal extent of surface materials. The impact of both preservation and detection problems can be minimized by careful research and sampling designs which are tailored to the particular conditions of the region or site under study. A discussion of possible sampling and field techniques that can be used to deal with these problems is outside the scope of this paper, however.

In conclusion, archaeologists should be cognizant of several cultural and transformational factors that may affect the size of archaeological sites and which can obscure the area/population relationship. Cultural practices are somewhat more difficult to control than are natural transformational processes, but good stratigraphic and distributional studies can help to detect such practices as reconstruction and expansion of houses and intrasite household mobility. The effect of transformational processes can be diminished through the use of information obtained from experimental studies (e.g. Roper 1976). Chronological control is also an important issue in estimating prehistoric populations to ensure contemporaneity across different house or settlement sectors. This can be accomplished by using a combination or relative and absolute chronometric techniques. Problems or preservation and detection of archaeological sites and features are very relevant in tropical archaeology. Some of these potential problems can be minimized with adequate research design and field methodology, however.

New formulae for estimating prehistoric populations

Previous attempts to develop formulae to estimate prehistoric populations from dwelling and settlement size in lowland South America and the Caribbean suffer from six main problems:

1 the use of a limited number of ethnographic cases for their development (Curer 1992b);

2 the lack of differentiation between nuclear family and communal dwellings (Curer 1992a);

3 misuse of quantitative techniques (i.e. regression analysis) as predictive tools by extending the predictions outside the scope of the model [Siegel 1989; 1990);

4 faulty ethnographic analogy due to strong European influence on the ethnographic group, or due to comparing incompatible social units (i.e, house-compound vs extended family dwellings) (Siegel 1989; 1990);

5 the use of population densities to estimate populations of dwellings or sites of all types and sizes (Schinkel 1992; Roosevelt 1980); and

6 miscalculation of the ethnographic settlement areas (Roosevelt 1980) (see note 1).

The refined equations included below were developed in an attempt to overcome the majority of these drawbacks.

Here I present and discuss new regression formulae to estimate prehistoric dwelling and site populations. Data obtained from a wide range of ethnographic reports (17 for dwellings and 10 for settlements) were used in the regression analyses. These data were selected according to the minimum criteria established above. First, only cultures or groups that have suffered minor external influence were selected. Examples were omitted from the study if there was any reason to suspect that western influence might have changed the traditional use of space. Also, special attention was taken to exclude settlements or dwellings whose sizes were strongly influenced by factors other than population. None of the settlements included in the research, for example, have any specialized use of space such as cemeteries, ceremonial plazas, 'temples', etc., which might have increased the site area and reduced the population density. Also, houses of high-status individuals or leaders were not considered in the development of the dwelling formulae. The data and their sources used in the following analyses are included in TABLES 1 & 2 for dwellings and settlements, respectively.

The regression analyses were conducted assuming that the relationship between population and habitation area is not constant in all sites, nor that it is linear. Other models were also considered, including logarithmic, polynomial and exponential formulae. As is shown below, some of the best-fit curves predictably did not follow a linear pattern. Regression formulae were evaluated according to the value of their r-squared and how well their corresponding curves fit the points on the graphs, especially the shape of the curve. For example, some exponential and polynomial formulae were discarded since their curves tended to show that site area either increased outside the lower limit of the scope of the model (i.e. as population decreased) or decreased past the largest case study (i.e. as population increased).

Population estimates from dwelling floor areas

In most of the ethnographic cases, the area of the floor plan used in the regression analyses was calculated from the dimensions of circular or square houses mentioned in the text, or from direct measurements from scaled maps and drawings provided in a report. To estimate the number of people housed in domestic structures, a simple linear regression analysis was first run to correlate floor area and number of occupants using the total ethnographic data set from lowland South America {TABLE 1, FIGURE 1). The regression analysis presented an acceptable value of r-squared (0.959). Thus, these results seemingly indicate that more than 97% of the variability among the number of house occupants can be explained on the basis of the linear relationship between human number and floor area. The other mathematical models (i.e. logarithmic, polynomial, and exponential) resulted in smaller r-squared values (less than 0.9).

While at first glance the linear regression equation seems to be appropriate and reliable, this approach suffers from a major weakness. It lumps together all types of houses in the analysis and does not discriminate for house type. In other words, it treats nuclear family and communal or multi-family houses equally, which is a procedure that might introduce inaccuracies. For this reason, dwellings were next divided into two groups, nuclear family vs multifamily dwellings, and a second series of regression analyses were performed. Houses were assigned to each one of these two types of dwellings according to the description of the ethnographers. Since most of the nuclear family houses had 10 individuals or fewer and measured 100 sq. m or less, I suggest classifying these two types of dwellings using these numbers as thresholds. In other words, households with 10 individuals or fewer, or dwellings that cover less than 100 sq. m can be considered nuclear family houses. Likewise, communal dwellings would include all those structures that housed more than 10 people or incorporated an area larger than 100 sq. m.

TABLE 1. Ethnographic information on house sizes.

source area (sq. m) no. of people

Wallace 1889 610 100
Farabee 1922 270 50
Gillin 1936 17.63 4
Gillin 1936 14.69 4
Gillin 1936 49.59 9
Gillin 1936 7.35 2
Gillin 1936 9.92 3
Gillin 1936 11.75 3
Gillin 1936 29-39 6
Gillin 1936 11-02 3
Gillin 1936 17.63 4
Gillin 1936 17.63 2
Gillin 1936 36.73 5
Metraux 1963 16.22 7
Goldman 1963 315 60
Yde 1965 202 41
Yde 1965 130 26
Thurn 1967 56 23
Carneiro 1970 176 32
Carneiro 1970 8782 7
Wilbert 1972 178 50
Wilbert 1972 707 120
Casselberry 1974 560 80
Casselberry 1974 70 13
Casselberry 1974 150 25
Casselberry 1974 90 31
Casselberry 1974 700 120
Dumont 1976 360 58
Henley 1982 94 25
Jackson 1983 177 32
Zeidler 1984 161 16
Gonzalez 1987 157 15
Gonzalez 1987 680 125
Chavez & Retrepo 1988 70 5
Chavez & Retrepo 1988 60 4
Chavez & Retrepo 1988 40 6
Chavez & Retrepo 1988 21 5
Chavez & Retrepo 1988 28 2
Meggers 1971 119 10
Meggers 1971 162 16
Meggers 1971 285 46
TABLE 2. Ethnographic information on settlement sizes.

source area (sq. m) population

Gillin 1936 2020 27
Gillin 1936 891 6
Nimuendaju 1946 19,359 298
Oberg 1953 11,575 110
Maybury-Lewis 1967 13,534 220
Maybury-Lewis 1967 12,563 175
Maybury-Lewis 1967 24,150 350
Carneiro 1957 8938 145
Cowell 1973 1868 45
Dumont 1976 2286 58
Smole 1976 2944 80
Smole 1976 1769 60
Smole 1976 2776 84
Smole 1976 1549 35
Smole 1976 18841 312
Smole 1976 2887 80
Fabian 1992 9177 92
Seeger 1981 5862 133

None of the regression analyses on the data from nuclear family dwellings using all the models mentioned above produced acceptable results. In other words, they all produced low values of r-squared, less than 0.6, and thus have low predictive value. This low correlation is related to the high variability represented in the data (FIGURE 2). The high degree of variability may have been produced mainly by two factors related to the small size of the dwellings. The first is that due to their small size a small change in the population of a nuclear family dwelling will proportionally represent a large percentage of the total number of occupants. The same is true for any variability in the floor area actually present in the ethnographic data, or produced by measuring and sampling errors. Thus, any small change in population and/or area is going to affect strongly the relationship between dwelling size and population.

Similarly, the second factor is related also to the small size of the structure and the relative change in population. Suppose we have a house inhabited by a single individual; if a second occupant is added, the population will double, but the structure will not necessarily double even if it gets larger, since there might be some areas or features which are not going to be replicated, such as hearths and some 'communal' activity areas that can be shared by both individuals. Thus, in some instances an increase in population might not produce a proportional change in floor area. Therefore, at this level of population the correlation between house size and population might be relatively low due to the high degree of variability in relation to their size. These effects are buffered in larger dwellings since small changes in population or structure size will be proportionally smaller.

As expected, the regression analyses for the communal dwellings presented a completely different picture. In this case, not only one but two models produced relatively high values for their r-squared: linear (r-squared = 0.940) and binomial (r-squared = 0-947) formulae. As can be seen from FIGURES 3 & 4, both regression lines reasonably approximate the distribution of the data points.

Three acceptable formulae developed for dwellings were further used in a comparative exercise to evaluate their performance in estimating populations of prehistoric houses. These formulae include the binomial formula obtained for the communal dwellings and the linear formulae obtained for all the houses together and also for the communal dwellings separately. In addition, I calculated the population of the same houses using

1 Casselberry's rule (1974) for multi-family houses of one person for every 6 sq. m and

2 Cook & Heizer's (1968) value of 25 sq. ft (2.3 sq. m) for each of the first 6 people, and then 100 sq. ft (9.3 sq. m) for every additional person.

These equations were applied to the prehistoric houses reported for the sites of Playa Blanca (Curet 1992a; Rivera & Rodriguez 1991), Maisabel (Siegel 1989; 1990), Golden Rock (Schinkel 1992) and Site FAL-7 (Oliver 1997). With the exception of the structure from [TABULAR DATA FOR TABLE 3 OMITTED] Maisabel, the floor areas of the houses were calculated using the post-mould distribution. The house from Maisabel was defined by the ditch that Siegel identified as part of the wall of the structure. Nuclear family houses were archaeologically differentiated from multi-family dwellings on the basis of their sizes. As mentioned above, I have somewhat arbitrarily defined a nuclear family house as any dwelling smaller than 100 sq. m and multi-family houses are those larger than 100 sq. m.

The population estimates obtained by applying these equations are presented in TABLE 3. In general, some discrepancies are apparent between the estimates obtained for hypothesized nuclear family houses. This is not surprising considering the high degree of variability in structure size and occupants for this type of house and the possible data distortions mentioned above. The discrepancy in terms of absolute numbers is relatively low; fewer than three people is the largest difference. Nevertheless, these are large differences in proportion to the size of the houses: between 2% and 45%. With two exceptions, all of the population estimates for nuclear family houses were larger than the estimates obtained under Cook & Heizer's rule.

The estimates for multi-family dwellings obtained the three formulae exhibit greater congruence: five people in the worst of the cases and less than one in most of them. In proportion to the size of the structures these differences are notably smaller than in the case of the nuclear family houses: from 3% to 10%, with most of the cases being less than 7%. Thus, the differences in the estimates between the formulae are small enough that any of them will perform equally satisfactorily. All of the population estimates were larger than the estimates obtained under Casselberry's and with Cook & Heizer's rules. Nevertheless, my values are considerably closer to the former than the latter. This is not surprising since Casselberry developed his rule specifically for multi-family dwellings.

While the linear and binomial formulae developed for multi-family dwellings should not be ignored, I recommend using the linear formula obtained for all houses for two reasons. The first is that it is the simplest one to use without the need to discriminate for structure size. The second is that, even though it might not provide the most precise estimate, it is the only one that provides a composite curve of population estimates that can be used to discriminate whether the archaeological houses represent nuclear family or multi-family dwellings (based on number of people) in one step.

In conclusion, the ethnographic data collected for this study provided relatively reasonable formulae to estimate prehistoric populations from floor areas. While it was impossible to obtain relatively good formulae to estimate the populations of small, nuclear family houses due to their high variability and inherent error factors, the linear formulae obtained for all types of houses seem to he more or less reliable. The data-set for multifamily or communal houses exhibited greater consistency and uniformity, but it produced at least three 'best fit' formulae, including the equation for all types of dwellings. Since these three estimates produced similar results when applied to archaeological data, further studies are necessary to determine which one is more realistic and precise. Nevertheless, for now I recommend using the formula developed for all houses together, since it is the only one that can provide a relatively acceptable quantitative population estimate and determine whether the dwelling is a nuclear family or multi-family dwelling all at once.

Population estimates for settlements

Data from lowland South American groups are available for developing an equation to estimate prehistoric settlement populations (see TABLE 2). While I wanted to differentiate sites according to size, shape and type of household included, the small sample size (n = 18) of case studies with adequate data allowed me to discriminate sites only according to size.

While none of the reports included measured settlement sizes, sufficient information is available to calculate approximate areas. In the cases where maps were used for this purpose, the area of the clearing around each village was considered an essential part of the settlement and it was included in each estimate, since various activities were performed there (e.g. refuse disposal and various inter-personal interactions). However, some reports simply mentioned the diameter of circular groups of houses, and not the entire extent of the settlement. This causes a problem, since refuse disposal and other activity areas behind the circle of houses were not normally included in the diameter, and these might be the most visible areas in the archaeological record. Although some of the ethnographers mention the presence of a cleared belt around the village and behind the houses, Smole (1976: 68) and Myers (1973: 244) are the only ones who provide estimates of how far beyond the houses the clearing extends. The former estimates that for the case of the Yanomamo the cleared area extends 50 ft (15.15 m) beyond the palisade surrounding the villages, while the latter reports 'an additional ring of rubbish 10 to 15 meters wide'. This means that the cleared area will increase the diameter of the village by at most 30 m more. Since these are the only cases where separate measurements of the cleared area are available, 30 m was added to the other cases where the diameter of the circular grouping of houses was the only information reported.

To discern the relationship between settlement area and population, regression analyses were conducted using the data from all the settlements presented in TABLE 2. Of the four mathematical models used in the analyses, the linear and binomial equations produced the best results. The regression line and equation produced by this analysis are shown in FIGURE 5. As can be observed from FIGURE 5, the regression analysis presented an acceptable value for r-squared of 0.926, and the line produced by the regression formula approximates the distribution of most of the cases. The equation developed with a binomial model (FIGURE 6) produced a slightly higher r-squared (0-931). This equation, however, tends to produce smaller estimates than the linear model for larger sites and larger values for smaller sites. Other models (exponential, polynomial and logarithmic) were also tried, but they produced considerably lower values for r-squared.

To test the precision of these equations, the population was estimated for the archaeological site of Playa Blanca 5 and compared to the population estimated from the floor area. In general, population estimates based on housefloor areas are considered to be more reliable and accurate than those using the total site area, as noted above. This site represents an isolated house which was fully excavated (Rivera & Rodriguez 1991). The area of the site (including trash middens and secondary structures such as possible ramadas) was 1050 sq. m (Rivera & Rodriguez 1991: 542) and the population estimated from the floor plan was about 7-8 people (Curet 1992b: table 2; see TABLE 3). This small value is supported by the number of burials found in the site, a total of eight.

When an area similar to the size of Playa Blanca 5 is used in the regression formulae an estimate of almost 34 persons is obtained with the linear model and 43 with the binomial equation. This seemingly demonstrates that these regression formulae are overestimating the prehistoric populations for some sites, presumably smaller ones. This imprecision in estimating the populations of small sites might be produced mainly by the same two factors that affected the regression analysis of small, nuclear family dwellings, as related to the limited size of the sites. However, it could have been produced also by the effects that larger sites have in the regression equation. In summary, it seems that at the level of small sites the relationship between site size and population is not linear, and other regression models have to be considered.

To search for a better estimate, a regression analysis was run using only those ethnographic settlements smaller than 9000 sq. m, and applying different regression models (i.e. linear, exponential, polynomial and logarithmic). The area of 9000 sq. m was chosen arbitrarily after reviewing the distribution of population size and site size in the ethnographic record. The chosen regression line and equation for small sites is shown in FIGURE 7. In this case it was found that a logarithmic formula fitted the data better than a linear, polynomial or exponential distribution, producing a higher r-squared (0.932) and better visual approximations. When the equation is applied to an area of 1000 sq. m, an estimate of nine people is obtained, which is considerably closer to the estimate from the Playa Blanca 5 house floor than the one estimated by the previous formulae. Consequently, it was decided to use this regression equation [ILLUSTRATION FOR FIGURE 7 OMITTED] to estimate the populations for sites smaller than 9000 sq. m.

Regression analyses based on different models were also conducted for 'large' sites (i.e. sites larger than 9000 sq. m) as well. In these cases, only the equations of the linear and logarithmic models presented acceptable values of r-squared: 0-923 and 0-953 respectively [ILLUSTRATION FOR FIGURES 8 & 9 OMITTED]. A visual examination of both curves, however, indicates that more points are associated with, or are closer to, the logarithmic curve than to the linear curve.

To compare the equations obtained for the large settlements and all the sites together, population estimates were calculated for some of the archaeological data on settlement sizes reported by Roosevelt (1980). Only settlements with sizes within the scope of the model of the regression analysis (i.e. [greater than] 9000 and [less than] 25,000 sq. m) were included in the comparison (TABLE 4). Unfortunately, there is no other reliable equation for estimating populations of settlements from lowland South America and the Caribbean which could be used here for comparison. While the differences between the estimates from the four formulae can be as large as 33 individuals, none of these disagreements were larger than 8%. In fact, the differences were about 14 individuals [i.e. [less than] 6%) in most of the cases The population estimates obtained from the four formulae are relatively similar to each other. Nevertheless, considering the high r-squared value and the visual inspection of the regression curve and distribution of points, I recommend using the logarithmic regression formula for large sites.

Conclusions

Ethnographic data from South America have allowed the generation of a series of regression formulae to estimate prehistoric populations in both lowland South America and the Caribbean. The basic assumption of the study is that under certain circumstances (e.g. no marked social stratification or specialization) house and site area are usually, but not always, determined by the number of residents. This assumption is supported by the regression analyses which established that, with the exception of the nuclear family dwellings, well over 90% of the variation in space/area in both ethnographic houses and settlements is explained by population size.

It is interesting to point out that in many of the cases where house type or settlement size [TABULAR DATA FOR TABLE 4 OMITTED] could be controlled, the best-fit equations demonstrated that:

1 habitation area and population size have an allometric relationship (specifically, logarithmic and binomial models) and

2 that population density varies in correlation with house or settlement type and size. This is in agreement with the conclusions reached by many previous students of population estimations (Casselberry 1974; Cook & Heizer 1968; Naroll 1962; Schacht 1981; Schreiber & Kintigh 1996; Wiessner 1974) and ignored by more recent research on this topic (Curet 1992a; Roosevelt 1980; Schinkel 1992; Siegel 1989; 1990).

It is important to stress here the conditions under which these formulae are applicable. First of all, these formulae were developed for lowland South America and Caribbean groups. Specifically, data from what are termed 'Tropical Forest' cultures (Lathrap 1970; Lowie 1948) were used in the ethnographic analogy. Thus, for this analogy to be applicable to the archaeological record, a strong relationship between the archaeological culture and the Tropical Forest 'tradition' from South America is assumed.

Second, all the cases included in the ethnographic data set consisted of permanent, nucleated habitation sites of horticultural groups who also depended on hunting and gathering. Furthermore, none of the groups were socially stratified or included a centralized, inherited position of power. Therefore, for these formulae to be properly applied, the archaeological culture should have had similar economic, political, and social structures, at least at the local or community level. These formulae are not valid, for example, to estimate populations from large ceremonial centres such as those found in Puerto Rico, nor for settlements with specialized structures such as ball courts, nor for houses of high status individuals which could have been used as meeting halls. Further research might improve some of these results by increasing the sample size of settlements, so formulae could be developed for the different types of sites as defined by Myers (1973) and Meggers (1995). Finally, as with any regression equation, these formulae are more reliable when used within the scope of the models. That is, estimates obtained from applying the equations in cases that are considerably larger or smaller than any of the cases included in the ethnographic data-set are unreliable and may well be inaccurate. For houses, the scope of the model is any dwelling smaller than about 700 sq. m, and for settlements, it is sites smaller than 25,000 sq. m.

In this paper I have presented a series of formulae that can be used to estimate prehistoric populations in lowland South America and the Caribbean. Even though I have recommended some of these formulae over others, sufficient information is included here for future researchers to decide for themselves which equation to use. While it is difficult to determine how precise and accurate these formulae may be, they were obtained using a more rigorous methodological approach and a larger data-base than previous studies. They are certainly valuable in determining some aspects of the internal structure of societies and how population changed diachronically and synchronically. Altogether, these formulae were developed anticipating that further South American and Caribbean studies using population as an independent or dependent variable would profit from having an empirical tool to estimate prehistoric populations in a more precise and accurate manner.

Acknowledgements. I would like to thank Heather Manley, Danielle O'Connor and Bryant Pappas for assistance in collecting the ethnographic data used in this paper. I am grateful to Mark Mitchell, Lee Newsom, Jose Oliver, James Petersen, Angela Rayne, Miguel Rodriguez and Paul Shen-Brown for providing insightful comments on earlier versions of the paper.

Note

1 One of the earliest attempts to estimate prehistoric populations systematically in lowland South America was undertaken by Anna Roosevelt in the region of Parmana in the Middle Orinoco. Roosevelt (1980) conducted a nonsystematic, non-intensive regional study in an attempt to demonstrate that population increase correlated with the introduction of maize agriculture in the region. To estimate prehistoric populations Roosevelt [1980: 218-19) developed an average population density based on the ethnographic study done by Smole (1976) on the Yanomamo. To arrive at the estimate of 75 people/hectare (0.0075 people/sq. m) she divided the average population for Yanomamo settlements (about 75 people) by the average size of those settlements (reportedly 10,000 sq. m). However, a careful reading of Smole's monograph suggests that Roosevelt made a mistake in her calculations of the average population density, due to an error in her derivation of the average settlement area. The average diameter of the circular settlements of the Yanomamo (or shabono) reported by Smole (1976: 61) is 100 ft which, once converted into metres, covers an area of about 730 sq. m and not 10,000 sq. m as Roosevelt reported. This means that the 'average' population density for Yanomamo settlements is about 0.1 people/sq. m (1000 people/ha), a figure more than 10 times higher than Roosevelt's estimate. In fact, this number is extremely high compared to other ethnographic cases which suggests that it is not a reliable figure for population estimates. The use of average densities rather than the mean density might have been more appropriate for Roosevelt's purposes (see Schacht 1981 for a brief discussion of the difference between mean and average densities). To be fair, mathematical errors in demographic calculations are not uncommon in the literature (e.g. Casteel 1979; Wiessner 1979).

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