Corporalidad: Un cambio conceptual

Within the context of palaeodietary studies, stable isotopes of carbon and nitrogen are most commonly analyzed (as discussed above), with a much smaller number of studies including sulfur isotopic analysis (Craig et al., 2006; Nehlich et al., 2010; Privat et al., 2007; Richards et al., 2001). Accordingly, this discussion is limited to interpretations of carbon and nitrogen isotopic data. While there have been substantial changes in the manner and scale with which isotopic data are generated, the interpretive techniques employed by archaeologists and anthropologists have remained fairly consistent over the last twenty years. The types of questions that have been asked have generally been

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limited to, “what was the diet composition of population/group/individual x” and “how

similar were the diets of groups x and y”. To answer the first of these questions requires

relatively detailed knowledge on the range and variation of the isotopic compositions of the foods that may have contributed to the diet. This requires the analysis of modern flora/fauna, archaeological fauna, or a combination of these. Isotopic data derived from archaeological humans or animals (mixtures) are then interpreted using these baselines (sources) as a reference point using a range of qualitative and quantitative approaches, as outlined below.

1.2.3.1

Isotopic Mixing Basics and the n+1 Model

Understanding isotopic mixing is crucial to the interpretation of isotopic data in a wide range of contexts, including in paleodietary studies. Before exploring any particular method in great detail, it is first necessary to introduce some of the basic concepts of isotopic mixing. To do so, a basic linear mixing model (n+1 Model) will be discussed. In isotopic mixing models, foods are often referred to as ‘sources’ and consumers are sometimes referred to as mixtures, but in this context are more frequently simply called ‘consumers’. As mentioned previously, the isotopic compositions of a consumer’s tissue represent an average of the isotopic composition of the foods (sources) consumed over a given period of time (depending on the tissue being analyzed). This relationship is summarized very simply in Figure 1.2. In this case, the consumer (solid dot) has a very similar isotopic composition to Source 2, which suggests this particular source (food) is prominent in the diet of this consumer. To make such comparisons, appropriate adjustments must be made to either the consumers or sources for trophic level fractionation. The interpretation of Source 2 being important can be made qualitatively by evaluating the proximity of the consumer to the source in bivariate (x, y) space. This relationship can also be expressed quantitatively: the contribution of a particular source to the diet of a consumer is inversely proportional to the line connecting the consumer and source. In other words, the shorter the line between the consumer and the source, the greater the contribution of that source to the diet/mixture. A series of equations can be performed in this case to determine the exact contributions of each source, as discussed by Schwarcz (1991).

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Equation 1.2

Equation 1.3 Equation 1.4

X1, X2, and X3 represent the % contribution of each of the three sources, Cx and Nx represent the carbon and nitrogen isotopic compositions of each of the sources, CM and NM represent the carbon and nitrogen isotopic compositions of the consumer/mixture. These three equations can be used to produce solutions for each source contribution. A related, but alternative approach is provided by Ben-David et al. (1997) that explicitly uses the Euclidean distance between the consumer and each source.

The limitation of both of these approaches is that calculations of source contributions are limited to n+1 sources, where n is the number of isotopes being measured (typically two); higher numbers of sources do not produce finite solutions. In most practical cases, this limits the number of sources being examined to two. This may be acceptable, for example, when only two distinct sources of primary production contribute to the diet of a consumer, as is sometimes the case in nearshore marine ecosystems (Bustamante and Branch, 1996; Duggins et al., 1989; Fredriksen, 2003; Hill and McQuaid, 2008; Kaehler et al., 2006; Kang et al., 2008; Schaal et al., 2009, 2010; Simenstad et al., 1993). In the case of more complex systems, as is often the case with humans, where food is consumed from multiple trophic levels and habitats, this approach has few practical applications. Nevertheless, it does illustrate the basic premises of isotopic mixing and paleodietary interpretation that form the basis of most other methods.

While the focus of the following section is not explicitly on reconstructing diet composition with mixing models, much more refined methods to do this have been developed in recent years, using computer-assisted iterative methods that are constrained to provide feasible solutions for larger numbers of sources (Newsome et al., 2004; Phillips and Gregg, 2001; Phillips and Koch, 2002; Phillips and Gregg, 2003; Phillips et al., 2005), and also methods that use a Bayesian framework to incorporate uncertainty in source isotopic compositions, trophic level fractionation estimates, and so on (Bond and

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Diamond, 2010; Moore and Semmens, 2008; Parnell et al., 2010; Semmens et al., 2009; Ward et al., 2010). Nevertheless, what remains of the utmost importance in such models is that the variation in isotopic baselines (in this case food) be understood as completely as possible. Moreover, if Bayesian models are used, it is useful to know how much uncertainty to expect in the isotopic compositions of the sources. The remainder of this section focuses on data presentation and interpretation methods currently employed and introduces some new approaches that are later utilized in Chapter 5.

1.2.3.2

Box Model Method

This approach to interpreting isotopic data visualizes source isotopic compositions as boxes in bivariate space (Figure 1.3). The dimensions of the boxes may be determined by the range, or the mean and standard deviations of the isotopic compositions of one or several sources. Sources may be grouped together based on functional and/or isotopic similarity, although this is not specific to this particular approach. Carbon and nitrogen isotopic data from consumers are plotted alongside the source boxes, with either the boxes or the consumers being adjusted to account for trophic level fractionation. These data are interpreted qualitatively, although the mechanistic basis for the interpretation is essentially quantitative and based in Euclidean geometry. Generally, if a consumer falls within a given box, that individual is interpreted as having been largely reliant on that particular food source, or more likely group of foods. In some instances such an assessment is entirely reasonable. Taking the data presented in Figure 1.3 as an example, individuals that fall within the C3 plant box (especially close to the bottom left of the box), the C4 plant box (especially close to the bottom right), or the marine animals box (especially close to the top right) are likely to have consumed primarily these resources. For most of the individuals plotted in Figure 1.3, however, we could interpret marine plants as having been the primary food source. While this may be mathematically sensible, it is only one possible solution to this mixing problem. Alternatively, a mixture of some proportion of marine animals and C3 plants can produce the same consumer isotopic signature. While this may be implicit for those who understand isotopic mixing, those reading such a figure with less knowledge of its mathematical basis may be prone to misinterpretation.

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Additional problems come in the forms of the boxes themselves. Rarely are animal or plant isotopic compositions distributed evenly within the rectangular bivariate space of one of these boxes. This is especially problematic if the boxes are defined on the basis of source ranges. If boxes are defined on the basis of means and standard deviations this better conveys the density of a particular source, but problems arise when collapsing multiple sources into one box. Finally, the actual distribution of carbon and nitrogen isotopic data within bivariate space is rarely even, and in many cases these variables may be correlated (this is explored in the following section). Again, the right angle boxes used in this approach do not adequately capture these aspects of typical isotopic data.

The Box Model Method is a very straightforward and somewhat attractive means of displaying the relationship between sources and consumers; it tends to be less cluttered than similar plots that utilize a mean and standard deviation for individual food sources (Beasley et al., 2013; Kinaston et al., 2013; Kusaka et al., 2010; Szpak et al., 2009; Szpak et al., 2012c). Problematic as this Box Model Method may be, it is still superior to presenting consumer isotopic data absent of any baseline information.

1.2.3.3

Polygons and the Convex Hull

The areas formed by isotopic data in bivariate space are significant in ways beyond the generation of mixing polygons as discussed previously. The basis for the Box Model Method, as well as many other qualitative interpretive approaches to bivariate isotopic plots, is that they rely on the spatial relationships (proximity of A to B, area of A relative to B) of the data. These spatial relationships are significant because the variation in isotopic compositions is associated with larger biological, chemical, or geological significance. The methods discussed in this section make use of the spatial nature of isotopic data and provide a number of ways that these data can be compared in a more quantitative approach. This understanding of bivariate data underpins the approaches used in Chapter 5. The crucial point here is that we are moving away from an approach that is primarily concerned with reconstructing diet composition to one that is instead focused on diet variation. While reconstructing diet composition has become a much more refined art with the introduction of more involved linear models (Newsome et al., 2004; Phillips and Gregg, 2001; Phillips and Koch, 2002; Phillips and Gregg, 2003;

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Phillips et al., 2005), and the incorporation of more complex Bayesian statistics (Bond and Diamond, 2010; Moore and Semmens, 2008; Parnell et al., 2010; Semmens et al., 2009; Ward et al., 2010), the uncertainty associated with these estimates remains problematic. Even under ideal conditions in modern contexts where prey species can be re-sampled in a much more unrestrictive manner and the temporal span is both known and extremely limited, these issues of uncertainty are still significant. In archaeological contexts this is taken to the extreme where source isotopic compositions will necessarily be even more uncertain. While it is certainly not a futile task to attempt these diet composition assessments, a more productive approach (either as an alternative, or as a complement) can be to focus on the variability in isotopic data.

Consider the three groups of isotopic data presented in Figure 1.4A for Holocene humans from central California (Beasley et al., 2013). Expressing these data as means and standard deviations (Figure 1.4B) does not adequately capture the distribution of the data, largely because there is clearly a correlation between 13C and 15N. Moreover, as a descriptive tool, Figure 1.4B does a poor job of conveying the spatial distribution of the isotopic variation around the means. If, as discussed previously, the isotopic variation is meaningful, this is particularly problematic. Two alternative approaches to displaying the variation in bivariate isotopic datasets have been proposed. The first is the convex hull area (or total area), which is simply the minimum area polygon that encloses all of the individual data in bivariate space (Figure 1.4C) (Layman et al., 2007a). The area occupied by this polygon can be used as a comparative metric in discussing the amount of isotopic variation (13C and 15N together, rather than separately) in a given dataset. The convex hull matches the distribution of the data faithfully, but it does not convey any information about the density or packing of the isotopic data in space. In Figure 1.4C, for example, one polygon is much larger than the other two, which is caused by the three individuals with low 13C and 15N values. The convex hull is therefore very sensitive to extreme values, and a single outlier or small number of outliers can drastically alter the calculated value. The circumvention of this problem, the standard ellipse, has recently become a popular tool for analyzing bivariate isotopic variation (Figure 1.4D). The standard ellipse is the bivariate equivalent of the univariate mean and standard deviation

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(Batschelet, 1981), and much like the convex hull, a numeric area can be computed that can be used to compare isotopic variation between groups (Jackson et al., 2011). Unlike the convex hull, however, the standard ellipse is much less sensitive to extreme values, and does account for the density or packing of data within bivariate space. Additionally, calculations can be employed to account for variations in sample size and large numbers of calculations of estimated standard ellipse areas can be generated using a Bayesian framework, both allowing for fairly robust comparison between groups (Jackson et al., 2011). These methods are outlined in greater detail in Chapter 5.

Aside from quantifying variation, the convex hull and standard ellipse allow several important questions about bivariate isotopic data (and in turn diet and ecology) to be addressed. For instance, two groups of bivariate isotopic data may be compared on the basis of their mean 13C and 15N values, respectively using an ANOVA, t-test, or similar approach to assess whether or not the means differ from one another (how similar is the diet of population A to population B?). This approach has some utility, but it does treat bivariate data as two unrelated sets of univariate data. The standard ellipse approach allows for a direct comparison of bivariate data, and similar questions can be asked by examining the extent of overlap between the two ellipses (how similar is the diet of population A to population B?). In cases of small sample size, robust estimates can be performed using an iterative re-sampling approach that generates a large number of areas for comparative purposes. Similarly, we can use these metrics to address whether one group is characterized by a greater amount of variability than another (is the diet of population A more variable than that of population B?). Therefore, we can ask the same questions using this approach, but we can do so in a way that is more appropriate for these types of data.