Multivariate Carbon and Nitrogen Stable Isotope Model for the Reconstruction of Prehistoric Human Diet A.W. Froehle, 1 * C.M. Kellner, 2 and M.J. Schoeninger 3,4 1 Department of Community Health, Wright State University, Dayton, OH 45435 2 Department of Anthropology, Northern Arizona University, Flagstaff, AZ 86011 3 Department of Anthropology, University of California, San Diego, La Jolla, CA 92093 4 Center for Academic Training and Research in Anthropogeny (CARTA), La Jolla, CA 92093 KEY WORDS cluster analysis; discriminant function analysis; apatite; collagen; bioarchaeology ABSTRACT Using a sample of published archaeolog- ical data, we expand on an earlier bivariate carbon model for diet reconstruction by adding bone collagen nitrogen stable isotope values (d 15 N), which provide in- formation on trophic level and consumption of terrestrial vs. marine protein. The bivariate carbon model (d 13 C apatite vs. d 13 C collagen ) provides detailed information on the isotopic signatures of whole diet and dietary pro- tein, but is limited in its ability to distinguish between C 4 and marine protein. Here, using cluster analysis and discriminant function analysis, we generate a multivari- ate diet reconstruction model that incorporates d 13 C apatite , d 13 C collagen , and d 15 N holistically. Inclusion of the d 15 N data proves useful in resolving protein-related limitations of the bivariate carbon model, and splits the sample into five distinct dietary clusters. Two significant discriminant functions account for 98.8% of the sample variance, providing a multivariate model for diet recon- struction. Both carbon variables dominate the first func- tion, while d 15 N most strongly influences the second. In- dependent support for the functions’ ability to accurately classify individuals according to diet comes from a small sample of experimental rats, which cluster as expected from their diets. The new model also provides a statisti- cal basis for distinguishing between food sources with similar isotopic signatures, as in a previously analyzed archaeological population from Saipan (see Ambrose et al.: AJPA 104(1997) 343-361). Our model suggests that the Saipan islanders’ 13 C-enriched signal derives mainly from sugarcane, not seaweed. Further develop- ment and application of this model can similarly improve dietary reconstructions in archaeological, paleontological, and primatological contexts. Am J Phys Anthropol 147:352–369, 2012. V V C 2011 Wiley Periodicals, Inc. Recent meta-analyses (Kellner and Schoeninger, 2007; Froehle et al., 2010) have developed a new, regression- based model for prehistoric diet reconstruction using published experimental animal bone stable isotope data (Hare et al., 1991; Ambrose and Norr, 1993; Tieszen and Fagre, 1993; Howland et al., 2003; Jim et al., 2004; War- inner and Tuross, 2009). When carbon stable isotope ratios ( 13 C: 12 C, represented as d 13 C) of bone collagen (d 13 C collagen ) and bone apatite (d 13 C apatite ) are plotted against one another, these experimental data sort into two discrete groups according to protein source (C 3 vs. C 4 /marine). The resulting d 13 C collagen vs. d 13 C apatite regression lines for the two protein-specific groups differ in their vertical intercepts (on the d 13 C collagen axis), but not for slope (Froehle et al., 2010). Applied to diet recon- struction, the position of an individual relative to one or the other line along the d 13 C collagen axis provides isotopic information on sources of dietary protein, while place- ment along the d 13 C apatite axis indicates the ratio of C 3 to C 4 foods in whole diet (d 13 C diet ), as Ambrose and Norr (1993) originally proposed. The regression model offers more detailed and accurate dietary estimates than either d 13 C collagen or d 13 C apatite does alone, and avoids much of the redundancy inherent in the apatite-collagen spacing model (the arithmetic difference between d 13 C apatite and d 13 C collagen values, denoted as D 13 C apatite-collagen : see Krueger and Sullivan, 1984; Lee-Thorp et al., 1989; Ambrose et al., 1997). Although the bivariate regression model has advan- tages over previous methods, a plot of archaeological human data against the experimentally derived regres- sion lines reveals two limitations concerning protein sources (Fig. 1a). First, the model distinguishes poorly between C 4 and marine sources of protein, confounding determination of protein sources in populations living in coastal areas that also harbor C 4 wild vegetation or agri- cultural crops. Second, many individuals fall between the protein-specific lines, the meaning of which, with regard to protein sources, remains somewhat unclear. Previous work showed that swine eating an experimen- tal diet with mixed protein (80% C 3 , 20% C 4 ) fell, as expected, slightly above the C 3 protein regression line derived from rodents consuming 100% C 3 protein (Froehle et al., 2010). Given the small rodent sample size and scatter within data, however, the swine were statistically indistinguishable from the 100% C 3 protein rodent population. It is therefore difficult to say whether the position of the archaeological humans close to, but not on, one of the protein-specific lines reflects normal variation in populations consuming monoisotopic protein, or whether it indicates mixed protein consumption. *Correspondence to: Andrew Froehle, Department of Community Health, Wright State University, Dayton, OH. E-mail: [email protected]Received 23 June 2011; accepted 29 October 2011 DOI 10.1002/ajpa.21651 Published online 30 December 2011 in Wiley Online Library (wileyonlinelibrary.com). V V C 2011 WILEY PERIODICALS, INC. AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 147:352–369 (2012)
Transcript
Multivariate Carbon and Nitrogen Stable Isotope Modelfor the Reconstruction of Prehistoric Human DietA.W. Froehle,1* C.M. Kellner,2 and M.J. Schoeninger3,4
1Department of Community Health, Wright State University, Dayton, OH 454352Department of Anthropology, Northern Arizona University, Flagstaff, AZ 860113Department of Anthropology, University of California, San Diego, La Jolla, CA 920934Center for Academic Training and Research in Anthropogeny (CARTA), La Jolla, CA 92093
KEY WORDS cluster analysis; discriminant function analysis; apatite; collagen; bioarchaeology
ABSTRACT Using a sample of published archaeolog-ical data, we expand on an earlier bivariate carbonmodel for diet reconstruction by adding bone collagennitrogen stable isotope values (d15N), which provide in-formation on trophic level and consumption of terrestrialvs. marine protein. The bivariate carbon model(d13Capatite vs. d13Ccollagen) provides detailed informationon the isotopic signatures of whole diet and dietary pro-tein, but is limited in its ability to distinguish betweenC4 and marine protein. Here, using cluster analysis anddiscriminant function analysis, we generate a multivari-ate diet reconstruction model that incorporatesd13Capatite, d
13Ccollagen, and d15N holistically. Inclusion ofthe d15N data proves useful in resolving protein-relatedlimitations of the bivariate carbon model, and splits thesample into five distinct dietary clusters. Two significantdiscriminant functions account for 98.8% of the sample
variance, providing a multivariate model for diet recon-struction. Both carbon variables dominate the first func-tion, while d15N most strongly influences the second. In-dependent support for the functions’ ability to accuratelyclassify individuals according to diet comes from a smallsample of experimental rats, which cluster as expectedfrom their diets. The new model also provides a statisti-cal basis for distinguishing between food sources withsimilar isotopic signatures, as in a previously analyzedarchaeological population from Saipan (see Ambroseet al.: AJPA 104(1997) 343-361). Our model suggeststhat the Saipan islanders’ 13C-enriched signal derivesmainly from sugarcane, not seaweed. Further develop-ment and application of this model can similarly improvedietary reconstructions in archaeological, paleontological,and primatological contexts. Am J Phys Anthropol147:352–369, 2012. VVC 2011 Wiley Periodicals, Inc.
Recent meta-analyses (Kellner and Schoeninger, 2007;Froehle et al., 2010) have developed a new, regression-based model for prehistoric diet reconstruction usingpublished experimental animal bone stable isotope data(Hare et al., 1991; Ambrose and Norr, 1993; Tieszen andFagre, 1993; Howland et al., 2003; Jim et al., 2004; War-inner and Tuross, 2009). When carbon stable isotoperatios (13C:12C, represented as d13C) of bone collagen(d13Ccollagen) and bone apatite (d13Capatite) are plottedagainst one another, these experimental data sort intotwo discrete groups according to protein source (C3 vs.C4/marine). The resulting d13Ccollagen vs. d13Capatite
regression lines for the two protein-specific groups differin their vertical intercepts (on the d13Ccollagen axis), butnot for slope (Froehle et al., 2010). Applied to diet recon-struction, the position of an individual relative to one orthe other line along the d13Ccollagen axis provides isotopicinformation on sources of dietary protein, while place-ment along the d13Capatite axis indicates the ratio of C3
to C4 foods in whole diet (d13Cdiet), as Ambrose and Norr(1993) originally proposed. The regression model offersmore detailed and accurate dietary estimates than eitherd13Ccollagen or d13Capatite does alone, and avoids much ofthe redundancy inherent in the apatite-collagen spacingmodel (the arithmetic difference between d13Capatite andd13Ccollagen values, denoted as D13Capatite-collagen: seeKrueger and Sullivan, 1984; Lee-Thorp et al., 1989;Ambrose et al., 1997).Although the bivariate regression model has advan-
tages over previous methods, a plot of archaeologicalhuman data against the experimentally derived regres-
sion lines reveals two limitations concerning proteinsources (Fig. 1a). First, the model distinguishes poorlybetween C4 and marine sources of protein, confoundingdetermination of protein sources in populations living incoastal areas that also harbor C4 wild vegetation or agri-cultural crops. Second, many individuals fall betweenthe protein-specific lines, the meaning of which, withregard to protein sources, remains somewhat unclear.Previous work showed that swine eating an experimen-tal diet with mixed protein (!80% C3, !20% C4) fell, asexpected, slightly above the C3 protein regression linederived from rodents consuming 100% C3 protein(Froehle et al., 2010). Given the small rodent samplesize and scatter within data, however, the swine werestatistically indistinguishable from the 100% C3 proteinrodent population. It is therefore difficult to say whetherthe position of the archaeological humans close to, butnot on, one of the protein-specific lines reflects normalvariation in populations consuming monoisotopic protein,or whether it indicates mixed protein consumption.
*Correspondence to: Andrew Froehle, Department of CommunityHealth, Wright State University, Dayton, OH.E-mail: [email protected]
Received 23 June 2011; accepted 29 October 2011
DOI 10.1002/ajpa.21651Published online 30 December 2011 in Wiley Online Library
(wileyonlinelibrary.com).
VVC 2011 WILEY PERIODICALS, INC.
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 147:352–369 (2012)
In order to resolve these protein-related ambiguities,here we expand the model beyond the sole use of carbonvariables by adding nitrogen stable isotope data (d15N).Values of d15N in bone collagen closely reflect proteinsources, varying with consumption of different propor-tions of plant vs. animal protein, as well as with terres-trial vs. marine protein sources (Schoeninger et al.,1983; Minagawa and Wada, 1984; Schoeninger andDeNiro, 1984). This study also introduces multivariatestatistical techniques to the study of stable isotopes. Weemploy cluster analysis to investigate relationshipsbetween diet and the three isotope variables holistically,and develop a discriminant function model for the simulta-neous use of the three variables in dietary reconstruction.
Because we are aware of only one study that hasreported experimental animal d15N values (Ambrose,2000), the present analysis uses published data fromarchaeological human populations with reliable, noniso-topic evidence of diet. The experimental animal data(Ambrose and Norr, 1993; Ambrose, 2000) serve as apost hoc check of our interpretation of the human data.Finally, we provide an example application of the newmodel to an archaeological dataset, for which previouswork left a dietary question unanswered (Ambrose et al.,1997).
STABLE ISOTOPE BIOGEOCHEMISTRY
It is well established that carbon and nitrogen stableisotope ratios in the tissues of animals, includinghumans, reflect the isotope ratios in the foods they eat(DeNiro and Epstein, 1978, 1981; Schoeninger andDeNiro, 1984; Lee-Thorp et al., 1989; Ambrose and Norr,1993; Tieszen and Fagre, 1993; Howland et al., 2003;Jim et al., 2004). Carbon-isotope ratios mainly reflect thephotosynthetic pathway of the plants an animal eats, orin carnivores, the plants that prey animals ate. The twomost common photosynthetic pathways are C3 and C4, sonamed because the resulting sugars contain three andfour carbon atoms, respectively. Compared to referencestandards, C3 plants are relatively depleted in the 13Cisotope compared to C4 plants, which are relatively 13C-enriched. Both d13Capatite and d13Ccollagen reflect overalld13Cdiet, but dietary sub-components appear to influencethe tissues’ carbon-isotope ratios differently (Sullivanand Krueger, 1981; Lee-Thorp et al., 1989; see Schwarcz,2000 for a review). Data from experimental feeding stud-ies (Ambrose and Norr, 1993; Tieszen and Fagre, 1993;Howland et al., 2003; Jim et al., 2004) and meta-analy-ses of those data (Kellner and Schoeninger, 2007) sug-gest that d13Capatite correlates most closely with d13Cdiet,equally reflecting all subcomponents in proportion totheir abundance in the diet. In contrast, d13Ccollagen alsoreflects d13Cdiet, but is skewed toward the isotopic signa-ture of protein (Kellner and Schoeninger, 2007; Warinnerand Tuross, 2009; Froehle et al., 2010).Nitrogen from the atmosphere enters the human food
web mainly through dietary plants and animals. Manyleguminous plants have symbiotic relationships withbacteria that fix nitrogen directly from the atmosphere,and are thus not enriched in nitrogen (d15N""0% by defi-nition). Other legumes do not participate in this kind ofsymbiosis (Muzuka, 1999; Codron et al., 2005), and arecorrespondingly enriched in 15N relative to the atmos-phere: this probably explains the lack of low d15N valuesin some human populations known to ingest beans andother leguminous plants (Schwarcz and Schoeninger,1991). Most nonleguminous plants obtain nitrogen fromcompounds in the soil and have higher values of d15Nthan the atmosphere (Rennie et al., 1976; Wada andHattori, 1976; Shearer and Kohl, 1978; Amarger et al.,1979; Delwiche et al., 1979; Virginia and Delwiche,1982). Animal nitrogen is enriched in 15N relative to theplants and animals they consume, such that animalshave d15N values !3% higher than their diets (Mina-gawa and Wada, 1984; Schoeninger and DeNiro, 1984;Ambrose, 2000). In marine ecosystems, vertebratesexhibit d15N values 6-8% higher than animals at similartrophic levels in most terrestrial environments(Schoeninger and DeNiro, 1984). Thus, d15N in humanbone collagen provides information on trophic position
Fig. 1. Means (with 95% confidence intervals of the mean)for d13Ccollagen and d13Capatite in (a) archaeological human popu-lations and (b) cluster centroids, plotted against experimentalanimal regression lines and their 95% prediction intervals (ex-perimental data compiled in Froehle et al., 2010; data fromAmbrose and Norr, 1993; Tieszen and Fagre, 1993; Howlandet al., 2003; Jim et al., 2004; Warinner and Tuross, 2009). Thelong-dashed lines represent the 95% prediction interval of themostly-C3-protein regression, while the short-dashed linesdelimit the 95% prediction interval of the C4/marine-proteinregression. Human data sources are in Table A1. The experi-mental data from which the regression lines derive have beenadjusted to reflect pre-industrial atmospheric carbon levels byadding 1.5% (Marino and McElroy, 1991). Cluster diets: (1)100% C3 diet/protein; (2) 30:70 C3:C4 diet, >50% C4 protein; (3)50:50 C3:C4 diet, marine protein; (4) 70:30 C3:C4 diet, #65% C3
(Schoeninger, 1985; Phillips and Koch, 2002) and thedegree of reliance on marine resources (Schoeninger etal., 1983). This latter aspect of nitrogen-isotope data iscritical to the present analysis, since the relationshipbetween d13Capatite and d13Ccollagenvalues in marineresources converges with that of C4 protein sources(Kellner and Schoeninger, 2007). By adding d15N valuesin this analysis, we expect to be capable of distinguishingbetween populations consuming C4 vs. marine protein.
METHODS
Archaeological data
The database includes only adults with individualmeasurements for each of the relevant variables (d13Ccolla-
gen, d13Capatite and d15N), resulting in a sample size of N 5
158 (see Table A1). The data come from eight differentpopulations for which substantial nonisotopic archaeologi-cal evidence for diet exists: Ontario preagriculturists andagriculturists; San Nicolas Island fisher-foragers (Har-rison and Katzenberg, 2003); American Bottom floodplainand upland agriculturists; Illinois River agriculturists(Hedman et al., 2002); Cahokia Mound 72 agriculturists(Ambrose et al., 2003); and Tierra del Fuego fisher-forag-ers (Yesner et al., 2003). All studies from which data weredrawn used established sample preparation and analysismethods. Although most studies sampled mainly ribs,other bones were occasionally included—this should notbe a problem for our meta-analysis given that only well-preserved samples were included (DeNiro and Schoe-ninger, 1983; Ubelaker, 1995).
Multivariate statistical analysis
We began by using cluster analysis to determinewhether individuals associated with one another accord-ing to their isotope values in the manner expected fromprevious evidence for diet. By comparing measures ofinterindividual proximity in multivariate space (Everittet al., 2001), cluster analysis assigns data to clustersthat maximize both intragroup homogeneity and inter-group heterogeneity. We constrained our analyses byassuming that the sample would divide into a minimumof one diet group, and a maximum of six groups, testingevery integer from one through six. The minimum repre-sents the case where no dietary differences exist in thesample, while the maximum represents every possiblecombination of diet and protein end-members (C3 vs. C4
for the nonprotein portion of diet; C3, C4, and marine forprotein). All three isotope variables use the same scaleand occupy roughly the same magnitude of range acrossthat scale: thus, for all analyses we used raw, untrans-formed isotope data, and used squared Euclidian dis-tance as the interindividual proximity measure. We con-ducted all analyses using SPSS 16.0 for Windows.To determine the optimal number of natural clusters in
this dataset, we used both agglomerative hierarchical andk-means clustering (Baxter, 1994). Agglomerative hier-archical cluster analysis proceeds via the stepwise merg-ing of individuals into larger and larger groups, usingdecreasingly stringent criteria for within-group homoge-neity. This analysis produces a dendrogram in whichbranch length expresses the relative degree of similaritybetween individuals and groups (Everitt et al., 2001).Because the specific branching pattern of any dendrogrampartly reflects the intergroup proximity method used, wecompared results from the unweighted pair-group method
using the average (UPGMA) and Ward’s method, two com-mon measures in archaeological analyses (Baxter, 1994).K-means cluster analysis differs from hierarchical analy-sis in that it does not combine discrete groups into a uni-fied, nested hierarchy (Everitt et al., 2001), but insteadproduces a user-specified number of centroids (geometriccluster centers, in this case numbering from one throughsix) around which group members aggregate.We used two main criteria to determine which number
of clusters best reflected natural groupings in the data.First, we sought the greatest level of consistencybetween hierarchical and k-means analyses in assign-ment of cases to clusters. Second, we evaluated the die-tary validity of the k-means cluster centroids, which aremultivariate-average cluster centers with cluster-specificaverage d13Ccollagen, d
13Capatite, and d15N values. We onlyaccepted centroids that we could interpret clearly in die-tary terms, deriving our judgments in part from theplacement of the centroids along the d13Ccollagen andd13Capatite axes relative to regression lines derived fromexperimental animal data (Froehle et al., 2010). We usedprevious evidence of diet for the populations in the data-set to check for consistency between cluster membershipand cluster diet as implied by the centroids, and to fur-ther refine our centroid diet interpretations.After determining the most realistic number of clusters,
we used linear discriminant function analysis to generateequations for predicting group membership fromd13Ccollagen, d13Capatite and d15N. Discriminant functionanalysis uses known group membership from a ‘‘trainingsample’’ (in this case, our database) to produce linearequations (functions) describing how groups vary in termsof the independent variables (Everitt and Dunn, 2001).Our data met the assumptions of multivariate normalitywithin groups and equality of covariance matricesbetween groups (Garrett, 1989; Everitt and Dunn, 2001).To estimate the resulting functions’ misclassification rate,we employed a post-hoc ‘‘leave-one-out’’ test, evaluatingthe results for consistency with classifications defined bythe cluster analysis. We further checked the functions’ va-lidity against the experimental rat data of Ambrose andNorr (1993) and Ambrose (2000).To demonstrate how archaeological studies of diet might
use our new model, we applied the discriminant functionsto a population from the island of Saipan, part of theMarianas Islands in the northwestern Pacific. Archaeologi-cal and isotopic evidence for diet have remained somewhatinconclusive (Ambrose et al., 1997): though Saipan’s eco-system is C3-dominated, stable isotope data indicated mod-erate consumption of 13C-enriched foods. Two candidates,C4 sugarcane and seaweed, were identified as potentialsources of this signal, but the previous analysis offered noclear choice between the two (Ambrose et al., 1997). Here,we show how our discriminant function model can distin-guish between the signals of the two foods in the bones ofthe Saipan islanders, a method that may be applicable tosimilar problems in other populations.
RESULTS
Cluster analysis
The data split best into five diet groups, on the basisof the degree of overlap between the clustering methods,and for consistency with previous archaeological and iso-topic interpretations of diet in the sample. The one-,two-, and three-group clustering regimes were thrownout: high degrees of within-cluster heterogeneity limited
354 A.W. FROEHLE ET AL.
American Journal of Physical Anthropology
their utility in precise dietary reconstruction, and wereinconsistent with the substantial variability in diet withinand between populations in the database. The six-groupregime was thrown out because it produced a lower rateof overlap between hierarchical and k-means case assign-ments than did the four- and five-group clusteringregimes. Assuming five groups, the UPGMA hierarchicaland k-means methods assigned 151 of 158 (96%) cases toclusters in the same way. When we assumed four groups,UPGMA and k-means also classified 151 of 158 cases thesame way, while Ward’s and k-means assigned a slightlyhigher number of cases, 154 of 158 (97%), to the sameclusters. Among all such comparisons, the latter had thehighest rate of consistency between clustering methods.We nevertheless chose to adopt the slightly less-con-
sistent five-group clustering regime because we foundthat it revealed more dietary discrimination than did thefour-groups cluster assignments. To interpret diet foreach group, we plotted the k-means cluster centroids’isotope values (Table 1) against the experimental animalcarbon-isotope regression lines (Fig. 1b): four of the cent-roids fell on or near one of the two protein-specific dietregression lines, while the fifth cluster fell between thelines. It is important to note that the sample from whichthe C3 protein regression line is derived includes ani-mals eating 95–100% (N 5 12), 75–85% (N 5 11), and65% (N 5 1) C3 protein: as such, centroids falling on thisline can be interpreted as consuming at least 65% C3
protein (although more likely #75% C3 protein). Dietarysimilarities and differences between clusters were alsoevaluated using Euclidian distances between centroids(Table 1) and the dendrogram’s splitting pattern (Fig. 2),both of which matched and confirmed that the two anal-yses organized the clusters similarly.The placement of centroids on the experimental animal
plot indicates that Cluster 1 likely represents a fully C3
diet, and that Cluster 4 encompasses a 70% C3 diet withmostly C3 protein. The similarity of these two clusters rela-tive to the rest of the sample is reflected in their low-levelsplit in the dendrogram, and their small Euclidian distance(4.17; smallest of any two centroids). The dendrogram’shighest-order split occurred between the high-C3 Clusters1 and 4 on the one hand, and Clusters 2, 3, and 5 on theother. Given their placement along the d13Capatite axis onthe experimental animal carbon plot, this is consistentwith the latter three groups all having diets consisting ofat least 50% C4 foods. Fitting with this split, the two great-est distances between centroids occurred between Clusters1 and 2 (13.47), and between Clusters 1 and 3 (13.29).Of the three high-C4 groups, Cluster 5 is the easiest
to interpret, consisting of a 70% C4 diet with mostlyC3 protein. Clusters 2 and 3 defy interpretation using
only carbon data because although they both clearly hadoverall diets high in C4 foods (70 and 50% of diet, respec-tively), protein sources remain indeterminate. It is clearthat the vast bulk of the protein consumed by membersof Cluster 3 came from 13C-enriched sources, but the car-bon data do not indicate whether those were C4 or ma-rine foods. Similarly, the position of Cluster 2 likely indi-cates a mix of protein from both C3 and 13C-enrichedsources: although the centroid falls within the 95% pre-diction interval of the C4/marine protein line, that inter-val is quite wide due to the regression being derivedfrom a small sample. Were the sample larger, akin tothat of the C3 protein line, we would expect the Cluster 2centroid to fall just outside the C4/marine predictioninterval (see Fig. 1b) and thus between the two lines. Wetake this to indicate that at least some of the protein con-sumed by members of Cluster 2 came from C3 sources.As with Cluster 3, however, whether the 13C-enriched
a Centroid carbon isotope values interpreted for percent C3 and C4 in whole diet using experimental animals analyzed in Froehleet al. (2010). For this comparison, experimental animal carbon data were adjusted to reflect preindustrial atmospheric carbon levelsby adding 1.5% (Marino and McElroy, 1991). Collagen carbon and nitrogen isotope values were interpreted for protein sources fol-lowing DeNiro (1987) and Froehle et al. (2010).
Fig. 2. Simplified dendrogram showing the results of hier-archical cluster analysis. Average diet descriptions are based oncentroid isotope values from the k-means cluster analysis andinterpretations of those values using Froehle et al. (2010) andDeNiro (1987), as well as archaeological evidence. Proximitycoefficients indicate the degree of similarity at which differentgroups split/merge. Higher coefficients indicate a higher toler-ance for dissimilarity within groups/branches.
portion of the protein for Cluster 2 comes from C4 or ma-rine foods is unclear from the carbon-isotope data alone.The inclusion of d15N data in the hierarchical and k-
means cluster analyses helps make sense of proteinsources for Clusters 2 and 3. For example, the high-levelsplit of Cluster 3 from Clusters 2 and 5 is suggestive ofmajor dietary differences between these sub-branches ofthe dendrogram. Clusters 2 and 5 had very closely posi-tioned k-means centroids with a Euclidian distance ofjust 4.28, similar to the distance between Clusters 1 and4, and so close that the split was not visible in the four-groups k-means clustering regime. Clusters 2 and 3 werealmost twice as far from each other than were Clusters 1and 4 (which split much lower in the dendrogram), de-spite smaller gaps between Clusters 2 and 3 in d13Capatite
and d13Ccollagen (Cluster 1 vs. 4 differences: d13Capatite 53.8%, d13Ccollagen 5 1.7%; Cluster 2 vs. 3 differences:d13Capatite 5 2.8%, d13Ccollagen 5 0.8%). This pattern sug-gests that differences in nitrogen, not carbon, are largelyresponsible for the high-level split between Clusters 2and 3, and indeed, their centroid d15N values are highlydivergent: 10.1% vs. 17.7%, respectively (Clusters 1 and4 differ by only 1.3% for d15N). Plotting the clusters inthree-dimensional space (Fig. 3) emphasizes the difference
between Clusters 2 and 3 due to their nitrogen values. Onthe basis of these comparisons, it seems reasonable to inter-pret the diets of these clusters in the following terms: Clus-ter 2 includes a 70% C4 diet with mixed C3 and C4 protein,while Cluster 3 encompasses a 50% C3 diet with mainly ma-rine protein (interpretations that are also consistent witharchaeological evidence for diet—see Discussion).
Discriminant function analysis
In the discriminant function analysis, we used clusterassignments according to k-means for five groups as thetraining sample. We chose k-means over hierarchical clas-sifications because the former revises cluster centroids andmembership with sequential iterations, while the latterdoes not (Baxter, 1994). Thus, in cases of disagreementbetween the two techniques, we expect k-means to betterreflect natural trends in the data. Clusters were multivari-ate normal (Mahalanobis distance/chi square plots), butexhibited unequal covariate matrices (Box’s M)—violatingthe latter assumption is not necessarily ‘‘fatal’’ to discrimi-nant function analysis (Baxter, 1994). Using the ‘‘leave-one-out’’ assessment, the discriminant functions incor-rectly classified just 4 of 158 cases, three of which werestatistical outliers in their original studies (see Discus-sion). Given this low rate of misclassification and the out-lier status of the misclassified individuals, we accept thediscriminant function analysis results as robust.All three isotope variables exerted a significant influence
(all P\0.01) on the clustering of cases (Table 2). Three sig-nificant linear functions were derived (all P\0.01) and thefirst two together accounted for 98.8% of variance in thesample (Table 3). Both carbon-isotope variables exercisedtheir heaviest relative influence on scores derived fromFunction 1 (indicated by structure coefficients—see Table3), while nitrogen exerted its strongest effect on scoresfrom Function 2. The third function explained only 1.2% ofvariance and coincided with none of the independent varia-bles’ highest structure coefficients, so we dropped it fromfurther use. The remaining functions are:
Fig. 3. Three-variable plot of archaeological sample accord-ing to k-means classifications, including cluster centroids. Clus-ter diets: (1) 100% C3 diet/protein; (2) 30:70 C3:C4 diet, >50% C4
a Smaller values indicate greater effect on the discriminantfunction(s). All three variables contribute significantly to thediscrimination between groups.
TABLE 3. Function Eigenvalues and structure matrix
Function Eigenvaluea % of Variance Cumulative % Canonical correlation
a Eigenvalues indicate the amount of variance in the sample each function accounts for. The higher an Eigenvalue for a particularfunction, the higher the percentage of variance that function explains, which is also noted in this table.b Structure coefficients indicate the relative level of association between each variable and each function. Where these values arelargest for a particular variable, the influence of that variable on that function is greatest. The largest values for each variable areindicated by ‘‘*’’ above, and allow the functions to be characterized according to the key influential variables. In this case, we canname Function 1 ‘‘Carbon,’’ and Function 2 ‘‘Nitrogen.’’ Because of its relatively low influence on the sample’s variance, and becausenone of the variables were most highly correlated with it, we dropped Function 3.
We calculated function scores for the individual casesin the dataset and the cluster centroids, generating plots
(Fig. 4a,b; see Table A1 for function scores) that facili-tate the application of the model to new cases.
DISCUSSION
Diet classifications and archaeological sites
Overall, the five-groups cluster assignments and theirdietary interpretations conform well to expectations fromprevious studies’ results, although in some cases ourresults differ somewhat from earlier conclusions, whichwe discuss below. We also address the seven individualsclassified differently in the hierarchical vs. k-means clus-tering analyses, as well as the four cases misclassifiedby the discriminant function analysis. Clustering dis-agreements occurred for Cahokia 120, American BottomESLSQ 25, Range 14, and IC 114, and Illinois River 65,66a, and 153. The discriminant function analysis mis-classified American Bottom ESLSQ 25 and IC 116, Illi-nois River 65, and Tierra del Fuego 13. See Table A1 forindividual data.
Ontario. Within the Ontario sub-sample, all individualsfrom the post-agricultural period fell in Cluster 2 (70%C4; mixed C3/C4 protein), consistent with heavy relianceon C4 maize (Harrison and Katzenberg, 2003). ElevenOntario preagriculturists dating to 400 CE or earlier fellinto Cluster 1, indicative of a 100% C3 diet as expectedgiven that they antedate the introduction of maize to theregion. Seven others aggregated with Cluster 4, whichincludes a small contribution of C4 foods to whole diet.All seven postdate 500 CE, a date that coincides withevidence for the early presence of maize in the region,possibly as a result of trade preceding full-scale cultiva-tion after 1000 CE (Crawford et al., 1997; Smith andCrawford, 1997; Harrison and Katzenberg, 2003).While we anticipated the above results, the analysis
also revealed some divergence from the overall trend.Four individuals predating 500 CE (three from theDonaldson site and one from Serpent Mounds) all fellinto Cluster 4, their d13Capatite and d13Ccollagen valueswell within the range of later samples from the pro-posed 500–1000 CE maize-importation period. Thus, ei-ther some people in Ontario consumed maize muchearlier than currently accepted, or this early C4 signalmay result from consumption of locally available amar-anths, as previous authors have suggested (Schwarczet al., 1985). Finally, an individual dating to 918 CEgrouped with Cluster 1, ostensibly due to little con-sumption of imported maize despite its apparent avail-ability.Across the entire Ontario sample, nitrogen-isotope val-
ues fell between !10 to 15%, with no difference inmean d15N between the subgroups assigned to Clusters1, 2 and 4 (one-way ANOVA: P 5 0.08; means, respec-tively: 12.5%, 11.7%, 11.9%). Although the differenceswere not significant, the tendency toward lower averagenitrogen values in Clusters 4 and 5 members coincideswith some protein coming from maize after its introduc-tion into the region. Overall, though, the similarity ofthe nitrogen-isotope data across subgroups fits with con-sumption of terrestrial game, waterfowl and freshwaterfish as the major sources of protein, and the mainte-nance of that pattern over time despite the introductionof maize (Schwarcz et al., 1985; Harrison and Katzen-berg, 2003). Because there were no discrepanciesbetween the hierarchical and k-means analyses for any
Fig. 4. Archaeological sample discriminant function scoresplotted by group, as assigned in the discriminant function analy-sis, along with function scores at the group centroids. Clusterdiets: (1) 100% C3 diet/protein; (2) 30:70 C3:C4 diet, >50% C4 pro-tein; (3) 50:50 C3:C4 diet, marine protein; (4) 70:30 C3:C4 diet,#65% C3 protein; (5) 30:70 C3:C4 diet, #65% C3 protein. (a) Indi-vidual data points from the archaeological sample. Using the‘‘leave-one-out’’ technique, the discriminant function analysis clas-sified only 4 of 158 cases (labeled on the plot) differently than didthe k-means analysis. Three of these cases were statistical outliersin the original studies from which we drew the data. (b) Plot usingthe same data as above, but without individual data points. Errorbars extend to 2r of the means of both sets of function scores(equivalent to functions at centroids) within each cluster. The lim-its of the boxes represent the extreme minimum and maximumindividual case scores for each function within each cluster. Thisplot is intended to provide a clean working space for the evalua-tion of new cases (i.e., those not included in the present study)where diet remains indeterminate using other methods.
individuals from Ontario, we accepted the classificationsas robust.
Greater Cahokia region. Data from three areas withinthe greater Cahokia region (Pauketat, 1998) wereincluded in this study: the American Bottom, the IllinoisRiver Valley, and Cahokia itself. The American Bottomfloodplain and upland sites together constitute the larg-est population in our analysis. As expected from the orig-inal study, which reported an extensive reliance on C4
foods in the overall diet (Hedman et al., 2002), 33 of 35floodplain individuals and 13 of 17 upland individualsfell into Cluster 2. Among those assigned to Cluster 2,d15N values fell within the range of 7.9–10.7% (mean 59.3 6 0.09%), subsuming the intersite variabilityreported in the original study (Hedman et al., 2002), butconsistent with a mixed protein base consisting of wildterrestrial and aquatic game supplemented with wildnuts and cultivated maize. The remaining two floodplainand four upland individuals split between Clusters 1(100% C3), 4 (70% C3) and 5 (70% C4). While their d15Nmeasurements fell well within the range of the largerpopulation, their d13C values indicated less relianceupon C4 foods, in particular as a source of protein. Threeof these individuals also caused disagreement betweenthe hierarchical and k-means analyses, which we discussbelow.The Illinois River specimens, from just outside the
American Bottom and Cahokia regions proper, splitmainly between the high-C4 Clusters 2 (70% C4; mixedprotein) and 5 (70% C4) with a single individual fallinginto Cluster 4 (mostly C3). Despite their seeming ran-domness, these classifications are consistent witharchaeological evidence that some of these people incor-porated a smaller proportion of C4 foods into their dietand displayed more dietary heterogeneity than theirneighbors in the American Bottom (Hedman et al., 2002).On the other hand, the Illinois River population did notappear to differ from the American Bottom in terms oftrophic level, demonstrated by their average d15N of 8.96 0.23% and the centroid d15N values for Clusters 2 and5 (10.1% and 8.8%, respectively). We discuss the singleIllinois River individual that fell into Cluster 4 below.Cahokia Mound individuals split between Clusters 4
and 5, as expected, along the social status lines reportedin the original study (Ambrose et al., 2003). Low statusindividuals fell into Cluster 5, indicating a heavy reli-ance on maize as a dietary staple, but not as a source ofprotein. On the other hand, Cluster 4 incorporated thehigh status individuals, indicating that they obtainedthe bulk of their diet, including protein, from C3 sources,with a small overall maize component. Further, thesecluster assignments are consistent with a slightly highertrophic level among the high status subgroup, whosemean d15N value was significantly higher than the lowstatus group’s average (10.6 6 0.67% vs. 8.2 6 0.19%respectively; independent samples t-test, P \ 0.01).Interestingly, given the results from the nearly contem-poraneous American Bottom (within 125–225 years), thecluster assignments suggest that even low status indi-viduals from Cahokia consumed less C4 food, especiallyas protein, than populations from the surroundingregion. At the same time, however, low status Cahokianitrogen-isotope values indicate a trophic position at thelower end of the range for the entire region, while thehigh status mean falls near the top of that range (seeabove).
In the entire study sample, only seven individualsreceived conflicting cluster assignments for the five-groups analysis, the UPGMA hierarchical method plac-ing them in Cluster 2 while k-means relegated them toCluster 5. All seven came from the broader Cahokia/American Bottom/Illinois River regions, where the popu-lations appear to have had rather homogeneous diets (atleast relative to the overall sample in the present study),and where six of these seven individuals were statisticaloutliers within their respective populations (Cahokia120: Ambrose et al., 2003; American Bottom ESLSQ 25,Range 14, IC 114, Illinois River 66a, 153: Hedman et al.,2002; see Table A1 for individual data). It makes statisti-cal sense that different clustering methods might treatthese six outliers differently, especially given rather fineisotopic and dietary distinctions between Clusters 2 and5. The specific characteristics of these individuals, ratherthan general flaws in the clustering regime, probablyexplain the classificatory discrepancies, and may point tointraregional migration. For example, Cahokia 120appears to have eaten less C3 protein than other highstatus individuals at Mound 72, suggesting an origin inthe Illinois River or Corbin Mounds (American Bottom)areas (Ambrose et al., 2003). The converse may be trueof the three outliers from the American Bottom, all ofwhom appear to have eaten less C4 protein than theirneighbors. These findings may indicate an origin outsidethe region (Hedman et al., 2002), or possibly migrationfrom Cahokia to the American Bottom. The Illinois Riverdisagreements are more difficult to interpret due tosmall sample size and a high degree of variability at thissite (Hedman et al., 2002). Finally, it remains unclearwhat underlies disagreement over the seventh individ-ual, Illinois River 65 (Hedman et al., 2002), who fell intoCluster 2 per the hierarchical analysis, but Cluster 5 forthe k-means analysis. Archaeological details of the burialprovide no additional explanatory information (see Gold-stein, 1980), but given the overall sample size, this onedisagreement does not disqualify the clustering results.Three of the four misclassified individuals in the
leave-one-out test of the discriminant function analysisalso come from the American Bottom/Illinois Riverregion, and are similarly explained as being statisticaloutliers. Two of these individuals were already notedabove (ESLSQ 25, Illinois River 65) since they alsoreceived different classifications from the hierarchical vs.the k-means clustering methods. A third case (IC 116)was also an outlier for the American Bottom population,although the hierarchical and k-means results did notdisagree on this individual’s assignment. Again, the sta-tistical uniqueness of these individuals likely explainstheir misclassification by the discriminant functions. Thefourth individual misclassified in the discriminant func-tion analysis came from Tierra del Fuego (13), and is dis-cussed below.
Tierra del Fuego. No discrepancies between the hier-archical and k-means analyses occurred for any individu-als from Tierra del Fuego. The sample split mainlybetween Cluster 3 (50% C4 diet; marine protein) andCluster 1 (100% C3 diet), individuals in the former com-ing from southern and southeastern regions while thosein the latter came mainly from the northern part ofTierra del Fuego (except one from Navarino Island inthe south). This split agrees with the original study’ssuggestion that marine protein played an importantdietary role in the south, while C3 guanaco meat served
358 A.W. FROEHLE ET AL.
American Journal of Physical Anthropology
as the primary northern protein source (Yesner et al.,2003). Mean d15N values for the subgroups were alsoconsistent with this interpretation, being significantlyhigher in those assigned to Cluster 3 than those fallingin with Cluster 1 (17.5 6 0.47% vs. 11.5 6 0.54%respectively; independent samples t-test, P \ 0.01). Ourinterpretation of whole diet, however, differs from theprevious study’s, where D13Capatite-collagen spacing valueswere taken to indicate a small C4 component for thenorthern subsample. Compared with the experimentalanimal regression lines (Kellner and Schoeninger, 2007;Froehle et al., 2010) instead of tissue spacing, the north-ern subset falls at the 100% C3 diet end of the C3 proteinline. Therefore, it appears that people from northernTierra del Fuego also differed from southern populationsby eating a diet devoid of 13C-enriched foods, though weare unaware of any independent lines of evidence thatsupport this interpretation.One individual, Tierra del Fuego 13, came from the
south and was placed in Cluster 1 by the discriminantfunction analysis, in contrast to both clustering methodswhich assigned this individual to Cluster 4. The Cluster1 assignment would associate this individual with thenorthern Tierra del Fuegan subgroup, reliant entirelyupon C3 resources, while placement in Cluster 4 wouldindicate about 70% consumption of C3 foods. Tierra delFuego 13 falls midway between the centroids of Clusters1 and 4 for 13Capatite, but is enriched in d13Ccollagen andhas higher d15N than both cluster centroids. This posi-tion suggests a diet midway between Clusters 1 and 4 interms of C4 foods in overall diet, but also indicates theconsumption of higher trophic level and more 13C-enriched protein than in either Cluster 1 or 4. This com-bination is consistent with a largely C3 diet similar tothe northern Tierra del Fuego group, but with someincorporation of marine and perhaps C4 resources in thegeneral fashion of the southern regions (although notsufficient to fall into Cluster 3). Thus, Tierra del Fuego13 appears to have consumed a diet intermediate to thenorthern and southern patterns, which in its pairing ofmainly C3 resources with some marine foods, is uniquein the overall sample studied in the present meta-analy-sis. This individual’s uniqueness may underlie the dis-crepancy between the discriminant function analysis andthe clustering methods’ classifications.
San Nicolas Island. Finally, the entire subsample fromSan Nicolas Island fell into Cluster 3, the marine proteincluster. In fact, all three isotope values for the Cluster 3centroid match almost exactly the corresponding meansfor San Nicolas islanders as a group. There were no dis-
agreements between hierarchical, k-means, or discrimi-nant function analyses as to the classification of anyindividual from San Nicolas Island. This categorizationagrees with the emphasis on marine foods described inthe original study (Harrison and Katzenberg, 2003). Itdisagrees, however, in that it suggests a roughly 50% C4
contribution to diet, whereas the previous authors usedD13Capatite-collagen values to conclude that the San Nicolasislanders consumed no C4 foods. Adjusted for the indus-trial effect (Marino and McElroy, 1991), mean d13Capatite
and d13Ccollagen values for this sample (29.0% and211.7%, respectively) are very similar to experimentalvalues for rats consuming a controlled diet of 50:50C3:C4 nonprotein with tuna fish as the protein source(Jim et al., 2004: d13Capatite 5 28.6%; d13Ccollagen 5212.2%). Rats from the same experimental study, eatinga diet of 100% C3 nonprotein with tuna fish as the pro-tein source, have considerably less-enriched carbon-iso-tope values, especially for d13Capatite (213.4%). Together,our three-variable assessment and the experimental ratdata strongly suggest that the San Nicolas Island popu-lation indeed exploited both marine and C4 resources.The source of the C4 signal is unknown, but others havesuggested that mortars and pestles common to San Nico-las sites may have been used to process the seeds ofnative grasses (Meighan and Eberhart, 1953), some ofwhich use the C4 photosynthetic pathway (Thomas,1995). This hypothesis merits further exploration.
Experimental animal data
As an additional check of our results, we plotteddiscriminant function values for rats raised on experi-mental diets (N 5 7 diets; see Table 4) and looked forcompatibility with our model’s expectations. Despiteother experimental feeding studies of diet-tissue isotopefractionation, the data used here come from the onlysuch investigation to publish individual d13Ccollagen,d13Capatite and d15N values (Ambrose and Norr, 1993;Ambrose, 2000). In these experimental diets, the proteinand nonprotein components were within themselvesmonoisotopic, but in most cases the protein and nonpro-tein isotopic signatures diverged from one another. Forexample, the diet 6F (see Table 4) was 80% nonproteinand 20% protein by weight, with the nonprotein portioncoming entirely from C4 sources, and all protein comingfrom C3 foods (Ambrose and Norr, 1993). Below, this dietis thus referred to as being ‘‘80% C4 nonprotein and 20%C3 protein’’ by weight, and other diets are described inthe same manner.
TABLE 4. Experimental rat bone stable isotope values and discriminant function scoresa
a Carbon data from Ambrose and Norr (1993); nitrogen data from Ambrose (2000).b Diet composition from Ambrose and Norr (1993). Protein as percent of total diet by weight in parentheses.c Carbon data adjusted to reflect preindustrial atmosphere by adding 1.5% (Marino and McElroy, 1991).
For the most part, given the composition of theirexperimental diets, the rats fell as expected on ourdiscriminant function plot (Fig. 5). For example, the100% C3 diet 1A fell within the range of the 100% C3
Cluster 1. Diet 5E, which was 30% C4 nonprotein and
70% C3 protein by weight, fell accordingly into Cluster 4where the centroid indicates an overall 30% C4 diet with#65% of protein coming from C3 sources. In Cluster 5,diet 12/13G fell very near the centroid while diet 6F fellwithin 2 standard deviations of the centroid, indicatingan overall !70% C4 diet with protein coming from #65%C3 sources. This positioning matches well with the com-positions of these diets, both of which were 80% C4 non-protein by weight, with the remainder consistingentirely of C3 protein. Interestingly, despite similarplacement along the Function 1/’’Carbon’’ axis, diet 6Ffell lower on the Function 2/’’Nitrogen’’ axis than did 12/13G. The difference corresponds to the lower d15N valuesobserved in the rats on diet 6F vs. 12/13G, and fits giventhat 6F contained protein from soy and wheat, while 12/13G’s protein source was milk casein (Ambrose andNorr, 1993). This finding supports the idea that position-ing along the Function 2/’’Nitrogen’’ axis provides infor-mation about trophic level when other aspects of diet arethe same.Positioning on the discriminant function plot of
diets 2B and 3C was somewhat less straightforwardthan for the other diets. Diet 2B fell outside of theboundaries of all Clusters, which may be explained bythe fact that its specific diet (95% C3 nonprotein and5% C4 protein by weight) was not represented in ourarchaeological sample. We might have expected 2B tofall closer to Cluster 1, however, considering that thevast majority of the diet carried a C3 isotopic signa-ture. Diet 3C consisted of 95% C4 nonprotein and 5%C3 protein, and fell just within the boundaries ofCluster 2. This was to be expected in a general senseon the basis of the high C4 content of diet 3C, butwith its C3 protein content, we might have predictedit to fall further to the left along the Function 1/’’Carbon’’ axis, and nearer to Cluster 5.
Fig. 5. Discriminant function values calculated from pub-lished bone isotope values for rats fed experimental diets(Ambrose and Norr, 1993; Ambrose, 2000), and plotted againstarchaeological human clusters from this study. Rat carbon iso-tope values were adjusted to match the preindustrial atmos-phere (and thus the archaeological data) by adding 1.5%(Marino and McElroy, 1991). Information on the composition ofthe experimental diets is in Table 4. Cluster diets: (1) 100% C3
a As reported in Ambrose et al. (1997), reflecting preindustrial atmospheric carbon levels.b Calculated using the present study’s discriminant functions.c Plant/Diet values adjusted to preindustrial atmospheric carbon levels by adding 1.5% to reported modern values (Marino andMcElroy, 1991).d Values assume enrichment of d13C in apatite by 10.2% over diet (Froehle et al., 2010), and reflect expected values where the foodin question constitutes 100% of diet.e Values based on C3 protein linear equation for d13Ccollagen vs. d13Cdiet from experimental data (Froehle et al., 2010), assuming thefood in question constitutes 100% of diet.
360 A.W. FROEHLE ET AL.
American Journal of Physical Anthropology
Low protein content (5% of diet by weight) was com-mon to both 2B and 3C, and may explain their some-what abnormal positioning relative to the other rat dietsand this study’s clusters. Ambrose (2000) reports thatrats from litters eating diets 2B and 3C were protein-limited, since they achieved adult weights much lowerthan those on normal-to-high-protein diets. It may there-fore be the case that the rats on diets 2B and 3C synthe-sized amino acids endogenously from nonprotein dietaryprecursors in order to build bone collagen, rather thanincorporating most or all of those amino acids intactfrom dietary protein (see Schwarcz, 2000). In both cases,the low protein rats fell approximately where expectedalong the Function 2/’’Nitrogen’’ axis, but were shifted!4 to 6 units to the right of the centroids for theirexpected clusters along the Function 1/’’Carbon’’ axis.This finding makes sense, in that (barring starvation)tissue nitrogen will be derived largely from dietary pro-tein, no matter its percentage contribution to diet. Onthe other hand, collagen carbon could be skewed towardnonprotein dietary components when protein intake isvery low, which may explain why d13Ccollagen values for
rats on diets 2B and 3C were very similar to oneanother, and intermediate to those of rats consumingeither C3 or C4 protein in sufficient amounts (see Table4). A similar pattern of divergence from population-basedexpectations in human individuals may indicate proteindeficiencies, and is worth exploring further. Comparingskeletal remains with evidence for protein malnutritionto apparently healthy individuals within the same popu-lation, where diet is otherwise known to be homogene-ous, could test the validity of this particular applicationof the model.
Example application of the model: addressingdietary ambiguity on Saipan
To demonstrate the use of the discriminant functionmodel, we applied it to an unexplained aspect of diet inan archaeological population from Saipan (Marianas Ar-chipelago, western Pacific, 1250–1350 CE). Ambrose etal. (1997) originally investigated the diet of these people,reconstructing the isotopic composition of the ancientfoodweb by analyzing modern foods matched to archaeo-logical data (Table 5). Their analysis revealed that peo-ple on Saipan consumed less marine protein and moreprotein from C3 sources compared with other nearbyislands populations. This finding, along with very high,positive D13Capatite-collagen values (mean 5 8.8 6 0.64%)led Ambrose et al. (1997) to conclude that the Saipanpopulation ate a relatively high proportion of 13C-enriched foods, despite a mainly C3 local ecosystem. Twocandidates for this enriched signal were sugarcane andseaweed, both of which are consumed in the regiontoday, but neither of which appears in the relevantarchaeological record. While the D13Capatite-collagenvaluespointed to the presence of a 13C-enriched dietary compo-nent, they could not determine its specific source. Thus,it is unclear whether sugarcane, seaweed, or a mixtureof the two accounts for 13C-enrichment in the bones ofSaipan islanders.To apply the discriminant function model to the Sai-
pan data, we estimated the proportions of C3 and 13C-enriched resources each individual (excluding Nansay4, who postdates the main population; and Nansay 7,who was not an adult) consumed, which we accom-plished by examining their placement along the axis ofthe experimental animal carbon-isotope plots (Fig. 6,see Froehle et al., 2010). Our results confirm that, aspreviously concluded (Ambrose et al., 1997), the Sai-pan islanders ingested a 65–70% C3 overall diet (indi-vidual ratios are in Table 6), with #65% of proteincoming from terrestrial C3 sources and the remaindercoming from lagoon and reef species. We used thesepercentages and the food web data to generate hypo-thetical d13Cdiet values that included either sugarcaneor seaweed as the 13C-enriched component, making up30–35% of total diet. We estimated hypothetical 13Cdiet
values from the individual diet composition ratios,using the Saipan C3-end member (d13CC3) and eithersugarcane or seaweed (d13Csugarcane and d13Cseaweed,respectively), as follows:
Fig. 6. Collagen and apatite carbon stable isotope values forSaipan islanders from Ambrose et al. (1997) plotted againstcompiled experimental animal data (see Froehle et al., 2010).Long-dashed lines represent the 95% prediction interval of themostly-C3-protein regression, while the short-dashed linesdefine the 95% prediction interval of the C4/marine-proteinregression. Human data sources are in Table A1. The experi-mental data from which the regression lines derive have beenadjusted to reflect pre-industrial atmospheric carbon levels byadding 1.5% (Marino and McElroy, 1991). We used the positionof the Saipan data relative to the experimental animal regres-sion lines to determine protein sources as well as percent C3
diet. The ‘‘C4/marine protein line’’ is derived from animals con-suming either 100% C4 protein or 100% marine protein. The ‘‘C3
protein line’’ is derived from animals consuming #65% C3 pro-tein (13 of 25 individual animals in this group ate 5-35% C4 ma-rine protein; see Froehle et al., 2010). On the basis of this com-parison, Saipan islanders appear to have consumed mostly C3
protein, up to 35% marine protein, and on average had a dietconsisting of !65 to 70% C3 foods. This is consistent with theassessment of Ambrose et al. (1997), and falls closest to thisstudy’s Cluster 4, the centroid for which is plotted here alongwith error bars delimiting two sample standard deviations fromthe mean. Cluster diets: (1) 100% C3 diet/protein; (2) 30:70C3:C4 diet, >50% C4 protein; (3) 50:50 C3:C4 diet, marine pro-tein; (4) 70:30 C3:C4 diet, #65% C3 protein; (5) 30:70 C3:C4 diet,#65% C3 protein.
We then modeled expected human bone isotope valuesreflective of each hypothetical diet (Table 6), assumingan enrichment of 10.2% in apatite over d13Cdiet (seeFroehle et al., 2010) and using the d13Ccollagen /d13Cdiet
equation from Froehle et al. (2010: pooled C3 proteinequation, Table 2, p. 2664) to account for enrichment ofd13C in bone collagen. We did not adjust d15N values fordifferential contributions from seaweed vs. sugarcanesince both foods are very low in protein (Ambrose et al.,1997) and thus unlikely to differentially affect tissuenitrogen-isotope ratios.Individual hypothetical bone carbon-isotope values and
measured nitrogen-isotope values were used to derivecorresponding discriminant function scores for each hy-pothetical diet (Table 6). Euclidian distances were thencalculated between each individual’s scores for actualbone isotope measurements and their respective hypo-thetical diet-specific scores for the corresponding sea-weed or sugarcane diets. Euclidian distances of the bonedata from their respective hypothetical diet points pro-vided information on the proportions of sugarcane andseaweed responsible for the 13C-enriched isotopic signalon Saipan.On average, actual bone values fell significantly closer
(independent samples t-test, two-tailed P \ 0.01) to sug-arcane (mean Euclidian distance 5 0.60) than to sea-weed (mean Euclidian distance 5 1.22). As a population,the Saipan islanders’ actual discriminant function scoresfell almost entirely within the range expected for a diet
TABLE
6.Exp
ectedstable
isotop
eanddiscrim
inantfunctionva
lues
forSaipanhyp
otheticaldiets
C3:C
4dieta
Sugarcaneb
Sea
weedc
d13Cdiet%
(PDB)
d13Capatite%
(PDB)
d13Ccollagen%
(PDB)
d15N
%(A
IR)d
F1
F2
ED
ed1
3Cdiet%
(PDB)
d13Capatite%
(PDB)
d13Ccollagen%
(PDB)
d15N
%(A
IR)d
F1
F2
ED
e
MacH
omes
273:27
221.2
211
.0218.8
8.4
26.00
21.67
0.84
222.4
212.2
219.4
8.4
26.85
21.28
1.77
MacH
omes
552:48
217.9
27.7
217.0
8.4
23.67
22.73
0.94
220.0
29.8
218.2
8.4
25.17
22.05
1.02
Nansa
y6
68:32
220.5
210.3
218.4
7.9
25.64
22.20
0.37
221.9
211
.7219.2
7.9
26.63
21.75
1.08
Duty
FreeSite1
68:32
220.4
210.2
218.4
7.1
25.72
22.74
0.25
221.8
211
.6219.1
7.1
26.73
22.27
1.25
Duty
FreeSite2
58:42
218.9
28.7
217.6
6.1
24.92
23.82
0.91
220.8
210.6
218.6
6.1
26.21
23.23
0.95
Duty
FreeSite3
63:37
219.7
29.5
218.0
7.5
25.17
22.70
0.44
221.3
211
.1218.9
7.5
26.31
22.18
1.10
Duty
FreeSite4
71:29
220.9
210.7
218.7
9.2
25.64
21.26
0.42
222.2
212.0
219.3
9.2
26.54
20.85
1.41
Mea
n:
65:35
219.9
29.7
218.1
7.8
25.25
22.45
0.60f
221.5
211
.3219.0
7.8
26.35
21.94
1.22f
aPercentdietfrom
C3andC4sources
asderived
from
experim
entalanim
alregressionlines
from
Froeh
leet
al.(2010).See
textformethod
s.bCalculatedfrom
%C3:%
C4dietusingC3en
d-m
ember
andsu
garcaned1
3C
values
from
Ambrose
etal.(1997).See
textformethod
s.Discrim
inantfunctionvalues
(F1andF2)are
calculatedusingthepresentstudy’sdiscrim
inantfunctionsandthehypotheticalbon
estable
isotop
evalues
forthesu
garcanediet.
cCalculatedfrom
%C3:%
C4dietusingC3en
d-m
ember
andseawee
dd1
3C
values
from
Ambrose
etal.(1997).See
textformethod
s.Discrim
inantfunctionvalues
(F1andF2)are
cal-
culatedusingthepresentstudy’sdiscrim
inantfunctionsandthehypotheticalbon
estable
isotop
evalues
fortheseawee
ddiet.
dd1
5N
asmea
suredin
Ambrose
etal.(1997).Sugarcaneandseawee
dare
verylow
inprotein
andsh
ould
not
affectbon
ecollagen
d15N
values.
eEuclidian(geo
metric)
distance
betwee
ndiscrinmantfunctionvalues
ofmea
suredbon
estable
isotop
es(see
Table
5)andhypotheticalC3/sugarcaneor
C3/sea
weeddiets.
fEuclidiandistance
mea
nsforsu
garcaneandseawee
dhypotheticaldiets
are
siginficantlydifferentfrom
oneanother,indep
enden
tsa
mplest-test,tw
o-tailed
P\0.01.
Fig. 7. Plot of mean discriminant function values for actualbone vs. the hypothetical sugarcane and seaweed diets. Errorbars indicate the 95% confidence intervals of the means for eachfunction. The mean Euclidian distance between actual bone andsugarcane of 0.60 was significantly smaller than the distance of1.22 between bone and seaweed (independent samples t-test,two-tailed P < 0.01). One-way ANOVA revealed a significant dif-ference between group mean ‘‘Carbon’’/F1 function values (P <0.01). Post-hoc analysis (Tukey HSD) showed that for ‘‘Carbon’’/F1, seaweed differed significantly from bone (P 5 0.03) and sug-arcane (P < 0.01), but the latter two did not differ from oneanother significantly (P 5 0.86). The three groups of functionscores did not differ for ‘‘Nitrogen’’/F2 (one-way ANOVA; P 50.25), which follows from the manner in which we modeled thehypothetical diets (see text for a detailed description).
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consisting of roughly two-thirds C3 foods and one-thirdsugarcane, and fell completely outside the range of atwo-thirds C3/one-third seaweed diet (Fig. 7). MeanFunction 1/‘‘Carbon’’discriminant function scores did notdiffer between actual bone and sugarcane, whereasboth differed significantly from the hypothetical sea-weed diet (one-way ANOVA, P \ 0.01; post hoc TukeyHSD: seaweed vs. bone, P 5 0.03; seaweed vs. sugar-cane, P \ 0.01; sugarcane vs. bone, P 5 0.86). In con-trast, none of the diets’ Function 2/‘‘Nitrogen’’ meansdiffered (one-way ANOVA, P 5 0.25), which makessense given that d15N values exert the greatest influ-ence on Function 2/‘‘Nitrogen’’ values, and we did notmodel dietary differences in d15N values due to sugar-cane or seaweed.If our assumptions are valid, then these results sug-
gest that the Saipan population obtained the bulk ofits non-C3 dietary component from sugarcane, and notfrom seaweed. Although no archaeological evidence ofsugarcane harvesting exists, the relatively high preva-lence of dental caries in some Saipan populations vs.other nearby islands (various sources, discussed inAmbrose et al., 1997:359) appears to corroborate ourfindings. There is variation within the group, however,with two individuals (MacHomes 5 and Duty Free 2)falling midway between their hypothetical sugarcaneand seaweed diet points. Some individuals may havethus consumed seaweed in addition to sugarcane, butoverall our model points to sugarcane as the primaryproducer of the 13C-enriched signal in the bones ofthese Saipan islanders.
CONCLUSIONS
Stable isotope data reflect biological processes sub-ject to numerous influences that result in widely vary-ing outcomes. As such, biometric statistical techniques,which provide probabilistic statements about the rela-tionships between animal tissues and the macronu-trients in their diets (e.g., Sokal and Rohlf, 1997; Phil-lips and Koch, 2002; Bocherens, 2009), offer the bestmethod for understanding, predicting, and interpretingthis variation. Recent work applying these techniquesto experimental data (e.g., linear regression analysis:Kellner and Schoeninger, 2007; Froehle et al., 2010) isexpanded here by applying multivariate cluster analy-sis and discriminant function analysis to study threeisotope variables simultaneously in their relationshipsto diet.This analysis clarified two aspects of diet left ambig-
uous by previous d13Ccollagen vs. d13Capatite regressionmodels (Kellner and Schoeninger, 2007; Froehle et al.,2010). As expected, the inclusion of d15N data discrimi-nated between marine and C4 protein consumerswhere carbon-isotope values alone could not. Therefore,in the absence of strong supporting archaeologicaldata, it is important to measure both d13C and d15Nfrom collagen when reconstructing diet in populationsfrom regions where both marine and C4 protein areavailable. With regard to determining protein sourcesfrom positioning relative to the C3- and C4/marine-pro-tein regression lines in the carbon model, the presentanalysis suggests, at least at the population level, thatplacement between the lines does indeed indicatemixed protein consumption. This is evident from theplacement of Cluster 2 (see Fig. 1b), which included
the Ontario Agricultural and American Bottom popula-tions that clearly obtained both C3 and C4 protein, butis not necessarily true for individuals given consider-able scatter around population means even in peoplewith no access to mixed protein, such as Ontario prea-griculturalists.The distinction between individuals and populations
is an important one for the application of the discrimi-nant function model. While the position of any individ-ual relative to the clusters would provide at least someindication of diet, some overlap between the ranges ofdiet clusters and their members could weaken any con-clusions about individuals. This approach is better-applied to populations, although samples need not belarge—for example, the model was quite capable ofmaking clear dietary distinctions between the northern(N 5 5) and southern (N 5 6) samples from Tierra delFuego, or between high (N 5 3) and low (N 5 5) sta-tus groups from Cahokia.In large populations, this model could reveal nuances
of dietary differentiation between sexes, age classes, andsocial status groups, as well as between regions and overtime within societies. Differences within societies, how-ever, may be graded (rather than discreet) or too fine-grained for the present model to detect, given the widerange of diets included in this sample. In those cases, itwould be more productive to apply the same clusteranalysis and discriminant function techniques withinthose populations to look for patterns of distinction.Finally, we should emphasize that the type of fine-grained, analysis we conducted on the Saipan datarequires thorough study of the food web within which apopulation likely lived (see also Crowley, in press), with-out which reliable hypothetical diets could not be gener-ated. Contextual information is critical to drawing thestrongest conclusions about diet from the discriminantfunction model, although in the absence of any other in-formation, the model may still have utility—placementof an individual or population relative to this study’sclusters could be used to generate hypotheses, and todirect other, nonisotopic avenues of research.There is considerable room to expand upon and
refine this model. The outcomes of cluster analysisdepend heavily on the specific sample used, and whilethe archaeological populations we analyzed here covera wide range of diets, the addition of data from peopleeating other diets would likely alter slightly, butstrengthen the results. Also, the present model wasderived from data on well-preserved bone from healthyadults, potentially limiting the model’s applicabilityto other samples, such as children or individualswith clear evidence of malnutrition. Finally, furthercontrolled diet experiments measuring d13Capatite,d13Ccollagen and d15N, would also provide a good test ofthis study’s results, and would allow for the develop-ment of a similar model under circumstances of knownwhole diet and protein d13C and d15N. Continued workin this direction should produce even more effectivetools for testing competing hypotheses about prehis-toric diets.
ACKNOWLEDGMENTS
The authors thank Alyssa Crittenden and AndrewSomerville for helpful comments on early drafts of thisarticle. They also thank two anonymous reviewers fortheir thoughtful comments and suggestions.
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