fernandes archaeometry

A S IMPLE (R ) MODEL TO PREDICT THE SOURCE OFDIETARY CARBON IN INDIV IDUAL CONSUMERS*

R. FERNANDES

Institute for Ecosystem Research, University of Kiel, Olshausenstrasse 75, 24118 Kiel, Germany and Leibniz Laboratory forRadiometric Dating and Isotope Research, University of Kiel, Max-Eyth-Str. 11-13, 24118 Kiel, Germany and McDonald

Institute for Archaeological Research, University of Cambridge, Downing Street, Cambridge, CB2 3ER, UK

Quantitative individual human diet reconstruction using isotopic data and a Bayesianapproach typically requires the inclusion of several model parameters, such as individual iso-topic data, isotopic and macronutrient composition of food groups, diet-to-tissue isotopic off-sets and dietary routing. In an archaeological context, sparse data may hamper awidespread application of such models. However, simpler models may be proposed to addressspecic archaeological questions. As a consequence of the intake of marine foods, individualsfrom the rst century AD Roman site of Herculaneum showed well-dened bone collagen radio-carbon age offsets from the expected terrestrial value. Taking as reference these radiocarbonoffsets and using as model input stable isotope data (13C and 15N), the performance of twoBayesian mixing model instances (routed and concentration-dependent model versus non-routed and concentration-independent) was compared to predict the carbon contribution ofmarine foods to bone collagen. Predictions generated by both models were in good agreementwith observed values. The model with higher complexity showed only a slightly better perfor-mance in terms of accuracy and precision. This demonstrates that under similar circumstances,a simple Bayesian approach can be applied to quantify the carbon contribution of marine foodsto human bone collagen.

KEYWORDS: DIET RECONSTRUCTION, BAYESIAN MIXING MODELS, FRUITS, STABLEISOTOPES, BONE COLLAGEN, ROMAN DIET

INTRODUCTION

Human diet reconstruction studies relying on isotopic data have provided useful insights into thedietary habits of past populations (DeNiro and Epstein 1976; van der Merwe and Vogel 1978;Tauber 1981; van der Merwe and Vogel 1983; Schoeninger et al. 1983; Richards et al. 2003;Lee-Thorp 2008). Different mathematical and statistical approaches, including linear andstochastic methods, have been proposed to analyse isotopic data in diet reconstruction studies(Phillips 2001; Phillips and Gregg 2003; Moore and Semmens 2008). A recent methodologicaldevelopment has been the introduction of Bayesian mixing models (Fernandes et al. 2012b;Ugan and Coltrain 2012; Coltrain and Janetski 2013; Arcini et al. 2014). These models areparticularly attractive since they are able to handle the different sources of uncertainty associatedwith the diet reconstruction exercise. These uncertainties include the uncertainty in isotopicsignals of potential food groups, diet-to-tissue isotopic offsets and dietary routing.Diet reconstruction for single consumers also requires that uncertainties in isotopic values

associated with each consumer are taken into account. This capability has been introduced bythe Bayesian mixing model FRUITS (Food Reconstruction Using Isotopic Transferred Signals)

*Received 5 September 2014; accepted 2 February 2015Corresponding author: email [email protected]; [email protected]

Archaeometry , (2015) doi: 10.1111/arcm.12193

2015 University of Oxford

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(Fernandes et al. 2014c). FRUITS is a generic model and specic model instances are dened byselecting which of the different possible parameters are to be included. For example, a modelinstance may include the capability of handling dietary routing. Dietary routing occurs whendifferent food fractions (e.g., macronutrients) contribute in varying proportions towards a certainconsumer isotopic signal. Methodologies to reconstruct the diets of single individuals, includingmodels involving dietary routing, have been previously demonstrated (Fernandes et al. 2014c).Model instances that consider all possible dietary parameters can become complex and data-demanding, and in archaeological contexts data are often sparse and insufcient. Simpler models,with fewer parameters, can be dened in accordance with the relevant archaeological question.For example, the question of dietary carbon source when restricted to terrestrial and marine foodgroups may permit the denition of a simpler model. This simpler model could be used toprovide a straightforward correction to human collagen radiocarbon dates that exhibit a marinereservoir effect due to the dietary intake of marine foods.The goal of the research presented here was to compare the level of performance, in terms of

accuracy and precision, of two instances of dietary models having high and low complexity. Totest the performance of each model, data from Craig et al. (2013) was used. This data set containshigh-quality radiocarbon and isotopic measurements analysed on rst century AD humans fromthe Roman site of Herculaneum. Radiocarbon results obtained from human bone collagen areused as a reference to test the performance of the two proposed model instances. Differencesbetween the radiocarbon dates of human bone collagen and the expected terrestrial radiocarbonage provide an accurate quantication of the carbon contribution of marine foods to bone collagen.

MATERIALS AND METHODS

Material: data from Craig et al. (2009) and Craig et al. (2013)

This study relies on data from Craig et al. (2009) and Craig et al. (2013). The dietary habits ofnine adult human individuals from the Roman site of Herculaneum have previously been inves-tigated by Craig et al. (2013). These individuals were victims of the Eruption of Mount Vesuviusin AD 79. Extracted bone collagen from human bone ribs underwent isotopic analysis (13C and15N). Standard quality criteria of bone collagen preservation indicate a good preservation status(for further details, see Craig et al. 2013). Extracted human bone collagen was also AMSradiocarbon-dated in duplicate, showing an excellent reproducibility. Radiocarbon dates ofhuman bone collagen were compared to the radiocarbon bone date of collagen extracted froma contemporary domestic sheep (Ovis aries). Human radiocarbon dates were anomalously olderby varying amounts than the reference sheep date (197525yr BP). This constitutes an exampleof a human dietary radiocarbon reservoir effect (RRE) due to the consumption of marine foodsthat have a 14C concentration lower than terrestrial foods (Lanting and van der Plicht 1998; Cooket al. 2001; Olsen et al. 2010; Fernandes et al. 2014a). The marine carbon contribution towardshuman bone collagen can be obtained by simply dividing the values of the observed humandietary RREs by the local radiocarbon reservoir effect. The local reservoir effect at the Bay ofNaples, determined from radiocarbon measurements of bivalve shells collected in the late 19thcentury, is 46559 14C yr (Siani et al. 2000). This value is very similar to the reference reservoireffect value for the entire Mediterranean, of 45885 14C yr (Reimer and McCormac 2002).Table 1 lists human isotopic and radiocarbon results and the observed, without error propagation,dietary marine carbon contribution towards bone collagen determined by taking as reference alocal radiocarbon reservoir effect of 465 14C yr.

2 R. Fernandes

2015 University of Oxford, Archaeometry , (2015)

Well-preserved food remains recovered from the archaeological record provide a good indica-tion of the distribution of consumed food resources. This material should preferentially be used toprovide an isotopic reference baseline in human dietary studies. For the case study presentedhere, stable isotope data were compiled from the studies by Craig et al. (2009) and Craig et al.(2013). In these studies, isotopic measurements are reported for collagen extracted from bonesof terrestrial herbivores (n=18) and sh bones (n=9) recovered from the sites of Pompeii,Herculaneum and Velia. These rst century AD Roman sites are all located near the coast, facingthe Tyrrhenian Sea. Mean isotopic values of herbivore and sh collagen are listed in Table 2. Thereported uncertainty corresponds to the standard error of the mean (the standard deviation dividedby the square root of the number of measurements). This uncertainty was taken as referencegiven that human rib bones integrate dietary signals during an extended time period (>1 yr),effectively averaging food isotopic signals that have symmetrical distributions (Cox and Sealy1997). Isotopic values of herbivore and marine sh protein and lipids were estimated, from bonecollagen values, relying on previously reported offsets between macronutrient and collagen iso-topic values (Vogel 1978; Hare et al. 1991; Sholto-Douglas et al. 1991; Tieszen and Fagre 1993;Pinnegar and Polunin 1999; Fischer et al. 2007; Post et al. 2007; Logan et al. 2008; Warinnerand Tuross 2010; Fernandes et al. 2014b). The chosen offsets represent rough consensus values(herbivores, 13Cproteincollagen =2, 13Clipidscollagen =8, 15Nproteincollagen =+2;sh, 13Cproteincollagen =1, 13Clipidscollagen =7, 15Nproteincollagen =+2) and aconservative uncertainty of 1 was taken as reference for estimated protein and lipid values.This uncertainty also accounts for potential modications introduced to raw foods duringcooking (Fernandes et al. 2014b). The macronutrient composition of animal and sh foods can

Table 1 Isotopic and radiocarbon values of collagen from human rib collagen of Herculaneum victims from the eruption ofMount Vesuvius in AD 79 (data from Craig et al. 2013). Marine RRE values: the offset between the expected terrestrial age(1975 25 yr BP) and the radiocarbon age for the individual. See the text for a full description of the calculation of%marineCfrom human dietary RRE. For 13Cmodelled and

15Nmodelled, the values are rounded from the isotopic analysis, with 0.5 asper the text

Samplecode

Radiocarbonage (yr BP)

RRE(14C yr)

% marine C 13Cmeasured()

15Nmeasured()

13Cmodelled()

15Nmodelled()

F12I28 1982 18 7 2 19.89 0.05 8.89 0.04 19.9 0.5 8.9 0.5F10II11 1988 19 13 3 19.7 0.03 9.31 0.49 19.7 0.5 9.3 0.5F10I28 1993 18 18 4 19.65 0.03 9.16 0.17 19.7 0.5 9.2 0.5F12I3 2007 19 32 7 19.67 0.19 10.09 0.31 19.7 0.5 10.1 0.5F10I16 2016 18 41 9 19.79 0.09 10.09 0.02 19.8 0.5 10.1 0.5F9I13 2048 18 73 16 19.12 0.11 10.76 0.22 19.1 0.5 10.8 0.5F12I23 2049 19 74 16 18.57 0.1 10.93 0.12 18.6 0.5 10.9 0.5F7 10 2058 18 83 18 18.75 0.16 10.63 0.09 18.8 0.5 10.6 0.5F9I9 2061 19 86 18 18.8 0.12 11.45 0.18 18.8 0.5 11.5 0.5

Table 2 The averages of the measured herbivore and sh-bone collagen isotopic values (data from Craig et al. 2009,2013), the estimated protein and lipids isotopic values, and the macronutrient composition, expressed as dry weight

carbon content

Food 13Ccollagen()

15Ncollagen()

13Cprotein()

15Nprotein()

13Clipids()

Protein (% C) Lipids (% C)

Herbivores 21.3 0.2 4.1 0.4 23.3 1 6.1 1 29.3 1 30 2.5 70 2.5Fish 14.2 0.3 8.3 0.7 15.2 1 10.3 1 21.2 1 65 5 35 5

A simple(r) model to predict the source of dietary carbon 3


vary considerably according to species, body part and season. Recorded patterns of humandietary intakes provide a simple method of obtaining average macronutrient compositions offood groups (FAOSTAT 2009). These values are typically reported as caloric contributions;however, a similar value can be taken for dry weight carbon content, given that calorie to carbonratios are similar for the different macronutrients (Morrison et al. 2000; Otten et al. 2006). Table 2lists measured isotopic values for sh and herbivore bone collagen and estimated protein andlipid isotopic values together with macronutrient compositions expressed as dry weight carboncontent. For the latter, conservative uncertainties were taken as reference (see Table 2).

Modelling parameters

An efcient diet reconstruction exercise should preferentially handle all potential sources ofmodel uncertainty (diet-to-tissue isotopic offset, dietary routing, and isotopic and macronutrientcompositions of food groups) separately. In addition, diet reconstruction of individual consumersmust take into account the uncertainty in consumer isotopic values.

Consumer isotopic values

For the case study presented here, which relies on isotopic measurements of human bone material,an uncertainty (0.5) larger than the reported instrumental uncertainty was taken as reference(Table 1). The foregoing is based on the observed isotopic variability within and between bonesof the same individual (Schoeninger et al. 1983; Balasse et al. 1999; Waters-Rist et al. 2011).Modelled consumer isotopic values, with an uncertainty set at 0.5, are listed in Table 1.

Diet-to-tissue isotopic offsets and dietary routing

Ideally, diet-to-tissue isotopic offsets would be determined from human feeding experiments.However, for several reasons it is difcult to implement controlled human feeding experiments.Such experiments would have to rely on foods with constant and well-dened isotopic signals, becarried out for a period sufciently long to achieve isotopic equilibrium with the diets, andprovide direct access to the tissue of interest (e.g., bone collagen). The alternatives have beento perform feeding experiments on mammalian omnivores, or to perform short-term experimentson humans and measure isotopic signals in easily accessible material with a high turnover rate(e.g., blood cells, hair). This latter option implies that the isotopic offsets between measured tissue(e.g., hair keratin) and the tissue of interest (e.g., bone collagen) have been well characterized.Feeding experiments and anthropological studies have shown that the 15N offset between

dietary protein and human hair keratin is 4.5 (Minagawa et al. 1986; Schoeller et al. 1986;Minagawa 1992; Yoshinaga et al. 1996; Hedges et al. 2009; Huelsemann et al. 2009). Further-more, an offset value of about 1 between dietary protein and hair keratin needs to be added toobtain the 15N offset between dietary protein and human bone collagen (OConnell and Hedges1999; OConnell et al. 2001; Richards 2001). Thus the reference value taken here for the 15Noffset between dietary protein and human bone collagen is 5.5 0.5 and this relationship isexpressed by the following equation:

15Ncollagen 5:5 15Ndietaryprotein (1)This reference value is in good agreement with the 6 value estimated from isotopic values

measured in red blood cells during a human controlled feeding experiment (OConnell et al. 2012).

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A statistical study (Fernandes et al. 2012a) analysed the isotopic data collected by Froehleet al. (2010), which consisted of measurements done on omnivorous mammals during controlledfeeding experiments (Ambrose and Norr 1993; Tieszen and Fagre 1993; Howland et al. 2003;Jim et al. 2004; Warinner and Tuross 2009). Fernandes et al. (2012a) found that regressionanalysis provided an excellent correlation (R2 = 0.92, p< 0.001) between the 13C signals ofbone collagen and dietary protein and energy (the term energy is used here to signify combinedcarbohydrate and lipid macronutrients). This correlation is expressed by

13Ccollagen 4:8 0:74 13Cdietaryprotein 0:26 13Cdietaryenergy (2)and shows that a signicant contribution (26%) towards the collagen carbon signal is made fromenergy macronutrients. The collagen carbon signal is probably derived from dietary glucose thatacts as a precursor for the glycolytic amino acids (glycine, serine and alanine), which accountfor 28% of collagen carbon.The uncertainty associated with the protein contribution (0.74) given in equation (1) is 0.04

and the uncertainty associated with the isotopic offset (4.8) is 0.2. However, given well-known body size effects in 13C offsets between bone collagen and dietary protein (Passeyet al. 2005), a more conservative uncertainty of 0.5 was taken as reference for the isotopicoffset.Regression analysis of the same data provided by Fernandes et al. (2012a) relying on dietary

protein as the only explanatory variable shows a lower performance (R2 = 0.74, p< 0.001) whencompared with the model that includes both protein and energy as explanatory variables. Assuminga xed slope of value 1, the relationship between 13Ccollagen and 13Cprotein is represented by

13Ccollagen 5:0 13Cdietaryprotein (3)The residual standard error associated with the carbon isotopic offset (5.0) given in equation

(3) is 2.3 and thus larger than the 0.5 error reported for equation (1). This shows that there isa loss of model performance when the contribution of energy macronutrients is not taken intoaccount. However, the simpler relationship offered by equation (3), compared with equation(2), can be of use when it becomes difcult to estimate the isotopic signals of the energy macro-nutrients. This is particularly relevant when the archaeological question being consideredconcerns only the source of dietary protein.

Isotopic and macronutrient composition of food groups

Two food groups were dened here: marine and terrestrial. The reference macronutrient compo-sition and isotopic values (13Cprotein, 15Nprotein, 13Clipids) of the marine food group correspondto the values estimated for sh protein and lipids as listed in Table 2. Similarly, the terrestrialfood group macronutrient composition and isotopic values are those estimated for herbivoreprotein and lipids. A potentially missing modelling parameter is the contribution of plant foods.The validity of this approach is discussed later.

Model options

The generic model FRUITS (version 2 beta) provides multiple model options that dene specicmodel instances (Fernandes et al. 2014b). A model instance can be dened as routed ornon-routed and as concentration-dependent or concentration-independent. While equation (2)



requires a routed and concentration-dependent model, equation (3) requires a non-routed modeland can be either concentration-dependent or concentration-independent. A concentration-independent model does not consider the macronutrient composition and thus only providesestimates on xed protein contributions among different food groups. A concentration-dependentmodel allows for estimates of food intake; this is relevant since different food groups can havesignicantly different macronutrient compositions (Table 2).

MODELLING AND DISCUSSION

Dietary scenarios

Two different models, dened as dietary scenarios 1 and 2, were investigated. Dietary scenario 1corresponds to a non-routed and concentration-independent model. In this scenario, only the pro-tein contribution of the food groups was considered and the protein-to-collagen carbon isotopicoffset is as dened by equation (3) together with an associated uncertainty (2.3). Dietaryscenario 2 is a routed and concentration-dependent model. This model takes into account thedietary contributions of protein and energy macronutrients as expressed by equation (2) (fordescriptions of the model uncertainties, see the section on Diet-to-tissue isotopic offsets anddietary routing). In both dietary scenarios, the same protein-to-collagen nitrogen isotopic offsetwas used as expressed by equation (1) together with an associated uncertainty (0.5).

Model output

FRUITS (version 2.0 beta) generates different types of estimates expressed both graphically andnumerically. Estimates generated by FRUITS represent: (1) the dietary contributions of thedifferent food groups; (2) the dietary contributions of the different food fractions (in this case,macronutrients); and (3) the signal contribution towards a specic dietary proxy of each foodgroup (in this case, marine versus terrestrial). The interpretation of these outputs will vary accordingto the model denition and not all of these estimates are considered equally here. However, in thefollowing a brief description of each estimate is given so that adequate interpretations can be madein future applications.Figure 1 represents the probability distributions generated by FRUITS of the dietary carbon

contributions towards the diet of individual F10I28 of marine and terrestrial food groups. Giventhat the model denitions of dietary scenarios 1 and 2 are different, the interpretation of theoutcome shown in Fig. 1, although apparently similar, is also different. While the probabilitydistributions for dietary scenario 1 represent the protein carbon contribution of the two foodgroups, the probability distributions for dietary scenario 2 represent the total carbon (proteincarbon+ energy carbon) contribution of the two food groups.In a non-routed and concentration-independent model, as dened for dietary scenario 1, there

is only one fraction being considered, protein, and the relative concentrations of protein for thedifferent food groups were not taken into account. Thus estimates of the relative fraction(macronutrient) contribution will by denition be 100% protein, since this is the only fraction in-cluded in the model. However, in dietary scenario 2 two fractions were considered, protein andenergy, and FRUITS therefore provides estimates on the contributions of the fractions proteinand energy. These estimates are not discussed here since they are not relevant for the researchquestion being considered.

6 R. Fernandes


Here, the principal estimate of interest is the carbon contribution of the marine food grouptowards bone collagen. For both dietary scenarios, this is equivalent to the estimated carboncontribution of the marine food group towards 13Ccollagen. This value, for dietary scenario 1, willhave the same numerical value as the estimates of the total dietary carbon contribution of themarine food group. This is necessarily the case since, by denition, in dietary scenario 1 the foodgroups were dened as consisting only of protein. However, in dietary scenario 2 the relativeconcentrations of protein and energy were taken into account. Furthermore, dietary scenario 2uses a routed model and, in accordance with equation (2), part of the signal contribution(26%) towards 13Ccollagen originates from dietary energy. Table 3 lists the estimates generatedby FRUITS of the carbon contribution of terrestrial and marine foods groups towards 13Ccollagenor, equivalently, what the carbon contribution towards human bone collagen was from theterrestrial and marine food groups.

Figure 1 The probability distributions, for individual F10I28, of the dietary intakes of the marine and terrestrial foodgroups. Dietary scenario 1 corresponds to a non-routed and concentration-independent model, and dietary scenario 2 toa routed and concentration-dependent model.

Table 3 A comparison of the estimated and observed (marine only) carbon contribution of the terrestrial and marinefood groups to human bone collagen under each dietary scenario. The Absolute difference columns list the absolutedifference between the estimated and observed carbon contributions of the marine food group to human bone collagen

Dietary scenario 1 Dietary scenario 2

Samplecode

Observed%marine C

Estimated %terrestrial C

Estimated% marine C

Absolutedifference

Estimated %terrestrial C

Estimated% marine C

Absolutedifference

F12I28 2 94 5 6 5 4 94 5 6 5 4F10II11 3 93 6 7 6 4 93 5 7 5 4F10I28 4 93 6 7 6 3 93 5 7 5 3F12I3 7 91 7 9 7 2 91 6 9 6 2F10I16 9 91 7 9 7 0 91 6 9 6 0F9I13 16 88 9 11 9 5 86 8 14 8 2F12I23 16 89 9 12 9 4 82 8 18 8 2F7 10 18 87 10 11 8 7 85 8 15 8 3F9I9 18 85 11 15 11 3 81 8 19 8 1



For each individual, the estimates generated for each dietary scenario of the marine carboncontribution towards human bone collagen were within a one-sigma range of the observed value(Table 3 and Fig. 2). The one-sigma ranges varied between 5 and 11% for the estimates generatedin dietary scenario 1. The precision of the results obtained for dietary scenario 2 was better, withone-sigma intervals ranging between 5 and 8%. The performance of both models assessed by thedifference between the average values of observed and estimated collagen marine carboncontribution also demonstrates an excellent agreement. With the single exception of sampleF7 10 in dietary scenario 1, the maximum absolute difference between the observed andestimated collagen marine carbon contributions was equal to or smaller than 5% in both dietaryscenarios. The sum of all absolute difference values suggests only a slightly better performance

Figure 2 The estimated (dietary scenarios 1 and 2) and observed (marine only) carbon contributions of the terrestrialand marine food groups to the bone collagen of each individual.

8 R. Fernandes


in terms of the accuracy of dietary scenario 2 (sum=21) when compared to dietary scenario 1(sum=32). This implies that a simple model instance can be used to provide useful informationon the dietary habits of Roman Tyrrhenian populations. The same model can also be used tocorrect chronologies obtained from radiocarbon dating of human bone collagen that potentiallyhave a reservoir effect.For the more accurate dietary scenario 2, the largest differences (4%) between the observed

and estimated collagen marine carbon contributions correspond to the individuals with the lowestdietary RRE values (F12I28 and F10II11). This overestimation, albeit small, could be due to thecontribution of plant food groups not taken into account in the modelling process. It is wellknown that the standard Roman dietary package included olives, grapes, gs, cereals andlegumes (Murphy et al. 2013). Furthermore, existing assessments suggest that plant foods rep-resented 7075% of the calorie intake of Mediterranean populations during classical antiquity(Foxhall and Forbes 1982). The excellent model performance would then suggest that plantfood groups had isotopic and macronutrient concentrations that approached those of terrestrialanimal food groups. The cereals consumed during the period, mostly wheat and barley, have aprotein carbon content of ~10%, which is signicantly lower than that observed for herbivoremeat (Table 2). However, the intake of legumes (e.g., broad beans, peas, chickpeas andlentils), with a higher protein content than cereals, was prevalent, especially among the lowerclasses, during the Roman period (Garnsey 2008; Murphy et al. 2013). No plant isotopicvalues were available from the studied area and time period. However, the characteristiccarbon isotopic values of C3 plants (~ 25) were probably similar to those of animalfoods (Table 2). As for nitrogen isotopic values, unmanured C3 plants in temperate environ-ments typically show values of ~2 (Richards and Trinkaus 2009). However, the 15Nvalues of plant crops are elevated through the practice of manuring (Bogaard et al. 2007),which was widespread during the rst century AD within the Roman Empire (Spurr 1986;Kron 2008). Charred cereal grains from European Neolithic sites show 15N values of~4.5 (Bogaard et al. 2013). This value is close (a 1.6 difference) to the estimatedherbivore 15Nprotein signal (Table 2). Thus, potential small differences between the isotopicand macronutrient compositions of plant and animal foods groups would only have a signi-cant impact in model estimates for lower intakes of protein, as observed for individualsF12I28 and F10II11.The results shown here demonstrate that with only a minor loss in model precision and

accuracy, a simple concentration-independent and non-routed model can be applied to providereliable estimates of protein carbon contributions of marine and terrestrial food groups forTyrrhenian Roman coastal populations during the Imperial period. However, some caution isrecommended when applying either of the two models being compared here to a different archaeo-logical context. In quantitative diet reconstruction studies, it is recommended that the isotopic andmacronutrient composition of potential food groups is dened from material recovered from localarchaeological contexts. This could also imply having to take other food groups (e.g., plant foods)into account. In this case, different strategies could be adopted. Additional food groups could beconsidered separately with different isotopic and macronutrient compositions. Alternatively,individual foods can be aggregated as a single food group (e.g., aggregating herbivore and plantfoods as a terrestrial food group) with adequate uncertainty values that reect the full range ofmacronutrient and isotopic compositions. Both options will probably result in an increase of stan-dard deviations in generated estimates. In these cases, improvement of the precision of the modelwill require more complex models and the inclusion of additional dietary proxies or of other formsof prior information.



CONCLUSIONS

The comparative performance, in terms of accuracy and precision, of a routed and concentration-dependent model was moderately superior to that of a non-routed and concentration-independentmodel. In both model instances, the estimated average marine carbon contribution to human bonecollagen typically did not differ by more than 5% from the observed value. These results demon-strate that a simple Bayesian mixing model instance, dened using FRUITS, can be used to quan-tify the marine carbon contribution to bone collagen of individuals from Roman sites along theTyrrhenian coast. This can be used to provide useful information on past individual dietaryhabits, and constitutes the basis for necessary corrections to collagen radiocarbon dates that havea reservoir effect. For the present case study, in which the potential contribution of plant foodgroups was ignored, the achieved high model performance was probably due to the intake ofplants having isotopic and macronutrient compositions approaching those of animal foods. Theapplication of similar models to different locations and time periods requires an adequate identi-cation of potential food groups and of their isotopic and macronutrient composition. It maybecome necessary, for instance, to include additional food groups with separate isotopic andmacronutrient compositions.

ACKNOWLEDGEMENTS

The author would like to thank Dr Thomas Larsen, Dr Tamsin OConnell and two anonymousreviewers for their helpful comments. The work was supported by the German Research Founda-tion within the frame of the Priority Program SPP 1400 (DFG project NA 776/).

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fernandes archaeometry

Documents

isotopic data

diet reconstruction

bayesian mixing models

tissue isotopic offsets

model instances

model parameters

university of kiel

sparse data