Literature DB >> 29694436

Freshwater reservoir offsets and food crusts: Isotope, AMS, and lipid analyses of experimental cooking residues.

John P Hart1, Karine Taché2, William A Lovis3.   

Abstract

Freshwater reservoir offsets (FROs) occur when AMS dates on charred, encrusted food residues on pottery predate a pot's chronological context because of the presence of ancient carbon from aquatic resources such as fish. Research over the past two decades has demonstrated that FROs vary widely within and between water bodies and between fish in those water bodies. Lipid analyses have identified aquatic biomarkers that can be extracted from cooking residues as potential evidence for FROs. However, lacking has been efforts to determine empirically how much fish with FROs needs to be cooked in a pot with other resources to result in significant FRO on encrusted cooking residue and what percentage of fish C in a residue is needed to result in the recovery of aquatic biomarkers. Here we provide preliminary assessments of both issues. Our results indicate that in historically-contingent, high alkalinity environments <20% C from fish may result in a statistically significant FRO, but that biomarkers for aquatic resources may be present in the absence of a significant FRO.

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Year:  2018        PMID: 29694436      PMCID: PMC5918819          DOI: 10.1371/journal.pone.0196407

Source DB:  PubMed          Journal:  PLoS One        ISSN: 1932-6203            Impact factor:   3.240


Introduction

Pottery vessels and fragments thereof are mainstays of archaeological analyses worldwide. Because of uncertain chronological associations between these artifacts and spatially associated charred plant material and animal bone, the ability to directly date these vessels is important. With the development of accelerator mass spectrometry (AMS) radiocarbon dating, the direct dating of charred cooking residues adhering to the interior surfaces of pots and sherds became a common method of obtaining direct age estimates [1,2]. Concern about the accuracy of such age estimates was prominently raised in the early 2000s [3-5]. This concern arose because of the potential for ancient carbon present in freshwater bodies to be metabolized by aquatic organisms and contribute to cooking residue formation when those organisms are subjected to water-based cooking. The presence of ancient carbon in the residues results in radiocarbon ages that are older than the pottery in question. The freshwater reservoir effect (FRE) resulting in freshwater reservoir offsets (FROs) is now well established in the literature [6]. Questions have been raised as to the implication of the FRE in certain site-specific and regional radiocarbon age datasets [7,8] and the use of current hydrological conditions to interpret the past [9]. However, concern remains as to the accuracy of radiocarbon dates obtained on cooking residues, especially when those dates do not match accepted regional chronologies [10-12]. Of primary importance for investigating FROs is understanding how different resources contribute carbon to residue formation, and the variability of ancient carbon sequestered in freshwater bodies and as a result, aquatic organisms both spatially and temporally [13-15]. Experiments with water-based cooking have contributed to understanding how the contributions of C from varying resources affect residue formation [16,17]. Modeling using bulk-stable C isotopes has allowed the estimation of significant FROs with varying raw resource mixes and dead C fractions in aquatic organisms [7,9,18]. The extraction of fatty acids from charred cooking residues and pottery fabric has provided additional evidence for the presence of C from fish in residues. While most published analyses have focused on residues absorbed into the pottery fabric, recent lipid analyses of charred encrusted cooking residues have routinely yielded biomarkers for aquatic resources (e.g., [19-23]). Analyses of contemporary aquatic organisms and the chemistry of freshwater systems have contributed to understandings of spatial and temporal variability in the FRE [13,24]. Empirical investigations of how much fish C in charred residues is needed to produce statistically significant FROs in the presence of FRE and how much fish C is needed for aquatic biomarkers to be identified in residues have been lacking. In this article, we provide preliminary assessments of both issues. These were accomplished through cooking experiments with proportional mixes of fish and maize. AMS dates were obtained on fish of varying species from three lakes and one stream in New York. We used bulk isotope analyses to assess the proportion of C from fish that contributed to samples obtained from proportionally prepared mixes of dried fish and maize. We used subsamples for radiocarbon dating to determine what proportions of fish C in a residue resulted in significant FROs. We also extracted fatty acids from proportional mixes of maize and fish powders to determine when biomarkers for aquatic resources became evident. Our results provide important new insights into issues surrounding FROs from directly radiocarbon dating charred cooking residues.

Materials and methods

Cooking experiments

Twenty-three fish and two maize samples were subjected to radiocarbon dating (Table 1). The fish were captured from Lake Ontario in 2014, Seneca Lake in 2015, Cayuga Lake, and Catherine Creek, a tributary of Seneca Lake, in 2016 (Fig 1). The 2014 Lake Ontario Fish was provided dead to the Museum by the New York State Department of Environmental Conservation (NYS DEC). The other fish were obtained by the Museum’s Ichthyology Department during surveys under NYS DEC License to Collect or Possess: Scientific #1809. The fish were euthanized with MS-222 (Tricaine Methanesulfonate) using the methods and concentrations outlined in the 2013 American Veterinary Medical Association's Guidelines for the Euthanasia of Animals.
Table 1

14C dating and isotope results for fish from New York freshwater bodies.

UCIAMSYearSpeciesCommon NameLocationδ13CeFMCD14C14C age (BP)FROfFDCg
153202a2014Coregonus clupeaformiesLake WhitefishLake Ontario-21.91.0167±0.00188.8±1.8modern26±140.0000
166335b2015Scardinius erythrophthalmusCommon RuddSeneca Lake-17.21.0215±0.002021.5±2.0modern-7±160.0055
166336b2015Scardinius erythrophthalmusCommon RuddSeneca Lake-17.01.0264±0.001726.4±1.7modern-40±130.0218
166337b2015Scardinius erythrophthalmusCommon RuddSeneca Lake-16.01.0199±0.001619.9±1.6modern6±120.0246
1796502016Oncorhynchus mykissRainbow TroutCatherine Creek-22.01.0197±0.001619.7±1.6modern-12±120.0185
1796512016Oncorhynchus mykissRainbow TroutCatherine Creek-19.11.0126±0.001212.6±1.2modern44±90.0256
179652d2016Salvelinus namaycushLake Trout (1)Cayuga Lake-26.50.9960±0.0012-4.0±1.230±15177±100.0238
1796532016Salvelinus namaycushLake Trout (2)Cayuga Lake-27.70.9931±0.0012-6.9±1.255±15200±90.0217
179654d2016Salvelinus namaycushLake Trout (3)Cayuga Lake-24.20.9994±0.0012-0.6±1.25±15150±90.0265
179655c2016Salvelinus namaycushLake Trout (4)Cayuga Lake-24.90.9922±0.0012-7.8±1.265±15208±100.0224
179656d2016Salvelinus namaycushLake Trout (5)Cayuga Lake-26.80.9939±0.0013-6.1±1.350±15194±110.0209
179657d2016Micropterus salmoidesLargemouth BassCayuga Lake-23.70.9967±0.0013-3.9±1.330±15176±100.0275
1796582016Salmo salarAtlantic SalmonCayuga Lake-27.50.9913±0.0012-8.7±1.270±15215±100.028
1796592016Salmo salarAtlantic SalmonCayuga Lake-25.20.9954±0.0012-4.6±1.235±15182±90.0059
1796602016Salmo salarAtlantic SalmonCayuga Lake-24.10.9969±0.0012-3.1±1.225±15170±90.0000
1796612016Salmo salarAtlantic SalmonCayuga Lake-24.90.9902±0.0012-9.8±1.280±15224±100.0074
179662c2016Esox nigerChain PickerelCayuga Lake-20.90.9897±0.0013-10.3±1.385±15228±110.0111
1796632016Oncorhynchus mykissRainbow TroutCatherine Creek-19.21.0122±0.001212.2±1.2modern47±90.006
1796642016Catostomus commersoniiWhite SuckerCatherine Creek-21.91.0288±0.001328.8±1.3modern-83±100.0123
1796652016Catostomus commersoniiWhite SuckerCatherine Creek-20.61.0107±0.001310.7±1.3modern60±100.0000
1796662016Catostomus commersoniiWhite SuckerCatherine Creek-21.81.0069±0.00126.9±1.2modern90±100.0055
1796672016Catostomus commersoniiWhite SuckerCatherine Creek-23.61.0121±0.001212.1±1.2modern49±100.0218
1796682016Catostomus commersoniiWhite SuckerCatherine Creek-21.51.0057±0.00125.7±1.2modern99±100.0246
1663382015Zea mays ssp. maysMaizeWashington Co.-11.91.0205±0.001620.6±1.6modern00
1808842016Zea mays ssp. maysMaizeWashington Co.-11.91.0181±0.001618.2±1.6modern00

aUsed in 2014 proportional cooking experiments with maize meal.

bUsed in 2015 proportional cooking experiments with maize meal.

cUsed in 2016 proportional powder mixes with maize.

dUsed in 2016 proportional cooking experiments with maize kernels.

eMeasured to a precision <0.1‰.

fEquations from [13]

FRO = ‒8033*ln(FMCsample/FMCatmosphere)

FRO 1σ = ‒8033*ln((FMCsample)+(FMC1σ))+(8033*ln(FMCsample))

gFDC = (FMCmaize- FMCsample)/FMCmaize. Negative values round to 0

Fig 1

Locations of waterbodies from which fish were captured for the current experiments.

aUsed in 2014 proportional cooking experiments with maize meal. bUsed in 2015 proportional cooking experiments with maize meal. cUsed in 2016 proportional powder mixes with maize. dUsed in 2016 proportional cooking experiments with maize kernels. eMeasured to a precision <0.1‰. fEquations from [13] FRO = ‒8033*ln(FMCsample/FMCatmosphere) FRO 1σ = ‒8033*ln((FMCsample)+(FMC1σ))+(8033*ln(FMCsample)) gFDC = (FMCmaize- FMCsample)/FMCmaize. Negative values round to 0 All fish were kept frozen until muscle tissue was sampled. The sampled muscle tissue was freeze dried before submission for AMS dating. Commercial cornmeal was used in the 2014 cooking experiments. Ears of Dent maize (Zea mays ssp. mays) were obtained from an organic Amish farm in northern Washington County, New York USA for the 2015 and 2016 cooking experiments. Maize samples from 2015 and 2016 were submitted for AMS dating. The ears were allowed to completely dry in an unheated herbarium drying cabinet. Dried kernels were ground to meal. Whole kernels were rehydrated by soaking in ultra-purified water for ~16 hours. Whole kernel and meal were both used in water-based cooking in northeastern North America [25,26]. Raw fish muscle tissue from thawed fish with relatively large FROs (Table 1) was divided into 2.5g pieces, which were kept refrigerated until used in cooking experiments. Forty-five 25g resource mixes using whole kernels or meal with fish muscle tissue (Table 2) were prepared in 10% or 20% increments and placed in 400 ml of ultra-purified water in Pyrex beakers. The beakers were placed on a hot plate at 400°C and boiled for 1 hr. At 1 hr the material in solution and suspended in the liquid was sampled by pipette (whole kernel) or by decanting (meal) into glass test tubes (hereafter, “liquid” samples). Material adhering to the interior beaker wall was scraped off from the water line to the lip of the beaker and placed in a glass test tube containing ultra-purified water (hereafter, “wall” samples). All samples were frozen and then freeze dried. Freeze-dried samples were kept in a desiccation chamber until sampled for analyses.
Table 2

Percent Fish C in residues from all cooking experiments.

Lab No.FishMaize FormSource% Raw FishResidueδ 13C% Fish C in residuea
UCIAMS 185316Lake Trout 5kernelliquid90-22.970.38
UCIAMS 185315Lake Trout 3kernelliquid80-21.565.67
UCIAMS 185314Lake Trout 3kernelliquid70-20.055.31
UCIAMS 185313Lake Trout 3kernelliquid60-19.620.06
UCIAMS 185312Lake Trout 3kernelliquid50-17.538.62
UCIAMS 185311Lake Trout 3kernelliquid40-17.638.74
UCIAMS 185310Lake Trout 3kernelliquid30-15.222.71
UCIAMS 185309Lake Trout 3kernelliquid20-13.812.96
UCIAMS 185308Lake Trout 5kernelliquid10-13.28.12
UCIAMS 185325Largemouth Basskernelliquid90-22.992.92
UCIAMS 185324Largemouth Basskernelliquid80-20.269.76
UCIAMS 185323Largemouth Basskernelliquid70-19.362.75
UCIAMS 185322Largemouth Basskernelliquid60-17.547.55
UCIAMS 185321Largemouth Basskernelliquid50-17.446.79
UCIAMS 185320Largemouth Basskernelliquid40-16.437.68
UCIAMS 185319Largemouth Basskernelliquid30-15.127.21
UCIAMS 185318Largemouth Basskernelliquid20-17.446.11
UCIAMS 185317Largemouth Basskernelliquid10-13.916.90
UCB ISO-17-04_C5Lake Trout 5kernelwall90-25.492.60
UCB ISO-17-04 rerun_A3Lake Trout 3kernelwall80-26.096.40
UCB ISO-17-04_A6Lake Trout 3kernelwall70-25.593.25
UCB ISO-17-04_C2Lake Trout 3kernelwall60-24.884.83
UCB ISO-17-04_B1Lake Trout 3kernelwall50-24.373.77
UCB ISO-17-04_C4Lake Trout 3kernelwall40-22.776.75
UCB ISO-17-04_A9Lake Trout 3kernelwall30-23.160.18
UCB ISO-17-04_C12Lake Trout 3kernelwall20-20.790.96
UCB ISO-17-04_B5Lake Trout 5kernelwall10-25.292.60
UCB ISO-17-04_A2Largemouth Basskernelwall90-24.0102.55
UCB ISO-17-04_C9Largemouth Basskernelwall80-23.597.63
UCB ISO-17-04_A10Largemouth Basskernelwall70-23.698.93
UCB ISO-17-04_A4Largemouth Basskernelwall60-23.194.27
UCB ISO-17-04_A3Largemouth Basskernelwall50-22.387.53
UCB ISO-17-04_A11Largemouth Basskernelwall40-22.286.76
UCB ISO-17-04_A5Largemouth Basskernelwall30-21.177.56
UCB ISO-17-04_B10Largemouth Basskernelwall20-23.792.14
UCB ISO-17-04_B4Largemouth Basskernelwall10-22.8102.55
UCIAMS 166316Common Rudd 1mealliquid90-13.327.11
UCIAMS 166317Common Rudd 1mealliquid70-12.14.85
UCIAMS 166318Common Rudd 1mealliquid50-12.14.45
UCIAMS 166319Common Rudd 1mealliquid30-12.13.55
UCIAMS 166320Common Rudd 1mealliquid1012.02.28
UCIAMS 166321Common Rudd 2mealliquid90-13.226.99
UCIAMS 166322Common Rudd 2mealliquid80-12.614.86
UCIAMS 166323Common Rudd 2mealliquid70-12.38.73
UCIAMS 166324Common Rudd 2mealliquid60-12.26.00
UCIAMS 166325Common Rudd 2mealliquid50-12.02.27
UCIAMS 166326Common Rudd 2mealliquid40-12.14.03
UCIAMS 166327Common Rudd 2mealliquid30-12.13.85
UCIAMS 166328Common Rudd 2mealliquid20-12.13.88
UCIAMS 166329Common Rudd 2mealliquid10-11.90.00
UCIAMS 166330Common Rudd 3mealliquid90-13.335.36
UCIAMS 166331Common Rudd 3mealliquid70-12.27.69
UCIAMS 166332Common Rudd 3mealliquid50-12.15.39
UCIAMS 166333Common Rudd 3mealliquid30-12.15.65
UCIAMS 166334Common Rudd 3mealliquid10-11.80.00
UCB ISO-16-03_Tray2_C2Common Rudd 2mealwall90-13.327.13
UCB ISO-16-03_Tray2_C4Common Rudd 2mealwall80-13.735.55
UCB ISO-16-03_Tray2_C3Common Rudd 2mealwall70-13.021.79
UCB ISO-16-03_Tray2_B10Common Rudd 2mealwall60-12.37.62
UCB ISO-16-03_Tray2_B8Common Rudd 2mealwall50-12.25.60
UCB ISO-16-03_Tray2_C1Common Rudd 2mealwall40-12.511.57
UCB ISO-16-03_Tray2_B9Common Rudd 2mealwall30-12.37.68
UCB ISO-16-03_Tray2_B11Common Rudd 2mealwall20-12.13.08
UCB ISO-16-03_Tray2_B12Common Rudd 2mealwall10-12.410.16
UCIAMS 153203Whitefishmealwall80-15.339.27
UCIAMS 153204Whitefishmealwall70-12.412.58
UCIAMS 153205Whitefishmealwall60-14.229.12
UCIAMS 153206Whitefishmealwall50-14.532.15
UCIAMS 153207Whitefishmealwall40-13.119.71
UCIAMS 153208Whitefishmealwall30-12.09.36
UCIAMS 153209Whitefishmealwall20-11.54.34
UCIAMS 153210Whitefishmealwall10-10.90.00

aMass Balance:(δ13Csample ‒ δ13Cmaize)/(δ13Cfish ‒ δ13Cmaize))*100

aMass Balance:(δ13Csample ‒ δ13Cmaize)/(δ13Cfish ‒ δ13Cmaize))*100

Resource powder mixes

Freeze-dried Lake Trout and Chain Pickerel muscle tissue and dried whole maize kernels were ground into 0.5 mm powders. These were mixed in 10% increments in 1g samples (10% and 90% maize to 90% fish and 10% maize by weight). Each thoroughly mixed sample (~0.025 g) was subsampled for AMS dating, and the remainder was subjected to lipid analyses.

Isotope analysis and AMS dating

All samples for AMS dating were submitted to the W. M. Keck Carbon Cycle Accelerator Mass Spectrometry Laboratory at the University of California-Irvine. These included samples from the 23 fish, two maize kernels, 18 cooking experiments, and 18 resource powder mixes. Protocols for AMS dating modern samples are documented on the laboratory’s website (https://www.ess.uci.edu/group/ams/home). Stable carbon isotope assays (δ13C) were performed on samples at the Keck laboratory or the University of California Berkeley’s Center for Stable Isotope Biogeochemistry.

Lipid analysis of powder mixes

Fish-maize powder mixes were subjected to lipid analysis to determine when biomarkers for aquatic resources become evident. Liquid samples obtained after the cooking experiment were also analyzed but lipid yields obtained were too low to be interpretable (<0.5μg/mg of lipids per mg of residue sample). As described above, the samples consisted of freeze-dried fish muscle tissue and dried whole maize kernels ground into 0.5 mm powders. These were mixed in 10-percent increments in 1 g samples (10% and 90% maize to 10% fish and 90% maize by weight). To generate ω-(o-alkylphenyl)alkanoic acids, sterile clay powder was added to the fish-maize mixes [27,28]. Clay powder was obtained by drilling and reducing to powder 20 grams of a replica vessel using a DremelTM tool and placing the resulting clay powder in a furnace at 500°C for 6 hours to completely remove any organic material in the clay. Nine samples consisting of 1 gram of sterile ceramic powder mixed with different proportions of dried Chain Pickerel and maize were placed in sealed hach tubes in a furnace at 270°C for 17 hr, following previous experiments which established these conditions as prerequisite to the formation of ω-(o-alkylphenyl)alkanoic acids [28]. Three samples consisting of single ingredients (i.e., dried maize, dried Chain Pickerel, and dried Lake Trout) mixed with sterile clay powder were also exposed to intense heating in sealed hach tubes (270°C for 17 hours). Nine samples consisting of 1 gram of sterile ceramic powder mixed with different proportions of Lake Trout and maize were analyzed without being heated to assess the nature and quantity of aquatic biomarkers detected when resources are not subjected to intense heating. Lipids were extracted from the 21 samples by direct methylation with acidified methanol to maximize recovery [29]. Methanol (4mL) was added and homogenized with the ceramic-fish-maize samples. Each mixture was ultra-sonicated for 15 minutes and then acidified with concentrated sulphuric acid (800μL). The acidified suspension was heated in sealed tubes for four hours at 70°C and then cooled, and lipids were extracted with n-hexane (3×2mL). Lipids extracted from ceramic matrices were analyzed by gas chromatography–mass spectrometry (GC-MS), a technique that allows the separation of complex mixtures and the identification of plant- and animal-derived lipids. GC-MS analysis was performed using an Agilent 7890A Series gas chromatograph connected to an Agilent 5975 C Inert XL mass-selective detector with a quadrupole mass analyzer (Agilent Technologies, Cheadle, Cheshire, UK). The splitless injector and interface were maintained at 300°C and 280°C respectively. The carrier gas used was helium at a constant flow of 3ml/min, and the initial inlet/column head pressure was 24.012 psi. The GC column was inserted directly into the ion source of the mass spectrometer. The ionization energy was 70 eV and spectra were obtained by scanning between m/z 50 and 800. A DB-5ms (5%-phenyl)-methylpolysiloxane column (30 m x 0.25mm x 0.25μm; J&W Scientific, Folsom, CA, USA) was used for scanning and SIM. Two distinct runs in SIM mode were conducted. In the first run, a group of ions (m/z 74, 105, 262, 290, 318, 346) corresponding to ω-(o-alkylphenyl) alkanoic acids of carbon length C16 to C22 were monitored. In the second run, a first group of ions (m/z 74, 87, 213, 270) corresponding to 4,8,12-trimethyltridecanoic acid (TMTD) fragmentation, a second group of ions (m/z 74, 88, 101, 312) corresponding to pristanic acid, and a third group of ions (m/z 74, 101, 171, 326) corresponding to phytanic acid were monitored, respectively.The temperature program was 2 min at 50°C, 10°C min–1 to 325°C and 15 min at 325°C. The same chromatographic conditions were used in scanning and SIM mode.

Results

AMS dates on fish

Results of the AMS dating of the fish samples are presented in Table 1. FROs and their standard deviations were calculated using the formulae in [13]. Fraction of modern carbon (FMC) measures on maize were used in the FRO formula for the fish caught in 2015 and 2016. For the fish caught in 2014, a Northern Hemisphere atmospheric value of 1.020 was used [30]. Twelve of the samples returned modern ages. FROs for four of these ages are negative, while the others range from 6±12 to 99±10 14Cyr. Fish obtained from Cayuga Lake during September of 2016 were the only ones to produce non-modern 14C ages. The largest offsets for these fish ranged from 150±9 to 228±11 14Cyr. In total, the variation in FROs on fish were consistent with results obtained in other parts of the world, but which can range to >1,000 14Cyr [11,13,24] depending on the species of fish and the water body’s historically contingent total alkalinity. Oversaturation of carbonate (CO3‒2) and bicarbonate (HCO3‒) ions has been documented in Lake Cayuga through sediment analyses to have occurred during the historical and modern periods but not during all portions of the Holocene [31]. Measures of total alkalinity for this lake in September 2016 ranged from 93.8 to 114 mg CaCO3/L [32], consistent with expectations for the presence of FROs [9].

Contribution of fish C to residues

Previous experiments have investigated the relationship of resource mixes to bulk δ13C values on residues to determine if those values can be used to detect if maize was cooked in a given pot [7,17,33]. These experiments involved proportional mixes of maize, a C4 plant, with C3-resources, including wild rice (Zizania sp.), chenopodium (Chenopodium album), and C3-plant consuming white tailed deer (Odocoileus virginianus). While it was determined that it is possible to track changes in maize use through time using bulk δ13C values in some regions [34,35], it is not possible to use those values independently to determine if maize was cooked or processed in a specific pot [7,17,31] contrary to earlier suggestions [36,37]. Mass balance using δ13C values on charred residues cannot be used to determine the percentage of raw maize cooked in a pot as suggested by Morton and Schwarcz [33]. Rather, it indicates the contribution of maize C to residue formation, which itself is determined by C from maize and the resources it was cooked with entering into suspension and solution and being deposited and burned on pottery surfaces [7]. The amount of C from maize and other resources in suspension and solution depends on both boiling time and the form of maize being cooked, as well as the percentage of C in the respective resources [17]. The mass balance formula was used here with δ13C and FMC values to determine the percent of fish C in the 72 experimental residues and 18 fish-maize powder mixtures (Tables 2–4). Experiments suggest that heating has little effect on boiled bulk fish flesh δ13C (<0.5‰) values [38], and that charring has little effect on grain (<1.0‰) δ13C values [39].
Table 4

Fish and maize powder mix data.

UCIAMS#% Raw Fishδ13C (‰)FMCD14C (‰)14C age (BP)FRO% Fish C δ13Ca% Fish C FMCbFDC
Chain Pickerel
179662100-20.9±.010.9897±0.0013-10.3±1.385±15228±111001000.0280
18086790-20.1±.010.9904±0.0016-9.6±1.675±15222±1391.6497.640.0273
18086880-20.0±.010.9938±0.0017-6.2±1.750±15195±1490.3985.770.0240
18099670-18.8±.010.9982±0.0016-1.8±1.615±15160±1377.2570.410.0197
18086960-18.3±.010.9972±0.0016-2.8±1.625±15167±1370.8773.780.0206
18087050-17.2±.011.0018±0.00201.8±2.0modern130±1659.1557.650.0161
18087140-17.0±.010.9988±0.0017-1.2±1.710±15154±1456.6168.1450.0191
18087230-15.0±.011.0084±0.00168.4±1.6modern77±1334.8334.310.0096
18087320-15.1±.011.0092±0.00189.2±1.8modern71±1535.8031.600.0088
18087410-13.0±.011.0154±0.001615.4±1.6modern22±1312.659.750.0027
1808840-11.9±.011.0182±0.001618.2±1.6modern0000
Lake Trout
179656100-24.9±.010.9922±0.0012-7.8±1.265±15208±101001000.0255
18087590-24.4±.010.9925±0.0019-7.5±1.960±20205±1696.3098.670.0252
18087680-23.6±.010.9923±0.0016-7.7±1.660±15207±1390.0699.630.0254
18087770-22.3±.010.9984±0.0016-1.6±1.615±15158±1380.0376.190.0195
18087860-21.3±.010.9991±0.0018-0.9±1.85±15152±1571.9673.460.0188
18087950-19.4±.011.0036±0.00173.6±1.7modern116±1457.7355.960.0143
18088040-18.0±.011.0065±0.00166.5±1.6modern93±1346.6145.050.0115
18088130-16.7±.011.0082±0.00168.2±1.6modern79±1336.9638.390.0098
18088220-18.1±.011.0032±0.00163.2±1.6modern119±1347.3657.580.0147
18088310-14.2±.011.0135±0.001613.5±1.6modern37±1317.3517.960.0046
1808840-11.9±.011.0182±0.001618.2±1.6modern0000

Mass balance: a(δ13Csample ‒ δ13Cmaize)/(δ13Cfish ‒ δ13Cmaize))*100

b(FMCsample ‒ FMCmaize)/(FMCfish ‒ FMCmaize))*100.

Mass balance: a(δ13Csample ‒ δ13Cmaize)/(δ13Cfish ‒ δ13Cmaize))*100 b(FMCsample ‒ FMCmaize)/(FMCfish ‒ FMCmaize))*100 cLake Trout 3. dLake Trout 5. Mass balance: a(δ13Csample ‒ δ13Cmaize)/(δ13Cfish ‒ δ13Cmaize))*100 b(FMCsample ‒ FMCmaize)/(FMCfish ‒ FMCmaize))*100. Consistent with previous results [7,17], the form of maize and the origination of the sample affected the percent fish C that contributed to the residues (Table 5). Fish C in the wall scraped residues was overrepresented relative to raw resources percentages when cooked with whole kernels. It was underrepresented relative to raw resource percentages when cooked with meal. In the liquid samples, there was an almost linear relationship between the percent raw fish and fish C in the residue when fish was cooked with whole kernels (Fig 2). When cooked with meal, fish C was underrepresented in the liquid sample residues.
Table 5

Percent fish C in experimental residues calculated with mass balance from δ13C values.

FishMaize FormSamplePercent Raw Fish (wt)
102030405060708090
Largemouth BassKernelLiquid20.6143.2329.6339.4550.3159.2266.6773.8293.73
Lake TroutKernelLiquid8.9214.5724.1239.9640.2553.8258.8966.2783.30
Common Rudd 1MealLiquid2.283.554.454.8527.11
Common Rudd 2MealLiquid0.003.883.854.032.276.008.7314.8626.99
Common Rudd 3MealLiquid0.005.655.397.6935.36
Largemouth BassKernelWall92.1499.5077.5686.7687.5394.2798.9397.63100.00
Lake TroutKernelWall90.9660.1876.7573.7784.8388.3093.2596.4092.10
Common Rudd 2MealWall10.163.0897.6811.575.607.6221.7933.5527.13
Lake WhitefishMealWall0.004.349.3619.7132.1529.1212.5839.27
Fig 2

Plots of % raw fish vs. % fish C in residues based on mass balance using δ13C values.

AMS dates and FROs

AMS dates were obtained on the 18 liquid residue samples and 18 maize-fish powder mixes to assess when the contribution of fish C to residue formation may result in significant FROs (Tables 3 and 4). Two of the liquid residue age estimates (UCI 185313, 185318) were not used in the analyses because they produced ages that were substantially older than expected based on their position in the proportional mix sequences. We assume that old carbon was introduced to the samples at some point in processing.
Table 3

Fish and maize kernel liquid sample residue data.

UCIAMS#% Raw Fishδ13C (‰)FMCD14C (‰)14C age (BP)FRO% Fish C δ13Ca% Fish C FMCbFDC
Largemouth Bass
179657100-23.7±.010.9967±0.0013-3.9±1.330±15176±101001000.0275
18532590-22.9±.010.9962±0.0012-3.8±1.230±15176±1092.9299.050.0216
18532480-20.2±.010.9980±0.0016-2.0±1.615±15161±1369.7690.660.0198
18532370-19.3±.011.0015±0.00131.5±1.3>Modern133±1062.7575.060.0164
18532260-17.5±.011.0042±0.00134.2±1.3>Modern111±1047.5562.810.0137
18532150-17.4±.011.0043±0.00134.3±1.3>Modern110±1046.7962.520.0137
18532040-16.4±.011.0077±0.00137.7±1.3>Modern83±1037.6847.020.1030
18531930-15.1±.011.0084±0.00148.4±1.4>Modern78±1127.2144.110.0096
18531820-17.4±.011.0016±0.00191.6±1.9>Modern132±1546.1174.670.0163
18531710-13.9±.011.0130±0.001613.0±1.6>Modern41±1216.9023.500.0051
1808840-11.9±.011.0182±0.001618.2±1.6>Modern0000
Lake Trout
179654c100-24.2±.010.9994±0.0012-0.6±1.25±15150±91001000.0265
179656d100-26.8±.010.9939±0.0013-6.1±1.350±15194±111001000.0209
185316 d90-22.9±.010.9996±0.0013-0.4±1.35±15148±1070.3883.490.0182
185315c80-21.5±.011.0007±0.00130.7±1.30±15139±1065.6778.540.0172
185314c70-20.0±.011.0031±0.00133.1±1.3>Modern120±1055.3167.880.0148
185313c60-19.6±.010.9932±0.0013-6.8±.1.355±15200±1020.06112.570.0246
185312c50-17.5±.011.0074±0.00137.4±1.3>Modern86±1038.6248.770.0107
185311c40-17.6±.011.0081±0.00138.1±1.3>Modern80±1138.7445.330.0099
185310c30-15.2±.011.0110±0.001311.0±1.3>Modern57±1022.7132.140.0070
185309c20-13.8±.011.0160±0.001316.0±1.3>Modern17±1012.969.680.0021
185308d10-13.2±.011.0159±0.001315.9±1.3>Modern18±118.1210.400.0023
1808840-11.9±.011.0182±0.001618.2±1.6>Modern0000

Mass balance: a(δ13Csample ‒ δ13Cmaize)/(δ13Cfish ‒ δ13Cmaize))*100

b(FMCsample ‒ FMCmaize)/(FMCfish ‒ FMCmaize))*100

cLake Trout 3. dLake Trout 5.

There was a very high positive correlation (r = 0.989) between the fraction of fish C in the residues and Fraction Dead Carbon (FDC; Fig 3), and because there was a very high positive correlation between FDC and FRO, there was the same very high positive correlation between the percentage of fish C in residues and FRO. Ward and Wilson’s [40] test was used to determine significant FROs at varying error terms reported with radiocarbon dates. These results were used to calculate the FDC needed to result in statistically significant FROs. The least-squares regression formula in Fig 3 was used to determine the percentage fish C contributing to residue formation needed to result in the calculated FDC for the FROs. Least squares regression was performed for the fish and kernel liquid residues and fifth- and sixth-order polynomial regressions were performed to best fit for the other residues to determine what percentage of raw fish contributed sufficient C in the residues to result in the FDC to produce statistically significant FROs (Table 6, Fig 4).
Fig 3

Regression of fraction fish C on fraction dead carbon.

Table 6

Percent raw fish resulting in significant FRO with different radiocarbon date error terms.

Error (±yr)Significant FRO (yr)FDC% Residue Fish CPercent Raw Fish (wt)
Wall-MealWall-KernelLiquid-MealLiquid-Kernel
15420.0051918.1846.330.9446.6219.38
20560.0069028.8455.741.6655.0330.58
35970.0119044.1978.272.8664.5646.70
501390.0170564.1588.724.9773.3767.65
651810.0222084.2093.119.0779.4288.74
Fig 4

Regressions of % raw fish on % fish C in residues.

As is evident from the data in Table 6, there was no single relationship between the amount of raw fish in a cooking mixture and a statistically significant FRO as calculated with [40]. This was due to the amount of C in any given fish, and the form of the maize in the mix. This can be understood as follows: For wall scraped samples an age estimate with a typical 15-yr error term requires 18.18% fish C in the residue. This is realized when there is between 0.94% and 46.33% raw fish content in the mix for wall-scraped residues dependent on maize in whole kernel and meal form, respectively. Wall scraped samples with a less-typical 65-yr error require 84.20% fish C in a residue. Depending on the form of maize in the mix this is realized with between 9.07% and 91.11% raw fish in the mix, respectively. Results for the liquid-derived samples, representing potential C contribution to residue formation, can be understood as follows: For a 15-yr error, the mix would require between 46.62% and 19.38% raw fish for maize in meal and kernel form, respectively, to result in a statistically significant FRO. For a 65-yr error term, the mix would require from 79.42% to 88.74% raw fish, with maize meal and kernels, respectively, to result in a statistically significant FRO. These results demonstrate that it is possible for resource mixes including very little fish C, as low as 0.94%, to result in a statistically significant FRO depending on the form of the other resources in the mix and the radiocarbon date error term. It is also possible that fish must constitute the bulk of the resources being cooked depending on the same variables.

Lipid analysis and the identification of aquatic biomarkers in fish-maize powder mixes

Certain trends in fatty acid ratios are evident as the proportions of fish in unheated samples diminish, such as a general decrease in C14:0, C16:1, C16:0, C18:0 and C18:1, and an increase in C18:2 (Table 7, Fig 5). The sample containing 50% of Lake Trout consistently deviate from these trends, which we suspect is due to a manipulation error in the lab. Several of these trends, however, are not present in mixes subjected to intense heating (Table 8; Fig 6). Notably, ratios between palmitic and stearic fatty acids (C16:0/C18:0)—often used in the literature to distinguish between plant and animal resources—become ill-suited to distinguish between different categories of foods once samples have been exposed to heat. While the same failure does not apply to other ratios in this study, such as C16:1/C18:1 and (C15:0+C17:0)/C18:0, we maintain that a methodology based on fatty acid ratios alone is unsuitable for identifying the source of archaeological residues. Degradation processes undergone by lipids as a result of use and burial are in part dependent on the types of compounds present and therefore potentially traceable to original vessel contents. However, variation in the circumstances of use (e.g., time, temperature, oxidative conditions) and the nature of the ceramics (e.g., porosity, clay matrix) complicates comparison with experimental analogues. Furthermore, a range of post-burial chemical and enzymatic processes, not fully replicated in our experiment where sherds were only heated, also affect the distribution of lipids in a residue. Such conditions are hard to simulate even through burial experiments. Therefore, we contend that the biomarker approach and the criteria described in [27,28,41] provide the only robust methodology for aquatic identification in archaeological pottery, supplemented where possible by carbon isotope measurements of individual fatty acids.
Table 7

Lake Trout and maize unheated powder mixture lipid and biomarker results.

Cx:y = fatty acids with carbon length x and number of unsaturations y (C18:1s and C18:2s are the sum of all isomers); br = branched chain acids; TMTD = 4,8,12‐trimethyltridecanoic acid, chol = cholesterol, stig = stigmasterol.

Percentages of Lake Trout
Raw resource based on weight90.080.070.060.050.040.030.020.010.0
Residue based on δ13Ca96.390.180.072.047.457.746.637.017.3
Residue based on FMCa98.799.676.273.557.655.645.138.418.0
Fatty Acids (relative %)C14:04.964.133.402.644.091.731.390.930.47
C15br0.570.670.550.310.450.210.160.100.04
C15:00.600.520.430.320.430.210.170.110.06
C16br0.340.310.310.23trace0.170.150.090.00
C16:110.529.047.505.848.764.083.132.281.12
C16:028.2025.3921.4520.7422.5617.0916.8616.3015.84
C17br1.030.630.481.101.770.730.200.410.21
C17:10.791.130.920.000.000.000.000.000.00
C17:00.590.560.430.360.520.240.200.160.09
C18:30.781.011.193.154.131.251.291.371.83
C18:2s6.229.4614.4419.653.3928.9335.2940.9947.68
C18:1s33.7734.1230.8630.5732.1827.3026.9825.7624.57
C18:04.794.633.453.194.592.382.241.951.62
C19:0tracetracetracetracetracetracetrace0.050.00
C20:31.932.234.373.054.564.274.123.963.20
C20:20.590.871.141.021.450.960.880.10trace
C20:11.021.791.590.871.270.910.760.560.45
C20:00.710.160.15tracetrace0.170.180.160.21
C22:20.271.334.815.938.678.385.124.032.11
C22:1trace0.200.240.000.000.000.000.000.00
C22:0tracetracetracetrace0.00tracetracetracetrace
C24:1trace0.170.15trace0.00tracetracetracetrace
C24:00.000.000.000.000.00tracetracetracetrace
BiomarkersTMTDTMTDTMTDTMTDTMTDTMTDTMTDTMTDTMTD
cholcholcholcholcholcholcholcholchol
stigstigstigstig

aCalculated with mass balance equation.

Fig 5

Gas chromatograms of lipid extracts from unheated maize-fish powder mixes consisting of 90% Lake Trout and 10% maize (A) and 10% Lake Trout and 90% maize (B). Cn:x are fatty acids with carbon length n and number of unsaturations x; br are branched-chain acids; IS is internal standard (n-hexatriacontane).

Table 8

Chain Pickerel and maize heated powder mixture lipid and biomarker results.

Cx:y = fatty acids with carbon length x and number of unsaturations y (C18:1s and C18:2s are the sum of all isomers); br = branched chain acids; APFA Cx = ω‐(o‐alkylphenyl) alkanoic acids with carbon length x; chol = cholesterol.

Percentages of Chain Pickerel
Raw resource based on weight90.080.070.060.050.040.030.020.010.0
Residue based on δ13Ca91.690.477.370.959.256.634.835.812.7
Residue based on FMCa97.685.870.473.857.668.134.331.69.7
Fatty Acids (relative %)C14:02.662.651.942.022.011.721.651.812.15
C15:00.890.720.590.51tracetracetracetracetrace
C16:12.322.121.990.930.620.630.000.000.00
C16:033.4033.1531.7332.6729.7332.1633.6635.5133.53
C17br1.841.581.311.271.311.090.44trace0.59
C17:01.481.280.941.171.431.101.150.961.40
C18:2s0.000.000.000.391.050.990.900.891.07
C18:1s18.5721.3526.7524.4721.6223.3922.9625.7521.27
C18:023.1620.2714.2922.5933.1024.8228.0824.4034.56
C20:10.750.790.770.630.460.730.660.820.82
C20:01.131.141.031.261.001.521.551.711.92
C22:00.360.380.490.420.340.480.510.590.43
C23:0tracetracetracetracetrace0.32tracetracetrace
C24:11.381.201.520.91tracetracetrace0.000.00
C24:00.630.470.800.84trace0.660.580.580.00
BiomarkersTMTDTMTDTMTDTMTDTMTDTMTDTMTDTMTDTMTD
phytanicphytanicphytanicphytanicphytanicphytanicphytanicphytanicphytanic
APFA C18APFA C18APFA C18APFA C18APFA C18APFA C18APFA C18APFA C18APFA C18
APFA C20APFA C20APFA C20APFA C20APFA C20APFA C20APFA C20APFA C20APFA C20
cholcholcholcholcholcholchol

aCalculated with mass balance equation.

Fig 6

Gas chromatograms of lipid extracts from heated maize-fish powder mixes consisting of 90% Chain Pickerel and 10% maize (A) and 10% Chain Pickerel and 90% maize (B). Cn:x are fatty acids with carbon length n and number of unsaturations x; br are branched-chain acids; APFA Cx are ω‐(o‐alkylphenyl) alkanoic acids with carbon length x.

Gas chromatograms of lipid extracts from unheated maize-fish powder mixes consisting of 90% Lake Trout and 10% maize (A) and 10% Lake Trout and 90% maize (B). Cn:x are fatty acids with carbon length n and number of unsaturations x; br are branched-chain acids; IS is internal standard (n-hexatriacontane). Gas chromatograms of lipid extracts from heated maize-fish powder mixes consisting of 90% Chain Pickerel and 10% maize (A) and 10% Chain Pickerel and 90% maize (B). Cn:x are fatty acids with carbon length n and number of unsaturations x; br are branched-chain acids; APFA Cx are ω‐(o‐alkylphenyl) alkanoic acids with carbon length x.

Lake Trout and maize unheated powder mixture lipid and biomarker results.

Cx:y = fatty acids with carbon length x and number of unsaturations y (C18:1s and C18:2s are the sum of all isomers); br = branched chain acids; TMTD = 4,8,12‐trimethyltridecanoic acid, chol = cholesterol, stig = stigmasterol. aCalculated with mass balance equation.

Chain Pickerel and maize heated powder mixture lipid and biomarker results.

Cx:y = fatty acids with carbon length x and number of unsaturations y (C18:1s and C18:2s are the sum of all isomers); br = branched chain acids; APFA Cx = ω‐(o‐alkylphenyl) alkanoic acids with carbon length x; chol = cholesterol. aCalculated with mass balance equation. The presence of ω-(o-alkylphenyl)alkanoic acids with 18 and 20 carbon atoms, together with at least one of the three isoprenoid fatty acids (phytanic, pristanic or 4,8,12-tetramethyltridecanoic acid) have been established in the literature as the full set of molecular criteria needed for the identification of degraded aquatic products in archaeological residues [27,28]. These biomarkers are routinely recovered from prehistoric encrusted charred cooking residues (e.g., [19-23]). Isoprenoid alkanoic acids (phytanic, pristanic or 4,8,12-TMTD) are at high concentration in freshwater and marine organisms, and positional alisomers of ω-(o-alkylphenyl)alkanoic acids with 16–22 carbon atoms are produced through the protracted heating of polyunsaturated fatty acids present in aquatic organisms at temperatures of at least 270°C [28]. Polyunsaturated fatty acids degrade easily and are thus unlikely to survive in organic residues from archaeological pottery. However, clays can act as an acid or base catalyzing agent and thereby promote the isomerization of double bonds involved in the formation of ω-(o-alkylphenyl)alkanoic acids [27,28]. The latter are more stable compounds and offer a reliable means of detecting the processing of commodities containing unsaturated fatty acids. Because vegetable oils are also rich in C18 triunsaturated alkanoic acids, only residues containing both the C18 and C20 ω-(o-alkylphenyl)alkanoic acids are indicators of aquatic lipid residues. In this experiment, we were able to confirm the formation of ω-(o-alkylphenyl)alkanoic acids with 16–20 carbon atoms when food sources containing unsaturated fatty acids are exposed to prolonged and intense heating (270°C for 17 hours) in the presence of a clay matrix. Analysis of single ingredients (e.g., dried maize, dried Chain Pickerel, and dried Lake Trout) confirmed that degraded aquatic and plant oils cannot be distinguished based on the presence of ω-(o-alkylphenyl)octadecanoic acids alone (Table 9), although Fig 7 suggests that maize and freshwater fish may contain varying proportions of different ω-(o-alkylphenyl)octadecanoic acid isomers, defined by the length of the alkyl side chain.
Table 9

Single resource heated lipid and biomarker results.

Cx:y = fatty acids with carbon length x and number of unsaturations y (C18:1s and C18:2s are the sum of all isomers); br = branched chain acids; TMTD = 4,8,12‐trimethyltridecanoic acid; APFA Cx = ω‐(o‐alkylphenyl) alkanoic acids with carbon length x.

CompoundsMaizeChain PickerelLake Trout
Fatty Acids (relative %)C120.000.00trace
C130.000.00trace
C140.001.934.76
C15br0.000.702.03
C150.004.958.79
C16:10.002.603.11
C1638.4127.8729.43
C17br0.002.723.82
C170.001.491.86
C18:2s1.980.000.00
C18:1s22.9916.1518.77
C1812.2613.3812.80
C20:10.001.312.53
C203.740.751.15
C22:10.00trace0.55
C223.12trace0.40
C230.000.00trace
C24:10.002.950.79
C240.000.63trace
BiomarkersTMTDTMTD
phytanicphytanic
APFA C18APFA C18APFA C18
APFA C20APFA C20
CholChol
Fig 7

Partial m/z 105 ion chromatograms showing ω-(o-alkylphenyl)alkanoicacids with 16(+), 18(*), and 20(#) carbon atoms in heated samples containing lake trout (A), chain pickerel (B) and maize (C).

Partial m/z 105 ion chromatograms showing ω-(o-alkylphenyl)alkanoicacids with 16(+), 18(*), and 20(#) carbon atoms in heated samples containing lake trout (A), chain pickerel (B) and maize (C).

Single resource heated lipid and biomarker results.

Cx:y = fatty acids with carbon length x and number of unsaturations y (C18:1s and C18:2s are the sum of all isomers); br = branched chain acids; TMTD = 4,8,12‐trimethyltridecanoic acid; APFA Cx = ω‐(o‐alkylphenyl) alkanoic acids with carbon length x. Significantly, the complete set of aquatic biomarkers, specifically ω-(o-alkylphenyl)alkanoic acids with 18 and 20 carbon atoms and two isoprenoid alkanoic acids (phytanic acid and 4,8,12-tetramethyltridecanoic acid) were detected in all heated maize-fish powder samples. Interestingly, 4,8,12-TMTD was also detected in all unheated Lake Trout-maize samples, even when the raw fish represented as little as 10% of the mixture. Cholesterol, sometimes in combination with its oxidation products, was also identified in all unheated Lake Trout-maize powder mixes, which also contain stigmasterol when maize composed over 60% of the mixture. In heated samples, however, cholesterol bi-products were not detected when raw Chain Pickerel represented less than 30% of the mixture. In sum, in this experiment the full set of aquatic biomarkers (i.e., ω-(o-alkylphenyl)alkanoic acids with 18 and 20 carbon atoms two isoprenoid fatty acids) was present in all samples, even when raw fish represented as little as 10% of the mixture. Of note is that our results suggest that these biomarkers may be present in a residue without a statistically significant FRO.

Discussion and conclusions

Potential problems with 14C ages on charred cooking residues encrusted on pottery resulting from the presence of ancient carbon from aquatic resources has drawn considerable attention over the last decade and a half. This has been particularly true in northern Europe but has also been identified as a potential problem in other regions [42]. Most often concerns are raised when 14C ages obtained on residues are older than those obtained on terrestrial resource remains recovered from the same archaeological contexts as the radiocarbon-dated residues. A more parsimonious methodology would be to determine if C from fish is present in residues where the possibility of an FRE for the location and time in question has been established through independent lines of evidence (e.g., dates on fish remains, lake sediment analyses). Laboratory work has identified specific biomarkers for aquatic resources that can be extracted from absorbed and encrusted residues [6]. However, empirical work has not been done to establish how much fish needed to have been cooked in a pot to contribute sufficient ancient carbon to residue formation to produce statistically significant FROs and result in the presence of aquatic biomarkers. Our goals here were to provide preliminary assessments of these issues. Our results indicate that there is a very high positive correlation between the percentage of C from fish in residues and FROs. However, there is no such direct relationship between the fraction of raw fish cooked in a pot and the fraction of fish C in the residue. Statistically significant FROs may occur when fish constitute <1% of the raw resource mix, but may also not occur until fish represent over 90% of raw resources depending on the resource(s) with which it was cooked and the size of the 14C age error. Our results also indicate that the complete sets of biomarkers, in this case the presence of ω-(o-alkylphenyl)alkanoic acids with 18 and 20 carbon atoms and phytanic acid, may be detected when fish C contributes little to residue formation. Thus, it is possible for aquatic biomarkers to be identified in a residue in the absence of a statistically significant FRO when a freshwater reservoir effect was present. This in turn emphasizes the need to assess the potential for ancient carbon reservoirs for specific periods of time in question prior to considering charred, encrusted residues for radiocarbon dating. Contemporary water chemistry and aquatic organisms are not adequate analogues for prehistoric reservoirs because modern land practices have significant effects on freshwater reservoirs [43]. Moreover, our results demonstrate compound-specific14C analysis (CSRA) could also be applied to issues surrounding FROs from charred cooking residues. To date, applications of CSRA to pottery residues have targeted C16:0 and C18:0 fatty acids, which typically are the most abundant fatty acids preserved in potsherds [4,5,44]. Recent advances in preparative gas chromatography (PGC), however, have decreased sample size requirements and opened the door to dating and comparing ages associated with a wider range of discrete biomarkers [45].
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