Why Date Shell?

Given that archaeologists now commonly date short-lived plant remains in order to generate local ΔR values (e.g., Kennedy et al. Reference Kennedy, Russell and Guilderson2005), why continue to date marine shell at all? In many cases the answer is one of expediency, shell often being the most abundant datable material in coastal archaeological deposits. For example, Gifford (Reference Gifford1916) estimated that the shell mounds in San Francisco Bay were 56% shell by weight, but that charcoal fragments accounted for only 0.2%. The ubiquity and abundance of shell is particularly relevant in large-scale reconnaissance and survey projects, where the aim is to quickly document shell midden sites that are actively eroding or being inundated by rising seas. Archaeological surveys of Chesapeake Bay (Reeder-Myers and Rick Reference Reeder-Myers and Rick2019) and the coastal Florida Everglades (Schwadron Reference Schwadron2017), for example, relied on oyster shells—easily recovered from eroding shorelines or from small test excavations—to facilitate rapid, large-scale sampling in order to develop chronologies of at-risk archaeological resources. In addition, ages on shell may be more readily tied to cultural activities, such as studies focused on shellfishing practices or the timing and tempo of the construction of shell-built environments (e.g., Macario et al. Reference Macario, Souza, Trindade, Decco, Lima, Aguilera and Marques2014; Martindale et al. Reference Martindale, Cook, McKechnie, Edinborough, Hutchinson, Eldridge, Supernant and Ames2018; Schwadron Reference Schwadron2017; Thompson et al. Reference Thompson, Marquardt, Cherkinsky, Roberts Thompson, Walker, Newsom and Savarese2016).

Alternative materials for dating are not only comparatively rare in coastal archaeology but do not necessarily produce more accurate dates (Thomas Reference Thomas2008). For example, wood charcoal dates often are older than their archaeological context (“old-wood” effects; Bronk Ramsey Reference Bronk Ramsey2009; Dee and Bronk Ramsey Reference Dee and Ramsey2014). Terrestrial animals that consume marine organisms, including humans, are subject to MRE, whereas dates on freshwater organisms from carbonate terrains need to be corrected for “hardwater effects”—the freshwater analog of MRE (Philippsen Reference Philippsen2013). No material type is without problems.

Last, shell carbonate is one of the easiest materials to date in terms of sample chemistry, even by the earliest conventional methods (e.g., Libby et al. Reference Libby, Anderson and Arnold1949; see Lindauer et al. [Reference Lindauer, Hadden, Macario and Guilderson2021] for an overview of the history of research on ¹⁴C in marine carbonates). Strategies for diagenetic screening and chemical pretreatment typically are more straightforward for shell carbonate (e.g., Brock et al. Reference Brock, Higham, Ditchfield and Ramsey2010), making it a more economical option compared to other materials. For some applications, ¹⁴C can even be measured in carbonate directly, without conversion to CO₂ or graphite (Bush et al. Reference Bush, Santos, Xu, Southon, Thiagarajan, Hines and Adkins2013).

Reservoir Age of the Global Ocean and the Need for a Marine Calibration Curve

¹⁴C is part of the global carbon cycle: the mechanical, chemical, and biological processes that move carbon atoms between the atmosphere, ocean, and biosphere. Some processes are fast and others slow, giving rise to differences in carbon turnover rates and residence times, and consequently, differences in the concentration of ¹⁴C among the various reservoirs. Here, we briefly review some important characteristics of the marine ¹⁴C cycle (Figure 2). We direct the reader to Alves and colleagues (Reference Alves, Macario, Ascough and Ramsey2018) for a detailed review of global marine ¹⁴C storage and fluxes.

Figure 2. Potential influences on and sources of ¹⁴C to marine mollusk shells. (Figure by Ian Hutchinson.) (Color online)

¹⁴C atoms are created from ¹⁴N atoms by neutron bombardment in the upper atmosphere and are rapidly oxidized to ¹⁴CO₂ in the lower atmosphere. Atmospheric ¹⁴CO₂ is introduced to the terrestrial biosphere via photosynthesis. Dead terrestrial biomass (detritus or soil organic matter) may be transported by wind or water to the surface ocean, contributing “old” (¹⁴C-depleted) carbon to marine dissolved organic carbon (DOC) and particulate organic carbon (POC) pools. Atmospheric ¹⁴CO₂ also diffuses directly from the atmosphere to the surface layer of the ocean. Some is converted to plankton biomass via photosynthesis; some remains as dissolved inorganic carbon (DIC), the form of carbon from which marine mollusks build their carbonate shells. Dead marine organisms sink to the deep ocean, where carbon atoms can remain for millennia before gradually circulating back to the surface as ¹⁴C-depleted DIC. The net effect is that the global ocean has proportionally less ¹⁴C (relative to the stable isotopes, ¹²C and ¹³C) than the atmosphere and terrestrial biosphere, as do all the organisms that incorporate carbon from the ocean into their tissues.

The foundation of the ¹⁴C dating technique is that the concentration of ¹⁴C declines in an organism's tissues at a predictable rate after its death. Because marine organisms have less ¹⁴C to begin with, their ¹⁴C clocks have a “head start” compared to terrestrial organisms, typically appearing several hundred ¹⁴C years older than terrestrial samples of the same calendar age. This gives rise to the need for a marine-specific ¹⁴C calibration curve. Where the terrestrial calibration curve accounts primarily for variation in ¹⁴C production, the marine calibration curve also accounts for carbon exchange between the atmosphere and the ocean.

The first marine calibration curve was published by Stuiver and colleagues in 1986, and it has been updated several times with additional datasets and more complex models of carbon circulation to more accurately describe the variability in marine radiocarbon dynamics throughout the radiocarbon record (Heaton et al. Reference Heaton, Köhler, Butzin, Bard, Reimer, Austin and Ramsey2020; Hughen et al. Reference Hughen, Baillie, Bard, Warren Beck, Bertrand, Blackwell and Buck2004; Reimer et al. Reference Reimer, Baillie, Bard, Bayliss, Warren Beck, Blackwell and Ramsey2009, Reference Reimer, Bard, Bayliss, Warren Beck, Blackwell, Ramsey and Buck2013; Stuiver and Braziunas Reference Stuiver and Braziunas1993; Stuiver et al. Reference Stuiver, Reimer and Braziunas1998). The current marine calibration curve, Marine20 (Heaton et al. Reference Heaton, Köhler, Butzin, Bard, Reimer, Austin and Ramsey2020), is based on simulations with an ocean-atmosphere-biosphere box-model of the global carbon cycle, and it incorporates updated information about variability in atmospheric ¹⁴C (i.e., IntCal20) and CO₂. The revised estimate for the rate of CO₂ diffusion is significantly slower than was estimated in earlier curves, meaning that the global-average marine reservoir age is greater than previously thought. The result is in an upward shift of Marine20 compared to previous marine calibration curves (Figure 3).

Figure 3. Relationships among the marine and atmospheric calibration curves, reservoir ages, and ΔR, with comparisons of estimated values based on the 2013 and 2020 calibration curves: (A) calculation of a local marine reservoir age from a hypothetical known-age marine sample; (B) visualization of global marine reservoir age with respect to atmosphere; (C) calculation of a hypothetical ΔR value from a known-age marine sample; and (D) example of a marine radiocarbon date calibrated using Marine13 versus Marine20, with updated ΔR values. (Figure by Carla S. Hadden.)

Some essential concepts associated with marine calibration are reviewed in Figure 3, using the 50–550 cal AD interval as an example. The degree of ¹⁴C depletion of a body of water compared to the atmosphere is known as its “reservoir age” (R), measured in ¹⁴C years. The reservoir age of a local body of marine water (e.g., a bay, lagoon, or portion of a coastline) is calculated from the ¹⁴C age of a local marine sample (e.g., shell carbonate) whose true calendar age is known independently. The local reservoir age is simply the difference between this measured ¹⁴C age and the expected ¹⁴C age for that calendar year, based on the atmospheric IntCal dataset (Reimer et al. Reference Reimer, Bard, Bayliss, Warren Beck, Blackwell, Ramsey and Buck2013, Reference Reimer, Austin, Bard, Bayliss, Blackwell, Ramsey and Butzin2020; Figure 3A). In contrast, the global marine reservoir age represents the average ¹⁴C offset between the atmosphere and the global average surface ocean at a point in time; it is the offset between the Marine and IntCal calibration curves in ¹⁴C years (Figure 3B).

ΔR: Local Offsets from the Global Ocean Reservoir Age

Differences in coastal geomorphology, ocean circulation, upwelling, and source-water chemistry produce localized deviations in ¹⁴C concentration compared to the global-average ocean. In addition, variations in mollusk habitats, feeding strategies, and growth rates may occur over small spatial and temporal scales. These and other sources of variability give rise to the need for local (ideally, species-specific) correction factors, termed ΔR, which are used in conjunction with the marine calibration curve to calibrate marine shell dates accurately.

ΔR estimates represent localized offsets from the global marine calibration curve (Figure 3C); they account for differences between local (Figure 3A) and global (Figure 3B) marine reservoir ages. Equivalently, ΔR estimates are calculated as the difference between the measured ¹⁴C age of a local marine sample whose true calendar age is known independently and the expected ¹⁴C age for that year as determined from the marine calibration dataset. “Local” in this usage represents regions of the ocean, or even species within those regions, where the many variables at work produce areas of similar ¹⁴C values. These can vary considerably across the globe and over time.

Because the marine calibration curve functions as the baseline for comparison, all ΔR values are necessarily specific to the version of the calibration curve that was used as the reference point. As updated marine calibration curves are released, existing ΔR values must be recalculated based on the new calibration curve. In general, the upward shift of the Marine20 curve compared to Marine13 (i.e., the larger global reservoir age) resulted in a shift toward lower ΔR values (see Figure 3C for a comparison of a ΔR value calculated using Marine13 versus Marine20). Calibrating a shell date using the new calibration curve and updated ΔR results in relatively minor differences in the calibrated date compared to using the old curve with the older ΔR (see Figure 3D for a comparison)—the changes to the former being largely canceled out by changes to the latter. On the other hand, combining an old ΔR with the new curve (or vice versa) would lead to an erroneous calibrated age, potentially wrong by a century or more.

A common mistake is to calibrate a shell date without specifying a ΔR value, which has the same effect as specifying that ΔR = 0 ± 0—a bold and likely wrong assumption that will lead to erroneous calibrated ages and problematic chronologies. First, the “global average ocean” is not a real location on Earth. By default, archaeologists should assume that every real place is offset from the global average, and that an estimate for ΔR is necessary. Second, a shell date calibrated without a ΔR value (i.e., ΔR = 0) would appear 100–200 years older if calibrated using the Marine13 curve compared to the same date calibrated using the Marine20 curve. Again, this curve-dependent offset is largely canceled out when appropriate, updated ΔR values are applied (see Figure 3D).

Published ΔR values derived from known-age shells, mostly dating to the nineteenth and early twentieth centuries, are compiled in the global marine reservoir database (calib.org/marine), accessible via mapping software (Reimer and Reimer Reference Reimer and Reimer2001). Conveniently, all ΔR values in the global marine reservoir database have been updated with respect to Marine20 and should only be used with the Marine20 curve. Note that although the database is an invaluable resource to coastal archaeologists, ¹⁴C dynamics change over time (as discussed in the following section). Consequently, ΔR values in the database may not be accurate for the more distant past—a source of additional uncertainty.

Sources of Variability in ΔR

Some of the major sources of regional variability that give rise to local reservoir age offsets are described below. The specific cases mentioned in this section are intended to demonstrate just some of the many ways that localized processes can impart localized ¹⁴C signatures on marine fauna. The goal is not a comprehensive predictive guide but rather an overview of some sources of variability that may complicate shell dates in their geographic region of interest.

Strategies for Estimating ΔR

Archaeologists need not quantitatively evaluate every single variable influencing local ΔR values. Rather, ΔR is estimated by measuring the net effect of all variables on a species at a given place and time, accounting for multiple sources of variability by calculating an appropriate measure of uncertainty. This involves measuring the ¹⁴C concentration of known-age marine materials and comparing the measured ages to expected ages, using the ¹⁴C calibration curves as a baseline for comparison (see Figure 3C). The relationship is often generalized in the literature as

$$\Delta {\rm R} = P - Q$$

where P is the measured conventional ¹⁴C age of a marine sample whose true calendar age is known, and Q is the expected ¹⁴C age for that calendar year according to the marine calibration curve (currently Marine20). The latter can be accessed as text files via http://intcal.qub.ac.uk and OxCal software. ΔR values based on earlier curves are updated by changing Q—the expected ¹⁴C date—based on the latest marine curve.

Estimates of ΔR rely on ¹⁴C measurements of marine materials whose age is known independently. Three general approaches for estimating ΔR are discussed here: (1) measuring the ¹⁴C age of known-age “pre-bomb” marine carbonates (e.g., live-collected museum specimens), (2) measuring the ¹⁴C ages of pairs of marine and terrestrial samples that are of unknown age but are assumed to be contemporaneous (Ascough et al. Reference Ascough, Cook and Dugmore2005), and (3) estimating from Bayesian chronological modeling.

Marine–Terrestrial Sample Pairs

Local marine reservoir offsets can be estimated from archaeological materials directly, without relying on materials whose age is known precisely, by comparing the measured ¹⁴C ages of pairs of marine and terrestrial archaeological specimens that are assumed to be the same age (Ascough et al. Reference Ascough, Cook and Dugmore2005; Southon et al. Reference Southon, Rodman and True1995). Typically, archaeologists target shells and seed or wood-charcoal samples from the same deposit (e.g., Schmuck et al. Reference Schmuck, Reuther, Baichtal and Carlson2021) or archaeological feature (e.g., Hadden and Cherkinsky Reference Hadden and Cherkinsky2017b) for sampling.

ΔR calculation is slightly more complicated in this case, but, as with pre-bomb shells, P is the measured ¹⁴C age of the marine sample. Q, the expected age, is calculated in three steps: (1) the ¹⁴C age of the contemporaneous terrestrial sample is measured and (2) calibrated with the IntCal calibration curve to determine the calendar age, and (3) the calendar age is reverse calibrated with the marine calibration curve (Figure 4). The reverse-calibrated marine age (Q) and resulting ΔR usually do not follow a Normal (Gaussian) distribution. Reimer and Reimer (Reference Reimer and Reimer2017) developed a ΔR calculator (http://calib.org/JS/JSdeltar20/) to simplify this calculation. Their solution uses a convolution integral—an integral that expresses the amount of overlap of one function as it is shifted over another function—to determine a confidence interval for the offset between the observed and expected values. The result is approximated as a Normal distribution, which allows for a simpler estimation of uncertainty.

Figure 4. Simplified overview of calculating ΔR from paired marine and terrestrial samples, where Q—the marine expected age—is estimated as follows: (1) the radiocarbon age of the terrestrial sample is measured, (2) the terrestrial date is calibrated with the IntCal calibration curve, and (3) the resulting calendar age is reverse calibrated with the marine calibration curve. (Figure by Carla S. Hadden.) (Color online)

ΔR estimates derived from paired samples generally are less precise (i.e., larger uncertainty terms) than those from pre-bomb shells (see Figure 5 for an extreme example), not only because the ¹⁴C ages of both the shell and the charcoal samples are inherently uncertain but also because their absolute contemporaneity usually cannot be independently established. For this reason, ΔR values estimated using this approach are excluded from the global marine reservoir database. Extreme variation in ΔR values among paired samples, as demonstrated in Figure 5, are likely the products of stratigraphic disturbance; the samples were incorrectly assumed to be contemporaneous.

Figure 5. Probability density functions (100-year bins) of ΔR values derived from 15 late Holocene shell–wood pairs from five archaeological sites in Puget Sound (Washington State; Deo et al. Reference Deo, Stone and Stein2004; ΔR recalculated with Marine20) and pre-bomb shells from 15 sites in Puget Sound and adjacent waters (calib.org/marine). (Figure by Ian Hutchinson.)

Like their pre-bomb counterparts, regional ΔR values derived from shell-wood pairs are specific to a time period. Attempts to quantify temporal variation in ΔR requires dating shell-wood pairs from a range of chronological contexts (e.g., Deo et al. Reference Deo, Stone and Stein2004), abetted and constrained, perhaps, by ΔR values from nonarchaeological data sources (e.g., Jazwa and Rosencrance Reference Jazwa and Rosencrance2019; Thakar Reference Thakar2014).

Regional ΔR Values and Uncertainty

A ΔR value derived from a single known-age shell date or marine–terrestrial pair does not provide a statistically robust estimate of ΔR value for the region/population of interest (Cook et al. Reference Cook, Ascough, Bonsall, Derek Hamilton, Russell, Sayle, Marian Scott and Bownes2015; Martindale et al. Reference Martindale, Cook, McKechnie, Edinborough, Hutchinson, Eldridge, Supernant and Ames2018). We join with Heinemann and colleagues who, commenting on a parallel research problem, noted that shell carbonate

can only be used as a proxy archive if the combination of environmental conditions and the major contribution of biology are considered. Therefore, the data stress the importance of replicating at the biological level, i.e., measure several animals from the same location and time, even though this drastically increases the measuring effort [Heinemann et al. Reference Heinemann, Hiebenthal, Fietzke, Eisenhauer and Wahl2011:7].

In addition to real variability in ΔR due to environment and biology, Cook and colleagues (Ascough et al. Reference Ascough, Cook, Church, Dugmore, McGovern, Dunbar, Frioriksson and Gestsdóttir2007; Cook et al. Reference Cook, Ascough, Bonsall, Derek Hamilton, Russell, Sayle, Marian Scott and Bownes2015; Russell et al. Reference Russell, Cook, Ascough, Marian Scott and Dugmore2011) argue that the implicit assumption of contemporaneity may lead to substantial errors, despite stringent precautionary measures to minimize spurious associations. Cook and colleagues (Reference Cook, Ascough, Bonsall, Derek Hamilton, Russell, Sayle, Marian Scott and Bownes2015) recommend that typically four marine-sourced materials and four contemporaneous terrestrial materials be dated from a stratigraphic unit, resulting in 16 individual ΔR values calculated pairwise, to calculate the average ΔR for a particular site or region. Fewer samples may be sufficient, or more samples may be necessary, depending on the size of the study area and the complexity of ¹⁴C dynamics therein. Replicate sampling adds considerably to the expense of the investigation but increases confidence in the resultant ΔR value and, therefore, the archaeological chronology (Martindale et al. Reference Martindale, Cook, McKechnie, Edinborough, Hutchinson, Eldridge, Supernant and Ames2018).

Chi-squared (χ²) tests as described by Ward and Wilson (Reference Ward and Wilson1978) are frequently used in ΔR research to test for homogeneity of replicate samples within a dataset. For example, Rick and colleagues (Reference Rick, Henkes, Lowery, Colman and Culleton2012) utilized the χ² test to evaluate whether individual ΔR values calculated from known-age pre-bomb museum specimens were similar throughout Chesapeake Bay and therefore could be combined to calculate a regional average ΔR, or whether subregional averages were necessary. Cook and colleagues (Reference Cook, Ascough, Bonsall, Derek Hamilton, Russell, Sayle, Marian Scott and Bownes2015) recommend using χ² tests with the paired-sample approach to verify that archaeological samples of the same material type are contemporaneous—and removing those that are not—prior to calculating ΔR. Schmuck and colleagues (Reference Schmuck, Reuther, Baichtal and Carlson2021), however, caution against the arbitrary removal of outliers, arguing that to do so sacrifices accuracy for the sake of precision. Although outliers that are obviously related to errors in measurement or context should be identified and removed, they argue that many outliers reflect real variability in animal biology or the environment and should be included in regional average ΔR estimates.

To calculate a regional or site-level average ΔR, the pooled mean (μ) of replicate samples generally is used:

$$\mu = \displaystyle{{\mathop \sum \nolimits_i \displaystyle{{\Delta R_i} \over {\sigma _i^2 }}} \over {\mathop \sum \nolimits_i \displaystyle{1 \over {\sigma _i^2 }}}}$$

where ΔR_i and σ _i are the individual ΔR values calculated for known-age samples or sample pairs and their individual uncertainties (based on Ward and Wilson's [Reference Ward and Wilson1978] method for combining ¹⁴C dates; see also Reimer and Reimer Reference Reimer and Reimer2001).

There are many methods for calculating the uncertainty for an average ΔR value, summarized by Alves and colleagues (Reference Alves, Macario, Ascough and Ramsey2018:Equations 13–16). Care must be exercised to ensure that an appropriate method for calculating uncertainty is applied for regional ΔR estimates derived from multiple individual animals or sample pairs. Reimer and Reimer (Reference Reimer and Reimer2001), citing Bevington (Reference Bevington1969), report uncertainty as the maximum of the weighted uncertainty in the mean of ΔR

$$\sigma _\mu = \sqrt {\displaystyle{1 \over {\mathop \sum \nolimits_i \displaystyle{1 \over {\sigma _i^2 }}}}} $$

and the standard deviation of ΔR

$$\sigma _w = \sqrt {\displaystyle{{\displaystyle{1 \over {n-1}}\mathop \sum \nolimits_i {\left({\displaystyle{{\Delta R_i-\;\mu } \over {\sigma_i}}} \right)}^2} \over {\displaystyle{1 \over n}\mathop \sum \nolimits_i \displaystyle{1 \over {\sigma _i^2 }}}}} \;.$$

Cook and colleagues (Reference Cook, Ascough, Bonsall, Derek Hamilton, Russell, Sayle, Marian Scott and Bownes2015) recommend the standard error for predicted values of ΔR, calculated as

$$\sigma = \sqrt {\sigma _\mu ^2 + \sigma _w^2 }\,.$$

The weighted uncertainty in the mean tends to decrease as the number of measurements increases, regardless of the dispersion and variance of the individual measurements. The weighted uncertainty may be appropriate if the individual ΔR values are statistically identical (i.e., they pass a χ² test). Otherwise, it tends to overestimate certainty and precision of the regional average ΔR. In contrast, the standard deviation and the standard error for predicted values of ΔR both account for the variance in the dataset. These tend to result in larger measures of uncertainty but better reflect the range of variability that might influence the ¹⁴C content of an archaeological assemblage of shells. The standard deviation and the standard error for predicted values usually produce comparable results (Schmuck et al. Reference Schmuck, Reuther, Baichtal and Carlson2021).

The goal in selecting a method for estimating uncertainty is not necessarily to calculate the smallest possible value. Rather, it is to ensure that the uncertainty term on a regional ΔR value adequately reflects the range of variability in ΔR over space and time. In practice, this means that a larger, more conservative uncertainty term is likely to produce a more accurate, albeit less precise, calibrated date for a sample of unknown age. In contrast, a smaller uncertainty term may result in a more precise calibrated age, but one that may not be accurate. When determining an appropriate measure of uncertainty for a regional average ΔR, often two measures of uncertainty are compared—such as the standard deviation and the weighted uncertainty—and the greater of the two values is used (e.g., Reimer and Reimer Reference Reimer and Reimer2001; Rick et al. Reference Rick, Henkes, Lowery, Colman and Culleton2012).

Issues of Archaeological Context

A ¹⁴C date on a wooden artifact, or charcoal from a hearth, reflects the time at which atmospheric carbon was permanently assimilated into the wood of the tree—not the year the tree was felled, when the timber was used, or when the wood was burned (Schiffer Reference Schiffer1986). Each tree ring represents a single year of growth, and many species have long lifespans. Therefore, different regions of the tree will yield different ¹⁴C ages. Often, ¹⁴C dates on wood are at least slightly older than their archaeological context (Dee and Bronk Ramsey Reference Dee and Ramsey2014). The potential for an “inbuilt age” of living wood, combined with the fact that wood could be used by people long after the death of the tree, is commonly referred to as the “old wood” problem.

Archaeological mollusks have an analogous problem: “old shell.” Like trees, marine mollusks grow incrementally and are potentially long lived, and different regions of a shell yield different ¹⁴C ages (e.g., Hadden and Cherkinsky Reference Hadden and Cherkinsky2017b; Kilada et al. Reference Kilada, Campana and Roddick2007). However, most shellfish gathered by Indigenous peoples on the shores of North America were relatively young individuals, typically under 20 years old (e.g., Cannon and Burchell Reference Cannon and Burchell2009). More problematically, archaeological deposits may include shells that predate the event of interest, such as reworked midden deposits, curated/heirloom shell objects, or “dead collected” shells (e.g., Edinborough et al. Reference Edinborough, Martindale, Cook, Supernant and Ames2016; Martindale et al. Reference Martindale, Letham, McLaren, Archer, Burchell and Schöne2009; Thompson et al. Reference Thompson, Marquardt, Cherkinsky, Roberts Thompson, Walker, Newsom and Savarese2016).

The archaeological record is “a massive palimpsest of derivatives from many separate episodes” (Binford Reference Binford1981:197). Resolving separate episodes is rarely possible, except at a very coarse chronological resolution. This, combined with the “old wood” and “old shell” problems, limits the accuracy and precision of ΔR values derived from archaeological samples because the paired-sample approach relies on the assumption that the samples are contemporaneous. If, for example, the wood charcoal was actually 50 years older than the shell with which it is “paired,” the resultant ΔR estimate would be off by 50 years. Culleton and colleagues (Reference Culleton, Kennett, Lynn Ingram, Erlandson and Southon2006) suggest averaging out the ¹⁴C variability within shells by sampling across multiple increments, analogous to dating bulk charcoal. Given that the trees may have lifespans that are an order of magnitude greater than those of harvested mollusks, the difference in time averaging represented by the two bulk samples may introduce additional error. Ideally, paired samples should be from secure contexts, and they should represent short periods of growth—for example, charcoal from seeds or twigs paired with juvenile, live-collected shells.

Last, selecting and applying an “appropriate” value for ΔR (and its uncertainty) introduces subjectivity to the dating process. Different assumptions about the origin of the shell and the ¹⁴C dynamics in the source water will alter the calibrated age. For marine-shell trade goods, such as beads, the potential source region may span hundreds of kilometers of coastline (e.g., Hadden et al. Reference Hadden, Cherkinsky, Smith, Ollivier and Pan2017). Even in cases where shellfish are assumed to have been harvested locally, ΔR can vary significantly within even small estuaries (Hadden and Cherkinsky Reference Hadden and Cherkinsky2017a). The archaeologist's choices about whether and how to incorporate this information directly impact the accuracy and precision of the resulting calibrated date.

Practically speaking, in most cases, marine shell dates are accurate within a few centuries. In some applications, such as regional reconnaissance surveys (e.g., Reeder-Myers and Rick Reference Reeder-Myers and Rick2019; Schwadron Reference Schwadron2017), this scale of chronological resolution is adequate (Martindale et al. Reference Martindale, Marsden, Patton, Ruggles, Letham, Supernant, Archer, McLaren and Ames2017). However, the palimpsest nature of shell midden sites, combined with the inherently limited resolution of archaeological chronologies derived from shell, limits the types and time scales of observable human behaviors (Bailey Reference Bailey2007). Century-scale patterns often can be ascertained from marine shell dates. Chronologies on the human generational scale are rare but possible (e.g., Letham et al. Reference Letham, Martindale, McLaren, Brown, Ames, Archer and Marsden2015). Attempts to resolve cultural phenomena at finer scales from shell dates alone, even with high-precision Bayesian modeling, warrant skepticism.

Concluding Remarks

Marine shell is commonly the most abundant material excavated in coastal North American archaeology and one of the most readily available materials for ¹⁴C dating in those contexts. However, building reliable archaeological chronologies from marine shell dates is fraught with challenges. Although we are of the opinion that a healthy skepticism of shell dates is warranted, we argue that the challenges are rarely insurmountable. To that end, we offer the following words of advice to the coastal archaeologist:

• • Always publish measured ¹⁴C ages and associated data (e.g., taxonomic information), not just calibrated age ranges, to allow comparison with previously published sources and to facilitate future recalibration efforts. This is true both for marine reservoir datasets and for cultural chronologies.

• • (Re)calibrate shell dates using the latest curve, especially when comparing new and old datasets. Beware that comparing shell dates calibrated with different curves may introduce systematic offsets if ΔR values are not updated.

• • ΔR values are calibration-curve specific. Old ΔR values must be updated for use with new calibration curves. All ΔR values in the global marine reservoir database (calib.org/marine) have been updated with respect to Marine20 and should only be used with the Marine20 curve. ΔR estimates obtained from other sources must be recalculated manually prior to use with the new curve.

• • The “global average ocean,” where ΔR = 0 by definition, is not a real place. Assume that a local offset exists in your region and that a ΔR value is necessary to accurately calibrate your marine shell dates.

• • Use replicate samples to calculate regional average ΔR values. Sample size depends on the heterogeneity ¹⁴C in the marine environment. A ΔR value from a single marine–terrestrial pair or known-age shell date is not a statistically robust estimate of a regional ΔR.

• • Many methods exist for calculating uncertainty for regional average ΔR values. The goal is to select one that adequately reflects the range of variability in ΔR over space and time. Accuracy is more important than precision. We recommend the standard deviation or the standard error for predicted values of ΔR in most cases.

• • Calibrated shell dates are inherently less precise than most terrestrial dates due to uncertainty in ΔR. This limits the types and time scales of observable human behaviors. The research question should guide the sampling strategy.

• • Decisions about the “appropriate” value for ΔR (and its uncertainty) introduces subjectivity to the dating process. These decisions may have unintended consequences.

Beyond coastal archaeology, the issues raised here about dating marine shell should prompt all archaeologists to think critically about chronology building, sample selection, and calibration. Other material types have similar or analogous issues: hardwater reservoir effects in freshwater systems (Philippsen Reference Philippsen2013), mixed and variable carbon sources in terrestrial animal tissues (Cramb and Hadden Reference Cramb and Hadden2020), and even offsets in terrestrial plants related to growing seasons (Manning et al. Reference Manning, Kromer, Cremaschi, Dee, Friedrich, Griggs and Hadden2020) introduce uncertainty in the ¹⁴C record. As archaeologists demand ever greater precision from ¹⁴C chronologies, understanding the nuances of ¹⁴C dynamics becomes increasingly important.