Depending on the sensitivity of the isotope ratio mass spectrometer (IRMS) used, there is a minimum mass of C and N required for accurate and precise isotope measurements. Uncharred and charred cereal grains comprise relatively high %C and relatively low %N, giving rise to relatively high C:N atomic ratios (Table 2). This means that it can be difficult to simultaneously determine the δ¹³C and δ¹⁵N values of a cereal grain without either having too little N or overloading the IRMS with carbon dioxide. Even in elemental analyser (EA)-IRMS instruments where it is possible to dilute the carbon dioxide peak relative to the nitrogen gas peak, there is still a minimum quantity of plant material required to yield sufficient N for an accurate and precise δ¹⁵N value. As a result, single grain analysis of small-grained crops such as millets and pseudocereals is not yet practical due to their low mass.

Most studies that have analyzed crop stable isotope values in modern experimental and farm plots homogenized multiple grains randomly sampled from across the growing plot to average out isotopic variation among plants (e.g., Blanz et al., 2019; Bogaard et al., 2007; Christensen et al., 2022; Fraser et al., 2011; Kanstrup et al., 2011; Styring et al., 2019; Treasure et al., 2016; Wallace et al., 2013). If single archaeological grains are to be analyzed individually, however, a good grasp of the isotopic variability among individual grains growing in the same conditions is needed in order to know whether differences in isotope values are representative of meaningful differences in growing conditions and not just a result of isotopic variability within a single plant/plot.

Relatively few studies have determined the isotopic variability among individual grains/seeds within a single cereal ear/pulse pod, but those that have been conducted have combined standard deviations below 0.4‰ (Table 3). The pooled standard deviation of δ¹⁵N values of 21 individual cereal ears is 0.36‰, while the pooled standard deviation of δ¹³C values of 11 individual cereal ears is 0.25‰. The pooled standard deviation of δ¹⁵N values of 8 pulse pods is 0.22‰. This variability is similar to the analytical uncertainty of stable isotope measurements, which is generally ~0.2‰−0.3‰, and therefore random sampling of grains/pulses from different parts of a cereal ear or pulse pod is unlikely to contribute significantly to inter-grain/pulse isotopic variability. However, more research is needed to expand the taxa investigated and to consider seasonal variations in flowering and/or grain filling conditions of a single plant/plot.

Even fewer studies have determined the isotopic variability among individual grains/pulses within a cultivation plot. Those that have been conducted show that the pooled standard deviation in δ¹⁵N from 7 plots is 0.76‰ and the pooled standard deviation in δ¹³C from 11 plots is 0.30‰ (Table 4). There are indications that there is greater isotopic variability among cereal grains grown in manured plots because of spatial variability in manure application (Larsson et al., 2019). For this reason, nitrogen isotopic variability within plots is likely constrained by the isotopic difference between the applied soil amendment and endogenous soil nitrogen. Similarly, the intra-plot variability in plant δ¹³C values is likely constrained by surface water availability and light intensity, which will vary more in plots with diverse topographies, and presence of or proximity to water bodies and/or overhanging vegetation. These values of intra-plot isotopic variability should therefore be treated as rough guidelines that will likely vary by context.

While the main focus of isotopic studies of archaeological crop remains has been to provide insights into past agricultural practices such as watering and soil amendment, there are environmental and physiological factors which also affect plant δ¹³C and δ¹⁵N values. Stable δ¹³C values of plants are influenced by the ratio of leaf intercellular (c_i) to ambient (c_a) carbon dioxide concentrations (Farquhar et al., 1982b). In C₃ plants, this ratio is strongly affected by stomatal conductance and photosynthetic activity, which are in turn affected by water availability, soil salinity, and light intensity (Farquhar et al., 1989). When soil moisture levels decrease, stomatal conductance decreases, decreasing the c_i and resulting in less negative δ¹³C values. The δ¹³C values of C₃ plants are therefore negatively correlated with mean annual precipitation (e.g., Kohn, 2010) and water inputs in general—which could include irrigation—but other factors such as soil texture and organic matter content can affect soil water retention and also contribute to variability in crop δ¹³C values (Hudson, 1994). There is no straightforward relationship between water availability and the δ¹³C values of C₄ plants (Cernusak et al., 2013), but a number of studies have observed that the δ¹³C values of C₄ plants increase slightly with increased water availability (i.e., along a rainfall gradient; Schulze et al., 1996; Tieszen and Boutton, 1989), the opposite trend to that observed in C₃ plants. High soil salinity reduces the ability of plants to take up water, thereby increasing the δ¹³C values of plant tissues of both halophytic and non-halophytic C₃ species (Farquhar et al., 1982a), but decreasing the δ¹³C values of C₄ plants slightly (Omoto et al., 2012).

Light intensity is an additional factor that has been found to influence plant δ¹³C values, with plants growing in lower light levels having lower rates of photosynthesis, leading to higher c_i that results in lower δ¹³C values (Ehleringer et al., 1986, 1987). While most crops would be expected to have been cultivated in open plots and so would have been unaffected by low light intensity, if plots were situated in woodland clearings, there could be shading from surrounding vegetation for part of the day. This effect could be particularly apparent in tropical or semi-tropical environments with horticultural traditions and where rainforests can form particularly dense canopies. Furthermore, the grains of different plant taxa grown in the same environmental conditions have been observed to have different δ¹³C values, which is likely due to different timing of grain filling resulting in the δ¹³C values reflecting water availability at different times of the year (e.g., Araus et al., 1997; Wallace et al., 2013).

The δ¹⁵N values of plants are affected by the N isotopic composition of the soil in which they grow, which is influenced by the isotopic composition of any N inputs and by the loss of any N as a result of N cycling processes (e.g., Högberg, 1997). N can be added in the form of human/animal manure, bird guano, and/or composted organic matter, all of which tend to have relatively high δ¹⁵N values but can vary according to their source (see Szpak, 2014 for a compilation of the d¹⁵N values of different soil amendments). Soil properties may also moderate the isotopic effect of soil amendments, with an experimental study finding that similar inputs of biogas residues as fertilizer at two locations with different soil types resulted in very different δ¹⁵N values of cereal grains (Larsson et al., 2024). However, any process that favors the volatilisation of ¹⁵N-depleted N also drives an increase in the δ¹⁵N value of soil and plants (Handley et al., 1999). Such processes include aridity (e.g., Hartman and Danin, 2010), waterlogging (Finlay and Kendall, 2008), recent forest clearance by burning (Ehrmann et al., 2014), and high levels of organic N relative to plant demand (Craine et al., 2009). The presence and type of mycorrhizal associations also affect plant δ¹⁵N values (e.g., Craine et al., 2009) and plants growing in saline soils tend to have higher δ¹⁵N values than those growing in non-saline soils (Heaton, 1987). Each of these factors can result in isotopic variability that can confound interpretation of plant isotope values in terms of agricultural practice.

The majority of plant remains in temperate contexts are preserved by charring (Zohary et al., 2012, p. 10). Charring results in changes to crop seed δ¹³C and δ¹⁵N values, the degree of which varies with the crop species and the temperature and duration of heating (Aguilera et al., 2008; Fraser et al., 2013a; Hart and Feranec, 2020; Hartman et al., 2020; Nitsch et al., 2015; Poole et al., 2002; Stroud et al., 2023a; Styring et al., 2019; Varalli et al., 2023). While it is not possible to determine the exact conditions in which crop remains were charred from morphological or chemical investigation, it has been shown that heating between 230 and 300°C results in well preserved cereal grains that are identifiable to species, although grains heated above 260°C tend to have a less dense matrix with voids that can become filled with soil (Stroud et al., 2023a). The average isotopic offset associated with heating cereal grains (barley, oat, pearl millet, rye, sorghum, wheat) between 230 and 300°C has been calculated to be ~0.2‰ for δ¹³C values and ~0.3‰ for δ¹⁵N values (Nitsch et al., 2015; Stroud et al., 2023a; Styring et al., 2019; Varalli et al., 2023).

While it has long been posited that the isotope values of desiccated plant remains are unreliable due to the effect of diagenesis (DeNiro and Hastorf, 1985), more recent studies have demonstrated that they can in fact yield reliable isotope values (Metcalfe and Mead, 2018; Szpak and Chiou, 2019). Szpak and Chiou (2019) propose plotting the C:N atomic ratios of archaeological plant remains against their δ¹⁵N values, and if a strong positive correlation is observed this could indicate the preferential loss of ¹⁴N during degradation. No investigation of the effect of waterlogging on the isotope values of uncharred plant remains has yet been carried out.

Plant remains that have been buried in the soil are susceptible to contamination. The main potential contaminants are carbonates (with δ¹³C values of ~0‰; Schidlowski, 2001), nitrates (with δ¹⁵N values that have been found to vary between −2 and +8‰; Rock et al., 2011), and soil-derived humic acids (with δ¹³C and δ¹⁵N values similar to those of plants because this is what soil organic matter is derived from; Schnitzer and Khan, 1975). Vaiglova et al. (2014) used Fourier Transform-Infrared Spectroscopy (FT-IR) to detect these contaminants in charred plant material down to 10 % by dry weight of the charred plant material analyzed (down to 5 % for carbonate; Figure 1). Figure 2 shows the change in the δ¹³C and δ¹⁵N values of a powdered sample of charred peas (δ¹³C = −22.9‰, δ¹⁵N = 6.4‰) from an archaeological site contaminated with different proportions of carbonate (δ¹³C = 2.5‰), nitrate fertilizer (δ¹³C = 43.8‰, δ¹⁵N = −1.8‰), and a commercially purchased humic acid sodium salt (δ¹³C = −25.9‰, δ¹⁵N = 2.7‰) (data from Vaiglova et al., 2014: Table 4). With the exception of the nitrate fertilizer, 10 % by dry weight contamination of the archaeological pea sample resulted in changes in its δ¹³C or δ¹⁵N value of < 0.5‰.

Approximately 2 mg of charred cereal grain will yield ~1,200 μg C and 60 μg N (assuming 60% C and 3% N content). This is at the lower end of most IRMS limits for accurate and precise δ¹⁵N value measurements. It is therefore useful to analyse reference materials comprising plant material alongside samples to get a reasonable idea of the accuracy and precision of the isotopic measurements carried out. Wheat flour and sorghum flour IRMS reference materials are available from Elemental Microanalysis and millet flour (USGS90) and rice flour (USGS91) are available from the Reston Stable Isotope Laboratory or Arndt Schimmelmann, Indiana University. These reference materials have a lower N content (~1.5% N) than charred cereals, however, meaning that they are even more challenging to analyse by EA-IRMS and require 2–4 mg per analysis, which proves costly when performing a large number of analyses.

The development of in-house reference materials with isotopic and elemental compositions approximating those of the measured samples will likely be necessary for any researchers performing large quantities of isotopic analyses of plant remains; commercially-produced flours, similar to the USGS standards mentioned above, are frequently homogenous enough to produce consistent internal reference materials with stable isotope values measured over many years.

The carbon dioxide peak will always need to be diluted relative to the nitrogen gas peak (or diverted) in plant samples to avoid carryover to the nitrogen gas peak. If dilution is not possible or can only be applied to some limited extent, the δ¹³C and δ¹⁵N values could be measured on a small (< 1 mg) aliquot of the sample. This analysis will produce a reliable δ¹³C value as well as a reliable %N (but not δ¹⁵N) value. Based on this %N value, the analyst can then produce a second aliquot weighed specifically to produce precisely the appropriate amount of nitrogen gas required, while removing any of the produced CO₂. The mass required for accurate and precise δ¹⁵N value measurements is higher for uncharred material (which tends to have lower %N) and lower for pulses that have higher %N (see Table 2). Given that preparation of samples (at a minimum involving crushing and weighing into tin capsules) invariably results in loss of material, it is advisable to weigh all potential samples before proceeding with any further preparative work to ensure that they are a minimum of 5–10 mg.

The method of “precision for planning” (also called Accuracy in Parameter Estimation, AIPE) is a powerful tool for determining optimal number of samples by specifying a desired statistical precision and calculating how many samples it would take to reach that precision. Tools such as the one provided on thenewstatistics.com > esci web > precision for planning (https://esci.thenewstatistics.com/esci-precision.html#tab-1) enable us to set the target precision on the x-axis and read the optimal sample size off the y-axis. Here, the margin of error (MoE)—which is one half of a confidence interval around a mean (i.e., the distance between the mean and the lower or upper limits of its confidence interval)—is used to determine the target precision. MoE can be standardized by dividing by the standard deviation, which makes it possible to work with samples that come from populations with different variabilities.

Here, we use precision for planning instead of statistical power because of the strong concerns that have been raised by the statistical community over null hypothesis significance testing (e.g., Amrhein et al., 2019; Byrd, 2007; Cohen, 1990; Cumming, 2014; Fidler et al., 2004; Goodman, 2008; Greenland et al., 2016; Ioannidis, 2005). In analyzing plant stable isotope datasets, we recommend the use of estimation science (i.e., focusing on describing what the actual difference between groups is) over declaring whether or not a test statistic passes an arbitrary threshold such as p = 0.01 or p = 0.05. Cumming and Calin-Jagerman (2024) provide many useful discussions and tools for applying estimation and inferential statistics in research in place of null hypothesis significance testing.

A common rule of thumb is to choose a MoE that is half of the expected effect size (i.e., the difference between the groups of interest). Let's consider a hypothetical archaeological scenario to illustrate how this works. Suppose we have archaeobotanical remains from a European site dating to three occupation phases: Neolithic, Bronze Age and Iron Age. The aim of our study is to determine whether barley was grown in different soil conditions during the three periods. Based on the differences in cereal grain δ¹⁵N values between low, medium and high levels of manuring established by Bogaard et al. (2013), we set our expected effect size to 3.0‰. In other words, we predict that if there is a true difference in soil management conditions, the mean δ¹⁵N values would differ by 3.0‰ or more. This would make the target MoE 1.5‰ (half of 3.0‰). Using the pooled standard deviation in δ¹⁵N values of individual grains/pulses from single cultivation plots of 0.76‰ (Section 2.2; Table 4), the standardized MoE would be 1.5/0.76 = 2 in standard deviation units.

Figure 3 demonstrates how the online esci web > precision for planning tool can be used to calculate the optimal number of samples. Figure 3A shows that setting the MoE to 2 (by toggling the slider on the x-axis) results in four barley grains required per phase. However, this precision will be reached only 51% of the times, since 49% of the distribution curve (in orange) lies above MoE = 2.0‰. To determine sample size at 99% assurance, the corresponding checkbox can be clicked in the panel on the left-hand side. When that is done (Figure 3B), the distribution curve (in orange) shifts so that 99% of the area falls under MoE = 2.0 and the optimal sample size changes to 6. However, because archaeobotanical grains rarely come from the same cultivation plot (or even the same temporal unit within an occupation phase), it should be expected that the real standard deviation is larger, in which case more conservative estimates should be made (e.g., MoE = 1.5/1 = 1.5, yielding a minimum of nine grains per period at 99% assurance).

It is useful during project preparation and grant application to consider what sample sizes would be required to detect realistic effect sizes under a range of expected standard deviations. Table 5 shows sample sizes required for capturing an effect size of 1.0‰ (Figure 3A) and an effect size of 3.0‰ (Figure 3B) with expected standard deviations between 0.2 and 1.0‰. As expected, fewer samples are needed to identify larger effect sizes. For example, only seven samples per group are needed to detect a difference of 3.0‰ with 99% assurance when SD = 0.8‰, but 30 samples per group are needed to detect a difference of 1.0‰ with 99% assurance when SD = 0.8%. However, even though large target MoE can in theory be achieved with very small sample sizes, we need to be particularly careful about using very small n (such as < 4). In replication studies, when the standard deviation of the underlying population is not actually known (as is the case in plant stable isotope studies), the width of the confidence intervals can bounce around substantially, so distinct sets of four samples can produce very different results, and the outcomes need to be treated with caution.

When performing precision for planning, it is best to be conservative about the expected standard deviation, especially given the difficulties with understanding variability in archaeological datasets (Section 2.2). If it is underestimated, the results could risk missing the detection of meaningful differences. Additionally, it is important to remember that this method only works under the assumption that the samples in each group come from the same population. Thus, six samples each of wheat and barley may detect a 3.0‰ difference in δ¹⁵N values between a plot of wheat and a plot of barley, but not across several fields from distinct time periods. If chronological change is of interest, six samples should be obtained of each species from each period. If contexts are primary storage deposits (which are often the richest contexts in terms of crop remains), it may be that all items in that deposit came from the same population (i.e., same cultivation plot), but they could alternatively represent grain sourced and pooled from several fields. If primary contexts are unavailable, and the optimal sample sizes are unachievable, a 3.0‰ difference might go undetected. Further details on using precision for planning using different research designs can be found in Cumming and Calin-Jagerman (2024: Chapter 10).

Lastly, small sample sizes lead to large confidence intervals (i.e., low precision) around the estimates of interest. In some cases, this may result in a meaningful difference being obscured and undetectable. In other cases, large confidence intervals may make it impossible to identify the direction of an effect. For example, if a study aims to identify a linear correlation between δ¹⁵N and grain width and measures a Pearson's r of 0.4 using 10 grains, when a confidence interval (CI) is attached to the correlation coefficient, the result is r = 0.4, 95% CI (−0.3, 0.8). This means that the true relationship could be anywhere from weakly negative (−0.3) to strongly positive (0.8). If the isotopic difference between wheat (n = 3) and barley (n = 4) is 0.3‰, 95% CI (−1.0, 1.6), it means that the true difference could be anywhere from −1.0‰ to 1.6‰. When small sample sizes are unavoidable, it is imperative to restrict interpretations to descriptive statistics, without making unrealistic predictions about what the trends imply for the underlying population.

It is often not possible to distinguish between the effect(s) of environmental variability and agricultural practice on crop isotope values, but the potential of environmental factors to contribute to any differences or changes in crop isotope values should be considered and discussed for each case. For this reason, care must be taken when applying the “manuring bands” and water availability frameworks established by modern studies in particular regions (Bogaard et al., 2013; Wallace et al., 2013) to others with very different climate and soil types. Previous studies comparing crop isotope values from sites located in areas with differing annual rainfall levels have attempted to account for the effect of aridity on crop δ¹⁵N values and to normalize crop δ¹⁵N values between sites using linear regression in order to avoid incorrect interpretation of high crop δ¹⁵N values as solely due to manuring (Styring et al., 2016, 2017a, 2022). More experimental studies investigating the interplay of environmental factors and agricultural practices on crop isotope values will only improve these attempts at disentangling such confounding variables.

Another approach has been to estimate a “base-interval” of isotope values to be expected for unmanaged plants, by subtracting the mean offset between bone collagen and diet (~4‰ for δ¹⁵N; e.g., Steele and Daniel, 1978) from the isotope values of preserved wild herbivore bone collagen from the same archaeological sites and contexts as crop remains (e.g., Aguilera et al., 2018; Bogaard et al., 2013; Styring et al., 2017b). This relies, however, on the presence of wild herbivore bones and on the assumption that the plants consumed by wild herbivores were growing in similar environments to crops but that their isotope values were unaffected by human management. Domestic herbivore bone collagen isotope values are not used because they are more likely to reflect isotope values of plants that have been affected by human management.

There exists a corpus of images of cereal grains and pulse seeds experimentally heated for between 215 and 260°C for 4–24 h (Stroud et al., 2023b) that can be compared with the external morphology of archaeological crop remains to identify those that are likely to have been charred in similar conditions and thus minimize any isotopic offset due to charring. These are generally crop remains that can be identified to species and conform to preservation grades P2 or P3 (after Hubbard and al Azm, 1990). It is possible that even those crop remains whose external morphology suggests that they are well-preserved have voids in their cross-section indicating that they were heated to a higher temperature. These voids can also have infilling of soil, making contamination a concern. Cereal grains/pulses can therefore be cut in half using a scalpel to examine the internal morphology of the cross-section (also pictured in Stroud et al., 2023a,b) and discarded if large voids or soil contamination are present.

Vaiglova et al. (2014) investigated the effectiveness of various pre-treatment methods in removing the most likely forms of contamination from soil: carbonates, nitrates and humic acids. They found that carbonate contamination was removed using a gentle acid wash (0.5 M HCl at 80°C for 30 min), nitrate was removed with three rinses in deionised water, and humic acid was removed with a gentle base-acid wash (0.1 M NaOH and 0.5 M HCl at 80°C, 60 min base treatment, 30 min acid treatment). This and various other studies have observed relatively small (< 1.0‰ for δ¹³C and < 1.5‰ for δ¹⁵N in 96% of cases; Brinkkemper et al., 2018) but variable changes in the isotope values of charred archaeological plant remains after varying combinations and concentrations of acid and base washes (Brinkkemper et al., 2018; Fraser et al., 2013a; Kanstrup et al., 2014; Vaiglova et al., 2014). It is very difficult to determine whether these changes in isotopic composition are due to removal of contaminants, or due to preferential removal of certain parts of the plant material that have different isotope values. Moreover, multiple washes of plant material results in its loss, with sample weight losses of 22 ± 9% with acid-only treatment, 37 ± 22% for base-acid treatment and 50 ± 17% for acid-base-acid treatment having been observed (Brinkkemper et al., 2018). In samples with low starting mass (such as single grains/seeds) pre-treatment could result in insufficient material remaining for isotopic analysis.

Given the uncertainties associated with the isotopic effect of pre-treatment methods on uncontaminated charred grains and seeds, and the relatively small changes that contaminants (and particularly humic acids) have on crop δ¹³C and δ¹⁵N values (Figure 2), three strategies have been proposed: (1) perform chemical pre-treatment on all samples, (2) screen a portion of archaeological crop samples from a range of context types and levels of preservation/visible dirtiness for potential contamination and only apply pre-treatment protocols if contamination is observed to be present, or (3) perform no chemical pre-treatment but undertake the physical removal of visible sediment, and report larger isotope value uncertainties to account for the unknown effect of contamination (cf. Brinkkemper et al., 2018). FT-IR spectroscopy is a good screening method as it uses minimal material, is very quick, and the spectra of contaminated crop material have been published (see Vaiglova et al., 2014; Figure 1). Researchers could also use their knowledge of the geology of an archaeological site to judge the likelihood of carbonate contamination, in particular. The only sites where carbonates have been detected in archaeological crop remains thus far are located on limestone geologies (e.g., Greece, northern Syria, south-east England, southern France; Alagich et al., 2018; Stroud, 2022; Styring et al., 2022; Vaiglova et al., 2020). Ultimately, more experimental studies on samples with known levels of contamination would be valuable to more conclusively determine how to effectively remove contamination in a wider range of situations.

The most successful isotopic studies are those that have a clear hypothesis to test, involving the comparison of two or more groups of interest or exploring the relationship between isotope values and an independent variable such as date. In archaeological studies, we are generally interested in how human actions have affected the isotope values of plants, to gain insights into the type and intensity of agricultural management. Given the multitude of environmental factors (e.g., soil type, climate, topography), aside from agricultural practices such as watering and fertilization, that can influence plant δ¹³C and δ¹⁵N values, comparisons of plant isotope values within sites are likely to be most robust because it can generally be assumed that these environmental factors are more consistent across the site. The isotope values of different crops recovered from the same archaeological contexts can be compared to investigate differences in management practices among crops; the isotope values of one or more crops can be determined through time to detect changing agricultural practices; and the isotope values of crops can be compared between/among discrete periods of occupation.

When comparing crop isotope values among sites, there is a greater chance that the isotope values will vary according to environmental differences rather than management practices per se. It is therefore useful to have a point of reference unlikely to be influenced by human management to act as an isotopic “base-interval” (cf. Vaiglova et al., 2022) for comparison with the crop isotope values (see Section 3.3).

If plant remains derive from a secondary context (e.g., floor, midden), it cannot be assumed that multiple seeds come from the same growing condition and therefore isotopic analysis of single seeds will conserve the true variation among contexts. If plant remains derive from primary storage contexts (e.g., storage bins, pots), it might be the case that all items came from the same cultivation plot. In this case, isotopic analysis of a “bulk sample” of multiple grains will average out the inherent isotopic variability within the growing condition, providing a more precise estimate of the mean isotope value for that growing condition when budget and time are limited. Large primary deposits (e.g., large pits, granaries), however, could comprise grains sourced and pooled from multiple fields, or even from multiple settlements, meaning that analysis of single grains is actually more appropriate. Regardless, it is important that archaeological context is recorded for each sample (e.g., in Supplementary information) so that the isotope values of samples (whether individual grains or “bulk samples” of multiple grains) can be interpreted correctly in terms of expected variability and context. This information could include the total number of grains/pulses recovered from an archaeological context (but not necessarily isotopically analyzed), since this would indicate whether a deposit was large and therefore more likely to have derived from multiple sources.

Given the variability in individual cereal grain isotope values within a cultivation plot (Table 4), it is necessary that sufficient samples are analyzed in order to robustly identify any meaningful differences in isotope values among the groups of interest that cannot be accounted for by this inherent variability. Determining the number of samples necessary to determine these differences depends on the research question, the estimated effect size of a management regime of interest and the expected variability within a management regime. Although it is notoriously difficult to estimate effect sizes and variability, the availability of isotope data from modern experimental farming sites means that we can make a reasonable attempt at estimating the number of samples required, following the approach in Section 3.2. Care should be taken to ensure comparability between the groups of interest, so if, for example, the research question is whether there is a difference in manuring practice between the Neolithic and Bronze Age at a particular site, the crop species sampled should be consistent for both time periods.

Well-preserved grains/seeds should be selected for isotopic analysis to minimize the isotopic offset resulting from charring and to minimize the risk of internal contamination with soil. Photographs of the dorsal and lateral views of intact grains provide a record of their external morphology that can be used for future geometric morphometric analysis (e.g., Bonhomme et al., 2017; Portillo et al., 2019; Wallace et al., 2019), and a photograph of the cross-section of each grain/pulse provides a record of the internal morphology which could be used to cross-reference to reference material charred under different conditions. It is possible that future research will enable better constraint of the isotopic changes associated with different preservation conditions and so having a visual record of the crop remains that have been analyzed (and ultimately destroyed) could be useful for refining interpretations.

Archaeobotanical remains could be screened for potential contamination and the spectra reported alongside isotopic data. FT-IR spectroscopy is a good method for this and we recommend that at least 10% of samples are screened in this way. This represents a balance between screening all samples (with the risk of sample loss that will preclude subsequent isotopic analysis) and screening enough to capture any potential contamination. If screening a sub-set of samples, it is advisable to screen samples from a range of context types and levels of preservation/visible dirtiness so that they are as representative as possible.

There is a lack of consensus on whether to pre-treat all samples, regardless of contamination, pre-treat only those with evidence of contamination, or not to pre-treat at all. We leave it up to the reader to judge whether the potential level of contamination is likely to affect the isotope values more than pre-treatment to remove any potential contamination. Nevertheless, we recommend in all cases to scrape any visible dirt from the surface of grains/seeds using a scalpel under a low-power microscope or magnifying glass and to rinse grains/seeds in deionised water prior to any analyses to remove substantial amounts of soil and any surface debris. Samples should then be dried in a low temperature oven (~40°C) or lyophilised. Samples can then be crushed using an agate mortar and pestle and the resulting powder stored wrapped in aluminum foil inside microcentrifuge tubes to reduce the effect of static that can disperse the sample.

Approximately 2 mg of charred cereal grain will yield enough C and N for accurate and precise δ¹³C and δ¹⁵N value measurements, although this depends on the EA-IRMS. The carbon dioxide peak will likely need to be diluted relative to the nitrogen gas peak if δ¹³C and δ¹⁵N values are to be determined simultaneously on the same sample. Best practice in terms of two-point normalization of isotopic data has been covered comprehensively in other publications (see Szpak et al., 2017). Wheat flour and sorghum flour IRMS reference materials from Elemental Microanalysis and millet flour (USGS90) and rice flour (USGS91) from Arndt Schimmelmann, Indiana University, are useful “check” standards as they are matrix-matched to plants, but other in-house reference materials could be used.

Again, best practice as to the reporting of isotope values has been discussed in other publications (e.g., Roberts et al., 2018; Vaiglova et al., 2022), but we recommend that the following information is published alongside the isotopic data when analyzing archaeobotanical remains: (1) archaeological context information for each sample, including the number of grains/pulses represented by each sample and the total number of that species recovered from the context, (2) photographs of external and internal morphology of each grain/seed, (3) FT-IR spectra where available, (4) detailed information of any pre-treatment of samples, and (5) elemental and isotopic data for all samples and reference materials included alongside these, including mass of plant sample analyzed.