From Measured Collagen to Dietary Source Values
Module 4: Isotopic Offsets & Source Corrections
Chronologies
11 April 2026
From Measured Collagen to Dietary Source Values
One-Day Training Programme · Module 4
The core problem
ReSources needs the isotope values of individual macronutrient fractions of each food source:
- Protein fraction δ¹³C and δ¹⁵N
- Lipid/carbohydrate fraction δ¹³C
But what is measured in the lab is collagen from modern or archaeological reference animals — which reflects a mixture of all those fractions.
The question this module answers
How do we work backwards from a measured bulk or collagen value to the separate protein and energy (lipid/carbohydrate) component values that ReSources requires as inputs?
Learning outcomes
By the end of this module you should be able to:
- Explain why raw collagen values cannot be used directly as source inputs to ReSources.
- Apply the correct tissue-to-component offsets for terrestrial animals and marine/freshwater fish.
- Apply the correct bulk-to-component offsets for C₃ cereals.
- Understand the trophic enrichment factors (Δ¹⁵Ncollagen–diet, Δ¹³Ccollagen–diet) used in ReSources.
- State appropriate uncertainties for source values and understand why conservative estimates are used.
- Identify where macronutrient concentration data come from.
Step 1 — Why We Need Offsets
What isotope measurements actually reflect
When we measure bone collagen δ¹³C from a human, we obtain:
\[\delta^{13}C_{\text{collagen, human}}\] This value reflects:
- ~74% of collagen carbon derived from dietary protein (i.e., muscle/soft tissue)
- ~26% from dietary lipids and carbohydrates (the energy fraction)
ReSources needs to know:
\[\delta^{13}C_{\text{muscle (protein fraction)}}\] \[\delta^{13}C_{\text{lipids (energy fraction)}}\]
These are not the same as the collagen measurement — we need to apply correction offsets.
The chain of corrections
The offsets are empirically derived from controlled feeding experiments and direct tissue measurements (Fernandes et al. 2012; updated by more recent studies).
Step 2 — Tissue Offsets for Animal Sources
Terrestrial animals — the offsets
Based on Fernandes et al. (2012) and corrected after more recent studies:
Carbon offsets:
\[\Delta^{13}C_{\text{muscle–collagen}} = -2 \text{ ‰}\]
\[\Delta^{13}C_{\text{lipids–collagen}} = -8 \text{ ‰}\]
Nitrogen offset:
\[\Delta^{15}N_{\text{muscle–collagen}} = 0 \text{ ‰}\]
In plain terms:
- Muscle (protein fraction) is 2 ‰ lighter in ¹³C than the collagen it produces
- Lipids are 8 ‰ lighter in ¹³C than the collagen they contribute to
- Muscle δ¹⁵N is effectively unchanged relative to collagen δ¹⁵N
Terrestrial animals — worked example
Suppose we measure δ¹³C = −19.5 ‰ and δ¹⁵N = +6.8 ‰ in sheep collagen.
Step 1 — Protein (muscle) fraction:
\[\delta^{13}C_{\text{muscle}} = \delta^{13}C_{\text{collagen}} + \Delta^{13}C_{\text{muscle–coll}} = -19.5 + (-2) = -21.5 \text{ ‰}\]
\[\delta^{15}N_{\text{muscle}} = \delta^{15}N_{\text{collagen}} + \Delta^{15}N_{\text{muscle–coll}} = +3.8 + 0 = +6.8 \text{ ‰}\]
Step 2 — Lipid/energy fraction:
\[\delta^{13}C_{\text{lipids}} = \delta^{13}C_{\text{collagen}} + \Delta^{13}C_{\text{lipids–coll}} = -19.5 + (-8) = -27.5 \text{ ‰}\]
These corrected values: −21.5 ‰ / +3.8 ‰ for protein and −27.5 ‰ for energy — become the terrestrial meat end-members in ReSources.
Marine/freshwater fish — the offsets
Collagen-to-tissue offsets are different for marine/freshwater fish, reflecting their distinct biochemistry:
Carbon offsets:
\[\Delta^{13}C_{\text{muscle–collagen}} = -1 \text{ ‰}\]
\[\Delta^{13}C_{\text{lipids–collagen}} = -7 \text{ ‰}\]
Nitrogen offset:
\[\Delta^{15}N_{\text{muscle–collagen}} = +1.5 \text{ ‰}\]
Key differences from terrestrial:
- Muscle is only 1 ‰ lighter in ¹³C (vs. 2 ‰ for terrestrial)
- Lipids are 7 ‰ lighter in ¹³C (vs. 8 ‰ for terrestrial)
- Muscle δ¹⁵N is +1.5 ‰ heavier than collagen δ¹⁵N (vs. 0 ‰ for terrestrial)
The δ¹⁵N difference reflects different amino acid routing in fish collagen biosynthesis.
Marine fish — worked example
Suppose we measure δ¹³C = −13.2 ‰ and δ¹⁵N = +15.5 ‰ in cod collagen.
Protein (muscle) fraction:
\[\delta^{13}C_{\text{muscle}} = -13.2 + (-1) = -14.2 \text{ ‰}\]
\[\delta^{15}N_{\text{muscle}} = +15.5 + (+1.5) = +17.0 \text{ ‰}\]
Lipid/energy fraction:
\[\delta^{13}C_{\text{lipids}} = -13.2 + (-7) = -20.2 \text{ ‰}\]
Note that marine fish lipids fall in a very similar δ¹³C range to terrestrial meat protein (~−20 ‰). This near-overlap is one reason why separating freshwater and marine sources from terrestrial sources can be difficult on carbon alone.
Comparing the offsets side by side
Step 3 — Bulk Offsets for C₃ Cereals
The cereal problem
For plant sources, we typically measure bulk stable isotope values from charred seeds or grain — not a tissue fraction. We must split the bulk value into its protein and carbohydrate (energy) fractions.
Offsets applied to C₃ cereal bulk δ¹³C:
\[\Delta^{13}C_{\text{protein–bulk}} = -2 \text{ ‰}\]
\[\Delta^{13}C_{\text{carb–bulk}} = +0.5 \text{ ‰}\]
Lipid contribution: negligible — lipid content of cereals is very low (~2–3% dry weight), so no lipid offset is applied.
Why different sign?
In cereals, starch (carbohydrates) tends to be slightly enriched in ¹³C relative to the bulk, while protein is depleted — the opposite pattern to animal tissues where lipids are the most depleted fraction.
C₃ cereals — worked example
Suppose we measure bulk δ¹³C = −25.0 ‰ for archaeological an wheat grain.
Protein fraction:
\[\delta^{13}C_{\text{protein}} = -25.0 + (-2) = -27.0 \text{ ‰}\]
Carbohydrate (energy) fraction:
\[\delta^{13}C_{\text{carb}} = -25.0 + (+0.5) = -24.5 \text{ ‰}\]
The two fractions are only 2.5 ‰ apart, but they contribute to collagen carbon via very different pathways (protein → amino acids; carbohydrates → de novo synthesis), so the distinction still matters for ReSources.
Charring can alter the isotopic composition of organic material through the preferential loss of isotopically light C and N, leading to systematic enrichment in both ¹³C and ¹⁵N relative to uncharred tissue. This needs to be accounted for.
All source offsets — summary table
| Source type | Measured value | Protein (δ¹³C) | Energy (δ¹³C) | Protein (δ¹⁵N) |
|---|---|---|---|---|
| Terrestrial animals | Collagen | coll + (−2 ‰) | coll + (−8 ‰) | coll + (0 ‰) |
| Marine/freshwater fish | Collagen | coll + (−1 ‰) | coll + (−7 ‰) | coll + (+1.5 ‰) |
| C₃ cereals | Bulk grain | bulk + (−2 ‰) | bulk + (+0.5 ‰) | measured directly |
Offsets follow Fernandes et al. (2012) as updated by more recent empirical studies. Lipid contribution from cereals is treated as negligible.
Step 4 — Trophic Enrichment Factors for ReSources
TEFs: from diet to consumer collagen
Once we have source macronutrient fractions, ReSources still needs to apply trophic enrichment factors — the isotopic shift between what a human eats and what is recorded in its bone collagen.
Following Fernandes et al. (2012):
Nitrogen TEF:
\[\Delta^{15}N_{\text{collagen–diet}} = +5.5 \pm 0.5 \text{ ‰}\]
- 100% contribution from protein
- No nitrogen routing from carbohydrates or lipids
Carbon TEF:
\[\Delta^{13}C_{\text{collagen–diet}} = +4.8 \pm 0.5 \text{ ‰}\]
- 74 ± 4% contribution from protein
- 26 ± 4% contribution from lipids and carbohydrates
TEFs — what the numbers mean
The routing split within the TEF
The carbon TEF contains a critical piece of information — the routing split:
\[\lambda = 0.74 \pm 0.04\]
This is the routing parameter introduced in Module 2:
74% of collagen carbon comes from dietary protein, and 26% from lipids and carbohydrates.
The ±4% uncertainty on λ propagates directly into uncertainty on all dietary proportion estimates — which is why ReSources treats λ as a probability distribution, not a fixed value.
Step 5 — Macronutrient Concentrations
Why macronutrient concentrations are needed
ReSources weights the contribution of each food source not just by its isotope value, but also by its macronutrient composition — because not all protein-rich foods contribute equally to collagen protein synthesis.
The model requires for each food source:
- % protein (dry weight) — determines contribution to the protein pool
- % lipid (dry weight) — determines contribution to the energy pool
- % carbohydrate (dry weight) — determines contribution to the energy pool
These are sourced from the USDA National Nutrient Database for Standard Reference
(https://fdc.nal.usda.gov/)
USDA data — practical considerations
Obtaining the values:
- Search for each food source by name
- Select the most appropriate entry (raw, cooked, dried)
- Record values as dry weight %
- If only fresh weight is available: divide by (1 − moisture fraction)
- Uncertainties are reported as standard error across database entries
Expressing as dry weight % is important because isotope values of reference materials are also measured on dried samples.
Example — approximate dry weight compositions:
| Food source | % Protein | % Lipid | % Carb |
|---|---|---|---|
| Beef muscle | 85 | 12 | 0 |
| Atlantic cod | 90 | 6 | 0 |
| Herring | 60 | 35 | 0 |
| Wheat grain | 13 | 2 | 82 |
| Peas (dried) | 25 | 2 | 67 |
Approximate values for illustration
How macronutrient concentrations enter the model
Putting It All Together
The complete source preparation workflow
For each animal source (terrestrial/marine/frehwater):
- Measure/collate δ¹³C and δ¹⁵N from reference collagen specimens
- Calculate SE across specimens
- Apply tissue-to-fraction offsets (muscle–collagen, lipids–collagen)
- Record macronutrient composition from USDA database (dry weight %)
For each plant source (C₃ cereals):
- Measure/collate δ¹³C and δ¹⁵N from carbonised grain
- Calculate SE across specimens
- Apply bulk-to-fraction offsets (protein–bulk, carb–bulk); no lipid fraction
- Record macronutrient composition from USDA database (dry weight %)
TEFs applied inside ReSources (not to source data):
- Δ¹⁵Ncoll–diet = +5.5 ± 0.5 ‰ (100% protein)
- Δ¹³Ccoll–diet = +4.8 ± 0.5 ‰ (λ = 74 ± 4% protein, 26 ± 4% energy)
Full offset reference sheet
| Parameter | Value | Applies to |
|---|---|---|
| Δ¹³Cmuscle–collagen (terrestrial) | −2 ‰ | Protein fraction of terrestrial animals |
| Δ¹³Clipids–collagen (terrestrial) | −8 ‰ | Energy fraction of terrestrial animals |
| Δ¹⁵Nmuscle–collagen (terrestrial) | 0 ‰ | N fraction of terrestrial animals |
| Δ¹³Cmuscle–collagen (fish) | −1 ‰ | Protein fraction of fish |
| Δ¹³Clipids–collagen ( fish) | −7 ‰ | Energy fraction of fish |
| Δ¹⁵Nmuscle–collagen ( fish) | +1.5 ‰ | N fraction of fish |
| Δ¹³Cprotein–bulk (C₃ cereals) | −2 ‰ | Protein fraction of cereals |
| Δ¹³Ccarb–bulk (C₃ cereals) | +0.5 ‰ | Energy fraction of cereals |
| Δ¹⁵Ncollagen–diet (TEF) | +5.5 ± 0.5 ‰ | Applied inside ReSources; 100% protein |
| Δ¹³Ccollagen–diet (TEF) | +4.8 ± 0.5 ‰ | Applied inside ReSources; λ = 74 ± 4% |
| Routing parameter λ | 0.74 ± 0.04 | Protein fraction of collagen C |
Primary source: Fernandes et al. (2012) as updated by more recent empirical studies. Uncertainties on source values should be calculated as SE ⊕ offset uncertainty (quadrature sum).
Common errors to avoid
❌ Using raw collagen values as source inputs
Collagen δ¹³C already incorporates TEF and routing — entering it directly double-counts the enrichment.
❌ Ignoring δ¹⁵N muscle–collagen offset for marine fish
The +1.5 ‰ offset is easy to overlook but can meaningfully shift nitrogen-based trophic estimates.
❌ Using SE without adding offset uncertainty
Produces artificially narrow source distributions and overconfident dietary posteriors.
❌ Applying lipid correction to cereals
Cereal lipid content is negligible — applying a lipid offset would introduce spurious error.
❌ Using fresh weight macronutrient values
Isotope measurements are on dry samples; macronutrient concentrations must also be on a dry weight basis.
❌ Using a single λ value without uncertainty
λ = 0.74 ± 0.04 — the ±0.04 matters and must be propagated as a distribution in ReSources.
Learning outcomes — checklist
- Explain why raw collagen values cannot be used directly as source inputs to ReSources
- Apply the terrestrial animal offsets: Δ¹³Cmuscle–coll = −2 ‰, Δ¹³Clipids–coll = −8 ‰, Δ¹⁵Nmuscle–coll = 0 ‰
- Apply the marine/frehwater fish offsets: Δ¹³Cmuscle–coll = −1 ‰, Δ¹³Clipids–coll = −7 ‰, Δ¹⁵Nmuscle–coll = +1.5 ‰
- Apply the C₃ cereal offsets: Δ¹³Cprotein–bulk = −2 ‰, Δ¹³Ccarb–bulk = +0.5 ‰ (no lipid term)
- State the TEFs used in ReSources: Δ¹⁵Ncoll–diet = +5.5 ± 0.5 ‰; Δ¹³Ccoll–diet = +4.8 ± 0.5 ‰ with λ = 0.74 ± 0.04
- Retrieve macronutrient concentrations from the USDA database and express as dry weight %
Key references for this module
Primary source for offsets and TEFs:
Fernandes, R. A simple(R) model to predict the source of dietary carbon in individual consumers. Archaeometry 58, 500–512 (2016).
Fernandes, R., Millard, A.R., Brabec, M., Nadeau, M.-J. & Grootes, P. (2014) Food reconstruction using isotopic transferred signals (FRUITS): a Bayesian model for diet reconstruction. PLoS ONE, 9, e87436.
Fernandes R, Nadeau MJ, Grootes PM. 2012. Macronutrient- based-model for dietary carbon routing in bone collagen and bioapatite. Archaeol Anthropol Sci 4:291–301.
Soncin, S. et al. 2021. High-resolution dietary reconstruction of victims of the 79 CE Vesuvius eruption at Herculaneum by compound-specific isotope analysis. Sci. Adv. 7,eabg5791.DOI:10.1126/sciadv.abg5791
Webb, E. C., Lewis, J., Shain, A., Kastrisianaki-Guyton, E., Honch, N. V., Stewart, A., … Evershed, R. P. (2017). The influence of varying proportions of terrestrial and marine dietary protein on the stable carbon-isotope compositions of pig tissues from a controlled feeding experiment. STAR: Science & Technology of Archaeological Research, 3(1), 28–44.
End of Module 4
Continue to Module 5 — Running ReSources in R: Three progressive examples for dietary reconstruction
Archaeological Isotope Laboratory · Chronologies
Module 4: Understanding Mixing Models