Stable Isotope Analysis: Predictive Power and Challenges

Table of Contents


The presence of stable isotopes, i.e., elements with extra (or missing) neutrons which do not decay over time, provides a strong tool for tracing of animal activities in both the near and distant past. Quantification of these stable isotopes using mass spectrometry, followed by mathematical analysis, allows scientists to make many inferences about past life. By using stable isotopes as ‘labels,’ it is possible to track the diets of animals through an analysis of fossilized tissues and bones. It is even possible to infer the environment in which an animal lived through such analyses, and as a result, scientists can make hypotheses about animal migration patterns as well as changes in environmental conditions over time. However, isotopic analysis does not come without its fair share of challenges. For example, during tooth enamel formation, the isotopic information recorded is an average over time and does not reflect the true temporal variation in conditions. Thankfully, paleontologists have developed a matrix which can account for this phenomenon. Additional issues in isotopic analysis revolve around the relatively rapid diagenesis of lighter isotopes found in soft tissues. Alternative isotopes which are not as susceptible to diagenesis can be analyzed as a work-around, extending the useful range of isotopic analysis much further into the past. These can provide additional insight about ancient organisms and can prove extremely useful when classification based on anatomy is unlikely due to lack of sufficient fossil material.


Stable isotopes are elements which do not decay into other elements over time. This contrasts unstable isotopes which do decay into other elements through the spontaneous radioactive release of energy. For example, carbon-14 decays into stable nitrogen-14 with a half-life of ~5730 years (Rogers, 2015). Given the property that stable isotopes do not change, and their abundance throughout the world, stable isotopes help preserve information and allow inferences to be drawn regarding past life. Through analysis and modelling, the measurable variations in the stable isotopic composition of fossils and the environment provide hints about ancient climates, patterns of animal migration, diet, and behaviour (Passey et al., 2002). Such ideas are discussed in the first section of this paper. Traditionally, quantification of stable isotopes is done through stable isotope analysis, which involves various techniques including mass spectrometry, laser ablation, and others. Machine learning algorithms have also been employed, enabling estimations of isotopic input in the Mediterranean Sea (Astray et al., 2021). Notably however, there are several challenges which face stable isotope analysis. For instance, fossil specimens under examination all have experienced Earth’s natural processes over extremely long periods of time. This factors into the validity of inferences that can be made from the measured stable isotope composition. These challenges and potential improvements will be explored in the second section of this paper.

How Does Knowing Stable Isotopic Content Enable Inferences About Past Life?

Overview of Stable Isotope Analysis

Scientists have long discovered the use of stable isotopes within mammalian materials and fossils, especially their ability in providing useful information on the dietary preferences of the deceased host. However, unpredictable factors such as relocation of the fossil from its native inhabitant and traits lost in natural selection in evolution contribute to a significant bias and restriction to the study of diet by stable isotope; the stable isotopic analysis, although with its own shortcomings, proved to be a more efficient method in determining the dietary preferences of past mammalians with its detachment from morphological traits and phylogenesis (Clementz et al., 2012). Stable isotopic analysis most commonly provides insights on ancient diets through identifying a common “identification label” between food sources and stable isotopes within the tissue of a mammal (Clementz et al., 2012), and then comparing the abundance of the isotopes in the tissue with an ideal material of its nature; in a real-world setting, the isotopic content, the amount of a given isotope in a natural compound, varies drastically from an “ideal” compound with precise isotopic composition. From the ratio of two stable isotopes, the mammal’s predominant types of the food can be determined. For example, from the ratio of 12C and 13C within the bone of an animal, the predominant type of plant-based food, whether C3 or C4 crops, can be inferred (O’Leary, 1988). The stable isotope equation giving the difference between rare to common stable isotope ratio of sample to that of a standard material is (O’Leary, 1988):

\delta X = [(R_{sample} / R_{standard}) - 1] \times 10^3

In the ecosystem, the isotopic abundance can be described by the above equation. The stable isotopic equation describes the proportion of isotopes of interest (δX) in a material measured in per thousand, with X denoting the isotope of interest. More precisely, it is measuring the parts per thousand deviation of sample isotopes content from the ideal material (Peterson & Fry, 1987). R represents the ratio of two isotopes in the sample or in the ideal material (standard), and a fluctuation in the value of δX indicates a change of abundance of isotopes within the sample in regards to the ideal material; the direction of fluctuation is directionally related to the increase and decrease of isotope (Peterson & Fry, 1987).

Paleoecological Implications from the Carbon Isotopes of Mammalian Bones

Stable isotopes’ “anti-decay” characteristics prove to be useful in analyzing ancient mammals and generating a paleoecological picture. Paleoecological reconstruction is facilitated by the naturally occurring distinction between the stable isotopic content of food sources, mainly of primary producers (Clementz et al., 2012). The properties of the food chain allow this distinction to be reflected in upper levels by influencing the isotopic content of the consumers such as herbivores, giving them the distinctive “label” as well. The two abundant elements contained in plants are carbon and nitrogen, and thus the four most studied isotopes (two isotope ratios) are 13C/12C and 15N/14N. According to Clementz et al. (2012), natural factors such as variation in primary producers metabolic pathways, nutrients uptake, and environmental settings are responsible for this dissimilarity between isotopic contents. As such, to find the environmental setting of a past herbivore, a reverse reasoning must be adopted: one must infer the dietary preferences through stable isotope analysis.

To infer and about the dietary preferences and habitation settings of several mammalian species, the stable isotopes of carbon and nitrogen were documented from a preserved bone collagen from the Middle-Pleistocene in a study done by Kuitems et al. (2015).

In the study by Kuitems et al. (2015), samples of bone collagens from depositional environments 1 to 4 were used. Depositional level 1 environment was assumed to be a more closed off forest system, while depositional level 4 environment was assumed to be a biome closer to a grassland plain. Samples were restricted to only have a carbon to nitrogen ratio of 2.9 to 3.6, and the difference of isotopic contents between sample and a standard (“ideal”) material was determined through stable isotope equation. Kuitems et al. (2015) determined the stable isotope equations of 13C and 15N to be:

\delta^{13}C = \frac{(^{13}C/^{12}C)_{sample}}{^{13}C/^{12}C)_{reference}} - 1(\times 1000‰)
\delta^{15}N = \frac{(^{15}N/^{14}N)_{sample}}{^{15}N/^{14}N)_{reference}} - 1(\times 1000‰)

The type of herbs consumed by the herbivores were determined by the 13C and 15N content in their tissue. For example, according to Kuitems et al. (2015), plants grown in a more closed off environment hovered by canopies tend to have a smaller 13C isotope than plants grown in a more open environment, and grass tend to have a greater 15N content than leaves and trees (Kuitems et al., 2015). When comparing the carbon and nitrogen isotopic content in the mammal tissues with the herbs, these characteristics can be useful in determining important paleoecological information such as whether the herbivore grazes on grass or browses on leaves, what kind of herbs it consumed mainly, and what kind of environment it lived in.

Through the results of Kuitems et al. (2015), it was discovered that most of the samples in depositional level 1 have a relatively low 13C content, which indicates that the environment of the sampled mammals were more closed off, potentially a forest; however, some samples did not show a δ13C of beyond -22.4‰ (Figure 1), which means that the environment of which they lived in were not incredibly dense (Kuitems et al., 2015); therefore, it can be inferred that depositional level 1 environment was alternating between a forest biome and a more open region. Dissimilarly, according to data, the depositional level 4 is a comparatively more open biome than level 1, and it can be seen by the data collected by the sample. The overall δ13C did not exceed -22.4‰. In addition, counter-intuitively, despite being what most believe grazers, horses (equidae) displayed the lowest δ15N out of all of the samples (Figure 1), which infers that these horses in fact took on a browsing diet (Kuitems et al., 2015). In contrast, elephant (elephantidae) tissues displayed a relatively high δ15N value out of all samples (Figure 1), which conjectures that elephant diets consisted mainly of grass (Kuitems et al., 2015). The usefulness of stable isotope analysis can be seen through this case study: through just the isotopic content of mammalian tissues, its habitats and diets can be inferred directly.

Figure 1: Deviation of 13C and 15N from the standard material in samples of Elephantidae (El), Rhinocerotidae (Rh), Equidae (Eq), Cervidae (Ce), and Bovidae (Bo) bone collagen. [Adapted from (Kuitems et al., 2015)]

Probabilistic Stable Isotope Models of Animal Migration

Obtaining the stable isotope composition of animals is also useful for understanding and predicting migratory trajectories. Particularly, animal bodies contain parts which are metabolically inert (e.g. keratin), such that they “snapshot” the dietary and environmental conditions under which the tissue was formed. That is to say that due to this inert property, stable isotopic information contained within the tissue is preserved even if the animal moves to a vastly different geographical location (Wunder, 2012). This is useful because geographical distributions of stable isotopes in the environment are dependent upon temperature and humidity gradients (Wunder, 2012). Thus, using these geographical distributions, if the stable isotope composition of a certain metabolically inert tissue is known, then the geographic location of where it was formed can be inferred. Linking inferences of geographic location across time therefore leads to predictions of animal migratory routes. For example, strontium isotope ratios in the tooth enamel of late Pleistocean mammal fossils from northern Florida are shown to resemble strontium isotope ratios observed in Florida environments (Hoppe and Koch, 2007). This leads to the prediction that these animals did not migrate far away from the Florida region, which may be due to vegetation patterns (Hoppe & Koch, 2007).

Inferences of where an animal was can be made using nominal assignment approaches. Here, a set of candidate geographic locations of origin are defined, and tissues of known origin then characterize the isotopic landscape of these locations (Wunder, 2012). Given this characterization, animals of unknown origin can then be assigned to the locations which most closely agree with their tissue isotopic composition (Wunder, 2012). Since biological measurements often entail a high degree of variance, a probabilistic assignment approach is warranted. Wunder (2012) described such an approach, where the probability of a tissue having originally formed in some location l given its isotope value i is modelled with Bayes’ rule. Let L be the set of all candidate locations, and then (Wunder, 2012):

P(l|i) = \frac{P(i|l)P(l)}{\int_l^LP(l)dl}

These probabilistic assignment approaches can be visualized graphically in Figure 2 below. Here, a, b, and c are 3 hypothetical locations where individual animals can be assigned (Wunder, 2012). By inputting carbon and nitrogen isotope values into the Bayesian assignment model, the location which returns the highest P(l|i) is then decided as the location of origin. Repeating this across the entire domain, one can obtain the probabilistic decision model in Figure 2.

Figure 2: Hypothetical assignment model using Bayes’ rule. Carbon and nitrogen isotope parameters determine the location from which an individual animal is most likely to have originated from. [Adapted from (Wunder, 2012)]

Overall, assignment approaches such as the one outlined here are useful for predicting where an individual animal was, and where it went. Such methods operate under the principle that isotopic distributions across geographic locations are reflected in the animals themselves.

Challenges of Stable Isotopic Analysis

Inverse Methods for Improving Estimations of Isotopic Input

During mammalian amelogenesis (tooth development), an animal’s isotopic composition is recorded into the tooth enamel along its growth axes (Passey et al., 2002). When excavated millions of years later, these tooth archives present an isotopic record of the temporal variations that occurred within the animal’s lifetime. Ancient seasonal changes in environment, animal behaviour, and plant diet can all be inferred (Passey et al., 2002). However, an obstacle facing such inferences is that the measured isotopic profile of teeth is time-averaged (Passey et al., 2002). That is, enamel is not fully mineralized when first formed and needs to undergo a maturation period (Passey et al., 2002). Thus, the final mineralized enamel records an average of isotopic changes that occurred during the maturation process, and does not fully reflect actual isotopic variations. Passey et al. (2002) explored this phenomenon and developed a mathematical model which predicts how the true isotopic characteristics of an animal across time will be transformed into the final measured isotopic profile in teeth. The model assumes a constant growth rate in teeth, and is described below from a high level, along with Figures 3 and 4.

Figure 3: The averaging matrix A that linearly transforms the vector m to d for a modern hippopotamus canine. [Adapted from (Passey et al., 2005)]
Figure 4: Schematic overview of the role of the averaging matrix A. It transforms the true temporal isotopic variations within an animal body (a) into the isotopic signal that would be observed in tooth enamel (b). Inverse transformation recovers a closer approximation of original isotopic variations (c). [Adapted from (Passey et al., 2005)]

Let d be the vector representing the measured tooth enamel isotopic profile. Let m be the vector representing the true pattern of temporal variations in the animal body’s isotopic composition. Then, let A be the set of functions mapping m to d such that A x m = d. The matrix A is an averaging matrix, modelling the forward linear transformation from m to d due to the averaging effects of amelogenesis. It is specific to the tooth being studied. Once A has been developed, the important consequence is that given d, m can then be solved for, because clearly m = A-1 x d. Passey et al. (2005) made use of this, demonstrating the inverse modelling of modern hippopotamus carbon isotope profiles using measured tooth enamel isotopic profiles in hippo canines (d). By reversing the averaging effects of amelogenesis, they reconstruct a closer approximation of the hippo’s true isotopic variations across time. In fact, their results reveal hippo dietary histories that are not apparent from simply examining the tooth enamel (Passey et al., 2002). Thus, by developing such forward models, Passey et al. (2005) showed that inverse methods can potentially overcome confounding limitations present in initial observations of tooth enamel.

Minor Element Concentrations as Indicators of Diagenetic Alterations

The isotope content of marine fossils provide very useful indicators for paleoclimatic estimations. In paleontology, it is common practice to use the carbon-13 and oxygen-18 isotope ratio in marine fossils for paleoenvironmental analysis. Namely, brachiopod fossils have been particularly useful for this because of their common availability in marine sediments and the shell tendency to keep isotopic equilibrium with the surrounding seawater (Fujioka et al., 2019). For these reasons, the brachiopod fossils are readily utilized as archives of past ocean environments. However, one crucial liability exists in this methodology, which is the variability in the isotopic content due to diagenesis during fossilization (Fujioka et al., 2019). Failure to account for this liability results in large uncertainties and frequent outliers in the data, more often than not generating inconclusive results (Fukioka et al., 2019). Therefore, in order to yield any useful inferences, researchers must find a way to eliminate samples that had undergone major alterations to the isotope composition due to diagenesis.

In particular, Fujioka et al. (2019) conducted a statistical study to determine some of the indicators of meteoric diagenesis (alterations from precipitation) in brachiopods. In this study, it was concluded that the manganese concentration was the most sensitive to the meteoric diagenetic alterations. Fujioka et al. (2019) reasoned that meteoric water generally contains more Mn and other trace elements compared to sea water therefore, diagenetically altered species must contain higher manganese concentration. This was confirmed by comparing Mn concentration data to the cathodoluminescence observations of the fossil, which is a quantifiable measure of the deformities in the microstructure of the fossil (Fujioka et al., 2019). As shown in Figure 5, Fujioka et al. (2019) discovered statistically significant (p < 0.01) strong positive correlation, indicating a statistical relationship between the Mn concentration and the degree of diagenetic alteration the sample has undergone. Necessarily, this implies that Mn concentration can be used as a benchmark to eliminate samples that have undergone significant diagenesis to improve the accuracy of the inferences taken from marine fossils. Although this is only a small portion of the tools paleontologists have at hand, this exemplifies how researchers can go about maneuvering challenges faced in paleoclimatology.

Figure 5: Combined scatterplot of two different species of brachiopods as a function of Mn concentration. [Adapted from (Fujioka et al., 2019)]

Analysis of Non-Traditional Isotopes:

The most widely-used isotopes in paleontological, archaeological and ecological studies are those of light elements which appear in high abundance, namely those of carbon (13C), nitrogen (15N), oxygen (18O) and sulfur (34S). These light isotope systems demonstrate a large degree of variability (greater than 10‰), but they are more susceptible to alteration in diagenesis (Martin et al., 2017). For example, nitrogen and carbon in bone collagen are an excellent tool for analyzing mammalian diets, but the relatively quick decay of collagen limits analyses to more recent eras (Kuitems et al., 2015). Heavier isotope systems, on the other hand, have a maximum variability of 2-3‰ (Martin et al., 2017). These systems require a much higher degree of precision from mass spectrometers, but display the unique advantage of being less affected by diagenetic processes.

Before delving into the practical applications of these non-traditional heavy isotope systems, it is necessary to quantify just how much (or how little) they have been altered by diagenesis. Two important measurements to consider here between the water (diagenetic fluid) and rock (fossil) are the concentration ratios (i.e. water to rock ratio) and the difference in isotopic composition between the water and the rock. These are called W/R equations (for water/rock). Martin et al. (2017) showed that the W/R isotope and concentration data can be modelled as follows:

\delta M_{mix} = \frac{xM_{bio} \times \delta M_{bio} \times [M]_{bio} + (1-x)M_{dia} \times \delta M_{dia} \times [M]_{dia}}{xM_{bio} \times [M]_{bio} + (1-x)M_{dia} \times [M]_{dia}}

Here, M represents the metal of interest; (M) represents the concentration of said metal while δM represents the isotopic composition. Mbio refers to the biological fraction while Mdia refers to the diagenetic fraction… x is the fraction of altered bioapatite, the major component in mineralized bones. Once the value δMmix is known, the deviation from the original isotopic composition is shown by the ratio:

deviation = \frac{\delta M_{mix}}{\delta M_{bio}} \times 100 \%

Plotting this ratio for various metals as a function of the W/R ratio displays the situations in which each metal is more or less susceptible to diagenesis, as can be seen in Figure 6 below. Note that the water to rock ratio is assumed to be indicative of the percentage of altered bioapatite in the fossil.

Figure 6: Percent deviation of δM as a function of W/R ratio, for magnesium, copper, calcium, zinc and iron. The effects of sea water and fresh water are both shown. Note the logarithmic scale on the y axis. [Adapted from (Martin et al., 2017)]

Summarizing the information presented in Figure 6 above, it is evident that Calcium is the least susceptible to diagenesis, as it is present in significantly higher concentrations in fossilized bone than in any water. The transition metals (copper, zinc and iron) are not susceptible to diagenesis in seawater, but they are quite susceptible to diagenesis in rivers (i.e. the concentration of these metals, especially copper, is greater in river water than in fossils). Inversely, magnesium is not very susceptible to diagenesis in river water, but is moderately susceptible to diagenesis in sea water. In all cases, percent diagenesis increases as the water to rock ratio increases.

While each of these metals tells its own story, the information held within Calcium isotopes is of particular interest. Calcium has six stable isotopes, the main isotope being 40Ca with an abundance of about 96.98% (Zhu & Macdougall, 1998). 44Ca makes up an additional 2.06%, 42Ca accounts for 0.64%, and the other three isotopes (43Ca, 46Ca, 48Ca) split the remaining third of a percent (Zhu & Macdougall, 1998). A 2017 study by Martin et al. (2017) investigated the isotope variability in δ42/44Ca of late-Pleistocene mammal specimens from caves in Belgium and France. Calcium was extracted from the 45 bone and enamel specimens representing 11 species and purified with cation-exchange resin. As the 40Ca could not be measured due to interference with 40Ar plasma used in the mass spectrometer, the isotopic ratios were expressed by the following equation:

\delta^{44/42}Ca = [\frac{(^{44}Ca/^{42}Ca)_{\text{sample}}}{(^{44}Ca/^{42}Ca)_{\text{ICP Ca Lyon}}}-1] \times 1000

Where ICP Ca Lyon represents the Lyon Standard of calcium in Inductively Coupled Plasma (ICP) mass spectrometry. The multiplication by 1000 is due to the expression of isotopic ratios as per thousand. The results of the analysis are shown in Figure 7 below.

Figure 7: Calcium isotopic ratios from bone and enamel of 11 Pleistocene mammal species. [Adapted from (Martin et al., 2017)]

Two conclusions are immediately evident from the above figure. First, the preservation of isotopes in bone tissue vs. enamel is susceptible to different amounts of diagenesis. It should thus be noted that for sound scientific comparison, tissues analyzed using stable isotopes must be of the same nature. Second, Figure 7 demonstrates a strong coherence (i.e. low dispersion) in isotopic ratios within taxonomic groups. C. crocuta, the only true carnivore in the bone dataset, shows the lowest (and thus most bio-purified) δ42/44Ca values, indicating that it occupies the highest trophic position (Martin et al., 2017). M. primigenius is an outlier here, showing δ42/44Ca levels similar to that of the hyena (C. crocuta). However, as discussed in our previous essay, mammoths have been known to practice coprophagy (Fisher et al., 2012), and as such could appear similar to carnivores isotopically. Conversely, as δ42/44Ca is much more variable in plants, herbivores (B. priscus, C. antiquitatis, E. caballus) and omnivores (U. arctos, U. spelaeus) display a much higher, less bio-purified range of δ42/44Ca values (Martin et al., 2017). Thus, although it presents some unique challenges, isotopic analysis of non-traditional elements can provide alternative insight into prehistoric inter-species relationships.


Stable isotopes provide useful insights about past life to researchers due to their unique preservative properties. Oftentimes, stable isotope ratios remain fixed after the formation of organic matter, acting as snapshots of the initial conditions during the formation. This property aids the inferences on the paleoecological picture of the mammals in question. For example, analysis of 12C and 13C in mammal bones can determine their probable diet and habitat, and with additional information from 14N and 15N, scientists can even begin to construct trophic chains of ancient ecosystems. In addition, mathematical analysis using Bayes’ rule allows paleontologists to predict migration trajectories. However, stable isotope analysis isn’t a walk in the park – there are quite a few challenges which obstruct progress. Frustratingly, time-averaging effects of amelogenesis blurs the actual variations in body isotopic composition. Thankfully, the Passey et al. matrix has been developed to reverse this process and clarify the dataset. Another confounding issue is diagenesis. While some elements might be particularly susceptible to diagenesis, other elements such as manganese and calcium are much more resistant. Unfortunately, these elements display less isotopic variation and thus require analysis with precisely-calibrated machinery. Of course, with the correct tools, these elements can provide equally significant data as carbon and nitrogen isotopes with the added advantage of being less altered over a large geological time scale.


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