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Isotope analysis is the identification of
isotopic signature An isotopic signature (also isotopic fingerprint) is a ratio of non-radiogenic ' stable isotopes', stable radiogenic isotopes, or unstable radioactive isotopes of particular elements in an investigated material. The ratios of isotopes in a sample ...
, abundance of certain stable isotopes of chemical elements within organic and
inorganic compounds An inorganic compound is typically a chemical compound that lacks carbon–hydrogen bonds⁠that is, a compound that is not an organic compound. The study of inorganic compounds is a subfield of chemistry known as '' inorganic chemistry''. Inorg ...
. Isotopic analysis can be used to understand the flow of energy through a food web, to reconstruct past environmental and climatic conditions, to investigate human and animal diets, for food authentification, and a variety of other physical, geological, palaeontological and chemical processes. Stable isotope ratios are measured using
mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a ''mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is used ...
, which separates the different isotopes of an element on the basis of their mass-to-charge ratio.


Tissues affected

Isotopic oxygen is incorporated into the body primarily through ingestion at which point it is used in the formation of, for archaeological purposes,
bone A bone is a rigid organ that constitutes part of the skeleton in most vertebrate animals. Bones protect the various other organs of the body, produce red and white blood cells, store minerals, provide structure and support for the body, ...
s and teeth. The oxygen is incorporated into the hydroxylcarbonic
apatite Apatite is a group of phosphate minerals, usually hydroxyapatite, fluorapatite and chlorapatite, with high concentrations of Hydroxide, OH−, Fluoride, F− and Chloride, Cl− ion, respectively, in the crystal. The formula of the admixture of ...
of bone and
tooth enamel Tooth enamel is one of the four major Tissue (biology), tissues that make up the tooth in humans and many animals, including some species of fish. It makes up the normally visible part of the tooth, covering the Crown (tooth), crown. The other ...
.
Bone A bone is a rigid organ that constitutes part of the skeleton in most vertebrate animals. Bones protect the various other organs of the body, produce red and white blood cells, store minerals, provide structure and support for the body, ...
is continually remodelled throughout the lifetime of an individual. Although the rate of turnover of isotopic oxygen in
hydroxyapatite Hydroxyapatite (International Mineralogical Association, IMA name: hydroxylapatite) (Hap, HAp, or HA) is a naturally occurring mineral form of calcium apatite with the Chemical formula, formula , often written to denote that the Crystal struc ...
is not fully known, it is assumed to be similar to that of
collagen Collagen () is the main structural protein in the extracellular matrix of the connective tissues of many animals. It is the most abundant protein in mammals, making up 25% to 35% of protein content. Amino acids are bound together to form a trip ...
; approximately 10 years. Consequently, should an individual remain in a region for 10 years or longer, the isotopic oxygen ratios in the bone hydroxyapatite would reflect the isotopic oxygen ratios present in that region. Teeth are not subject to continual remodelling and so their isotopic oxygen ratios remain constant from the time of formation. The isotopic oxygen ratios, then, of teeth represent the ratios of the region in which the individual was born and raised. Where
deciduous teeth Deciduous teeth or primary teeth, also informally known as baby teeth, milk teeth, or temporary teeth,Fehrenbach, MJ and Popowics, T. (2026). ''Illustrated Dental Embryology, Histology, and Anatomy'', 6th edition, Elsevier, page 287–296. are ...
are present, it is also possible to determine the age at which a child was weaned.
Breast milk Breast milk (sometimes spelled as breastmilk) or mother's milk is milk produced by the mammary glands in the breasts of women. Breast milk is the primary source of nutrition for newborn infants, comprising fats, proteins, carbohydrates, and a var ...
production draws upon the
body water In physiology, body water is the water content of an animal body that is contained in the tissues, the blood, the bones and elsewhere. The percentages of body water contained in various fluid compartments add up to total body water (TBW). This ...
of the mother, which has higher levels of 18O due to the preferential loss of 16O through sweat, urine, and expired water vapour. While teeth are more resistant to chemical and physical changes over time, both are subject to post-depositional diagenesis. As such, isotopic analysis makes use of the more resistant
phosphate Phosphates are the naturally occurring form of the element phosphorus. In chemistry, a phosphate is an anion, salt, functional group or ester derived from a phosphoric acid. It most commonly means orthophosphate, a derivative of orthop ...
groups, rather than the less abundant hydroxyl group or the more likely diagenetic
carbonate A carbonate is a salt of carbonic acid, (), characterized by the presence of the carbonate ion, a polyatomic ion with the formula . The word "carbonate" may also refer to a carbonate ester, an organic compound containing the carbonate group ...
groups present.


Applications

Isotope analysis has widespread applicability in the
natural science Natural science or empirical science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer ...
s. These include numerous applications in the biological,
earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...
and environmental sciences.


Archaeology


Reconstructing ancient diets

Archaeological Archaeology or archeology is the study of human activity through the recovery and analysis of material culture. The archaeological record consists of Artifact (archaeology), artifacts, architecture, biofact (archaeology), biofacts or ecofacts, ...
materials, such as bone, organic residues, hair, or sea shells, can serve as substrates for isotopic analysis.
Carbon Carbon () is a chemical element; it has chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetravalent—meaning that its atoms are able to form up to four covalent bonds due to its valence shell exhibiting 4 ...
,
nitrogen Nitrogen is a chemical element; it has Symbol (chemistry), symbol N and atomic number 7. Nitrogen is a Nonmetal (chemistry), nonmetal and the lightest member of pnictogen, group 15 of the periodic table, often called the Pnictogen, pnictogens. ...
and
zinc Zinc is a chemical element; it has symbol Zn and atomic number 30. It is a slightly brittle metal at room temperature and has a shiny-greyish appearance when oxidation is removed. It is the first element in group 12 (IIB) of the periodic tabl ...
isotope ratios are used to investigate the diets of past people; these isotopic systems can be used with others, such as strontium or oxygen, to answer questions about population movements and cultural interactions, such as trade. Carbon isotopes are analysed in archaeology to determine the source of carbon at the base of the foodchain. Examining the 12C/ 13C isotope ratio, it is possible to determine whether animals and humans ate predominantly C3 or C4 plants. Potential C3 food sources include
wheat Wheat is a group of wild and crop domestication, domesticated Poaceae, grasses of the genus ''Triticum'' (). They are Agriculture, cultivated for their cereal grains, which are staple foods around the world. Well-known Taxonomy of wheat, whe ...
,
rice Rice is a cereal grain and in its Domestication, domesticated form is the staple food of over half of the world's population, particularly in Asia and Africa. Rice is the seed of the grass species ''Oryza sativa'' (Asian rice)—or, much l ...
,
tuber Tubers are a type of enlarged structure that plants use as storage organs for nutrients, derived from stems or roots. Tubers help plants perennate (survive winter or dry months), provide energy and nutrients, and are a means of asexual reproduc ...
s,
fruit In botany, a fruit is the seed-bearing structure in flowering plants (angiosperms) that is formed from the ovary after flowering. Fruits are the means by which angiosperms disseminate their seeds. Edible fruits in particular have long propaga ...
s, nuts and many
vegetable Vegetables are edible parts of plants that are consumed by humans or other animals as food. This original meaning is still commonly used, and is applied to plants collectively to refer to all edible plant matter, including edible flower, flo ...
s, while C4 food sources include millet and sugar cane. Carbon isotope ratios can also be used to distinguish between marine, freshwater, and terrestrial food sources. Carbon isotope ratios can be measured in bone
collagen Collagen () is the main structural protein in the extracellular matrix of the connective tissues of many animals. It is the most abundant protein in mammals, making up 25% to 35% of protein content. Amino acids are bound together to form a trip ...
or bone mineral ( hydroxylapatite), and each of these fractions of bone can be analysed to shed light on different components of diet. The carbon in bone collagen is predominantly sourced from dietary protein, while the carbon found in bone mineral is sourced from all consumed dietary carbon, included carbohydrates, lipids, and protein. Nitrogen isotopes can be used to infer soil conditions, with enriched
δ15N In geochemistry, hydrology, paleoclimatology and paleoceanography, ''δ''15N (pronounced "delta fifteen n") or delta-N-15 is a measure of the ratio of the two stable isotopes of nitrogen, 15N: 14N. Formulas Two very similar expressions for a ...
used to infer the addition of
manure Manure is organic matter that is used as organic fertilizer in agriculture. Most manure consists of animal feces; other sources include compost and green manure. Manures contribute to the fertility of soil by adding organic matter and nut ...
. A complication is that enrichment also occurs as a result of environmental factors, such as wetland denitrification,
salinity Salinity () is the saltiness or amount of salt (chemistry), salt dissolved in a body of water, called saline water (see also soil salinity). It is usually measured in g/L or g/kg (grams of salt per liter/kilogram of water; the latter is dimensio ...
, aridity,
microbes A microorganism, or microbe, is an organism of microscopic size, which may exist in its single-celled form or as a colony of cells. The possible existence of unseen microbial life was suspected from antiquity, with an early attestation in ...
, and clearance. δ13C and δ15N measurements on medieval manor soils has shown that stable isotopes can differentiate between crop cultivation and grazing activities, revealing land use types such as cereal production and the presence of fertilization practices at historical sites. To obtain an accurate picture of palaeodiets, it is important to understand processes of diagenesis that may affect the original isotopic signal. It is also important for the researcher to know the variations of isotopes within individuals, between individuals, and over time.


Sourcing archaeological materials

Isotope analysis has been particularly useful in archaeology as a means of characterization. Characterization of artifacts involves determining the isotopic composition of possible source materials such as metal ore bodies and comparing these data to the isotopic composition of analyzed artifacts. A wide range of archaeological materials such as metals, glass and lead-based pigments have been sourced using isotopic characterization. Particularly in the Bronze Age Mediterranean, lead isotope analysis has been a useful tool for determining the sources of metals and an important indicator of trade patterns. Interpretation of lead isotope data is, however, often contentious and faces numerous instrumental and methodological challenges. Problems such as the mixing and re-using of metals from different sources, limited reliable data and contamination of samples can be difficult problems in interpretation.


Ecology

All biologically active elements exist in a number of different isotopic forms, of which two or more are stable. For example, most carbon is present as 12C, with approximately 1% being 13C. The ratio of the two isotopes may be altered by biological and geophysical processes, and these differences can be utilized in a number of ways by ecologists. The main elements used in isotope
ecology Ecology () is the natural science of the relationships among living organisms and their Natural environment, environment. Ecology considers organisms at the individual, population, community (ecology), community, ecosystem, and biosphere lev ...
are carbon, nitrogen, oxygen, hydrogen and sulfur, but also include silicon, iron, and strontium.


Stable isotope analysis in aquatic ecosystems

Stable isotopes have become a popular method for understanding
aquatic ecosystem An aquatic ecosystem is an ecosystem found in and around a body of water, in contrast to land-based terrestrial ecosystems. Aquatic ecosystems contain communities of organisms—aquatic life—that are dependent on each other and on their environ ...
s because they can help scientists in understanding source links and process information in marine food webs. These analyses can also be used to a certain degree in terrestrial systems. Certain isotopes can signify distinct primary producers forming the bases of food webs and trophic level positioning. The stable isotope compositions are expressed in terms of delta values (δ) in permil (‰), i.e. parts per thousand differences from a standard. They express the proportion of an isotope that is in a sample. The values are expressed as: : ''δX'' = ''R''sample / ''R''standard) – 1× 103 where X represents the isotope of interest (e.g., 13C) and R represents the ratio of the isotope of interest and its natural form (e.g., 13C/12C). Higher (or less negative) delta values indicate increases in a sample's isotope of interest, relative to the standard, and lower (or more negative) values indicate decreases. The standard reference materials for carbon, nitrogen, and sulfur are Pee Dee Belamnite limestone, nitrogen gas in the atmosphere, and Cañon Diablo meteorite respectively. Analysis is usually done using a mass spectrometer, detecting small differences between gaseous elements. Analysis of a sample can cost anywhere from $30 to $100. Stable isotopes assist scientists in analyzing animal diets and food webs by examining the animal tissues that bear a fixed isotopic enrichment or depletion vs. the diet. Muscle or protein fractions have become the most common animal tissue used to examine the isotopes because they represent the assimilated nutrients in their diet. The main advantage to using stable isotope analysis as opposed to stomach content observations is that no matter what the status is of the animal's stomach (empty or not), the isotope tracers in the tissues will give us an understanding of its trophic position and food source. The three major isotopes used in aquatic ecosystem food web analysis are 13C, 15N and 34S. While all three indicate information on trophic dynamics, it is common to perform analysis on at least two of the previously mentioned three isotopes for better understanding of marine trophic interactions and for stronger results.


=Hydrogen-2

= The ratio of 2H, also known as
deuterium Deuterium (hydrogen-2, symbol H or D, also known as heavy hydrogen) is one of two stable isotopes of hydrogen; the other is protium, or hydrogen-1, H. The deuterium nucleus (deuteron) contains one proton and one neutron, whereas the far more c ...
, to 1H has been studied in both plant and animal tissue. Hydrogen isotopes in plant tissue are correlated with local water values but vary based on fractionation during
photosynthesis Photosynthesis ( ) is a system of biological processes by which photosynthetic organisms, such as most plants, algae, and cyanobacteria, convert light energy, typically from sunlight, into the chemical energy necessary to fuel their metabo ...
, transpiration, and other processes in the formation of cellulose. A study on the isotope ratios of tissues from plants growing within a small area in Texas found tissues from CAM plants were enriched in deuterium relative to C4 plants. Hydrogen isotope ratios in animal tissue reflect diet, including drinking water, and have been used to study bird migration and aquatic food webs.


=Carbon-13

= Carbon isotopes aid us in determining the primary production source responsible for the energy flow in an ecosystem. The transfer of 13C through trophic levels remains relatively the same, except for a small increase (an enrichment < 1 ‰). Large differences of δ13C between animals indicate that they have different food sources or that their food webs are based on different primary producers (i.e. different species of phytoplankton, marsh grasses.) Because δ13C indicates the original source of primary producers, the isotopes can also help us determine shifts in diets, both short term, long term or permanent. These shifts may even correlate to seasonal changes, reflecting phytoplankton abundance. Scientists have found that there can be wide ranges of δ13C values in phytoplankton populations over a geographic region. While it is not quite certain as to why this may be, there are several hypotheses for this occurrence. These include isotopes within dissolved inorganic carbon pools (DIC) may vary with temperature and location and that growth rates of phytoplankton may affect their uptake of the isotopes. δ13C has been used in determining migration of juvenile animals from sheltered inshore areas to offshore locations by examining the changes in their diets. A study by Fry (1983) studied the isotopic compositions in juvenile shrimp of south Texas grass flats. Fry found that at the beginning of the study the shrimp had isotopic values of δ13C = -11 to -14‰ and 6-8‰ for δ15N and δ34S. As the shrimp matured and migrated offshore, the isotopic values changed to those resembling offshore organisms (δ13C= -15‰ and δ15N = 11.5‰ and δ34S = 16‰).


=Sulfur-34

= While there is no enrichment of 34S between trophic levels, the stable isotope can be useful in distinguishing
benthic The benthic zone is the ecological region at the lowest level of a body of water such as an ocean, lake, or stream, including the sediment surface and some sub-surface layers. The name comes from the Ancient Greek word (), meaning "the depths". ...
vs.
pelagic The pelagic zone consists of the water column of the open ocean and can be further divided into regions by depth. The word ''pelagic'' is derived . The pelagic zone can be thought of as an imaginary cylinder or water column between the sur ...
producers and
marsh In ecology, a marsh is a wetland that is dominated by herbaceous plants rather than by woody plants.Keddy, P.A. 2010. Wetland Ecology: Principles and Conservation (2nd edition). Cambridge University Press, Cambridge, UK. 497 p More in genera ...
vs. phytoplankton producers. Similar to 13C, it can also help distinguish between different phytoplankton as the key primary producers in food webs. The differences between seawater sulfates and sulfides (c. 21‰ vs -10‰) aid scientists in the discriminations. Sulfur tends to be more plentiful in less aerobic areas, such as benthic systems and marsh plants, than the pelagic and more aerobic systems. Thus, in the benthic systems, there are smaller δ34S values.


=Nitrogen-15

= Nitrogen isotopes indicate the trophic level position of organisms (reflective of the time the tissue samples were taken). There is a larger enrichment component with δ15N because its retention is higher than that of 14N. This can be seen by analyzing the waste of organisms. Cattle urine has shown that there is a depletion of 15N relative to the diet. As organisms eat each other, the 15N isotopes are transferred to the predators. Thus, organisms higher in the trophic pyramid have accumulated higher levels of 15N ( and higher δ15N values) relative to their prey and others before them in the food web. Numerous studies on marine ecosystems have shown that on average there is a 3.2‰ enrichment of 15N vs. diet between different trophic level species in ecosystems. In the Baltic sea, Hansson et al. (1997) found that when analyzing a variety of creatures (such as particulate organic matter (phytoplankton), zooplankton, mysids, sprat, smelt and herring,) there was an apparent fractionation of 2.4‰ between consumers and their apparent prey. In addition to trophic positioning of organisms, δ15N values have become commonly used in distinguishing between land derived and natural sources of nutrients. As water travels from septic tanks to aquifers, the nitrogen rich water is delivered into coastal areas. Waste-water nitrate has higher concentrations of 15N than the nitrate that is found in natural soils in near shore zones. For bacteria, it is more convenient for them to uptake 14N as opposed to 15N because it is a lighter element and easier to metabolize. Thus, due to bacteria's preference when performing biogeochemical processes such as denitrification and volatilization of ammonia, 14N is removed from the water at a faster rate than 15N, resulting in more 15N entering the aquifer. 15N is roughly 10-20‰ as opposed to the natural 15N values of 2-8‰. The inorganic nitrogen that is emitted from septic tanks and other human-derived sewage is usually in the form of NH4+. Once the nitrogen enters the estuaries via groundwater, it is thought that because there is more 15N entering, that there will also be more 15N in the inorganic nitrogen pool delivered and that it is picked up more by producers taking up N. Even though 14N is easier to take up, because there is much more 15N, there will still be higher amounts assimilated than normal. These levels of δ15N can be examined in creatures that live in the area and are non migratory (such as macrophytes, clams and even some fish). This method of identifying high levels of nitrogen input is becoming a more and more popular method in attempting to monitor nutrient input into estuaries and coastal ecosystems. Environmental managers have become more and more concerned about measuring anthropogenic nutrient inputs into estuaries because excess in nutrients can lead to
eutrophication Eutrophication is a general term describing a process in which nutrients accumulate in a body of water, resulting in an increased growth of organisms that may deplete the oxygen in the water; ie. the process of too many plants growing on the s ...
and hypoxic events, eliminating organisms from an area entirely.


=Oxygen-18

= Analysis of the ratio of 18O to 16O in the shells of the Colorado Delta clam was used to assess the historical extent of the
estuary An estuary is a partially enclosed coastal body of brackish water with one or more rivers or streams flowing into it, and with a free connection to the open sea. Estuaries form a transition zone between river environments and maritime enviro ...
in the Colorado River Delta prior to construction of upstream dams.


Forensic science

A recent development in
forensic science Forensic science combines principles of law and science to investigate criminal activity. Through crime scene investigations and laboratory analysis, forensic scientists are able to link suspects to evidence. An example is determining the time and ...
is the isotopic analysis of hair strands. Hair has a recognisable growth rate of 9-11mm per month or 15 cm per year. Human hair growth is primarily a function of diet, especially drinking water intake. The stable isotopic ratios of drinking water are a function of location, and the geology that the water percolates through. 87Sr, 88Sr and oxygen isotope variations are different all over the world. These differences in isotopic ratio are then biologically 'set' in our hair as it grows and it has therefore become possible to identify recent geographic histories by the analysis of hair strands. For example, it could be possible to identify whether a terrorist suspect had recently been to a particular location from hair analysis. This hair analysis is a non-invasive method which is becoming very popular in cases that DNA or other traditional means are bringing no answers. Isotope analysis can be used by forensic investigators to determine whether two or more samples of explosives are of a common origin. Most high explosives contain carbon, hydrogen, nitrogen and oxygen atoms and thus comparing their relative abundances of isotopes can reveal the existence of a common origin. Researchers have also shown that analysis of the 12C/13C ratios can locate the country of origin for a given explosive. Stable isotopic analysis has also been used in the identification of drug trafficking routes. Isotopic abundances are different in morphine grown from poppies in south-east Asia versus poppies grown in south-west Asia. The same is applied to cocaine that is derived from Bolivia and that from Colombia.


Traceability

Stable isotopic analysis has also been used for tracing the geographical origin of food, timber, and in tracing the sources and fates of nitrates in the environment.


Geology


Hydrology

In isotope hydrology, stable isotopes of water (2H and 18O) are used to estimate the source, age, and flow paths of water flowing through ecosystems. The main effects that change the stable isotope composition of water are
evaporation Evaporation is a type of vaporization that occurs on the Interface (chemistry), surface of a liquid as it changes into the gas phase. A high concentration of the evaporating substance in the surrounding gas significantly slows down evapora ...
and
condensation Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapor ...
. Variability in water isotopes is used to study sources of water to streams and rivers, evaporation rates, groundwater recharge, and other hydrological processes.


Paleoclimatology

The ratio of 18O to 16O in ice and deep sea cores is temperature dependent, and can be used as a proxy measure for reconstructing climate change. During colder periods of the Earth's history (glacials) such as during the
ice age An ice age is a long period of reduction in the temperature of Earth's surface and atmosphere, resulting in the presence or expansion of continental and polar ice sheets and alpine glaciers. Earth's climate alternates between ice ages, and g ...
s, 16O is preferentially evaporated from the colder oceans, leaving the slightly heavier and more sluggish 18O behind. Organisms such as
foraminifera Foraminifera ( ; Latin for "hole bearers"; informally called "forams") are unicellular organism, single-celled organisms, members of a phylum or class (biology), class of Rhizarian protists characterized by streaming granular Ectoplasm (cell bio ...
which combine oxygen dissolved in the surrounding water with carbon and calcium to build their shells therefore incorporate the temperature-dependent 18O to 16O ratio. When these organisms die, they settle out on the sea bed, preserving a long and invaluable record of global climate change through much of the
Quaternary The Quaternary ( ) is the current and most recent of the three periods of the Cenozoic Era in the geologic time scale of the International Commission on Stratigraphy (ICS), as well as the current and most recent of the twelve periods of the ...
. Similarly, ice cores on land are enriched in the heavier 18O relative to 16O during warmer climatic phases (
interglacial An interglacial period (or alternatively interglacial, interglaciation) is a geological interval of warmer global average temperature lasting thousands of years that separates consecutive glacial periods within an ice age. The current Holocene i ...
s) as more energy is available for the evaporation of the heavier 18O isotope. The oxygen isotope record preserved in the ice cores is therefore a "mirror" of the record contained in ocean sediments. Oxygen isotopes preserve a record of the effects of the Milankovitch cycles on climate change during the Quaternary, revealing an approximately 100,000-year cyclicity in the Earth's climate.


References


External links


MixSIAR
MixSIAR is an R package that helps you create and run Bayesian mixing models to analyze biotracer data (i.e. stable isotopes, fatty acids), following the MixSIAR model framework. Both graphical user interface (GUI) and script versions are available. Stock, B.C., Jackson, A.L., Ward, E.J., Parnell, A.C., Phillips, D.L., Semmens, B.X
Associated peer-reviewed research paper


Stable isotope mixing model for an excess number of sources (Visual Basic), (Phillips and Gregg, 2003). *

Bayesian mixing model package for the R environment. Parnell, A., Inger, R., Bearhop, S., Jackson, A.
SISUS: Stable Isotope Sourcing using Sampling
Stable Isotope Sourcing using Sampling (SISUS) (Erhardt, Wolf, and Bedrick, In Prep.) provides a more efficient algorithm to provide solutions to the same problem as the Phillips and Gregg (2003) IsoSource model and software for source partitioning using stable isotopes. *{{cite journal , doi=10.1371/journal.pone.0028478 , pmid=22235246 , pmc=3250396 , title=Estimating the Diets of Animals Using Stable Isotopes and a Comprehensive Bayesian Mixing Model , journal=PLOS ONE , volume=7 , issue=1 , pages=e28478 , year=2012 , last1=Hopkins , first1=John B , last2=Ferguson , first2=Jake M , bibcode=2012PLoSO...728478H , doi-access=free Isotopes