Answers for Problem 10, Chapter 5
Here are the answers for six steps, and graphs showing the details of the work can
be found in the appended powerpoint slides. You might want to check out the graphs
first, to see if you can get the gist of the progression, and see if your graphs look similar.
The complete data table accumulated from all the steps is given in Table A as the starting
point of the answers.
Table A. Final food web results in tabular form. Trophic level assignments are based on
δ15N data. The source assignments, %Corn and %Tree Leaves, were made using the
corrected δ13C values, values that had been adjusted for trophic level (TL) 13C
fractionation.
δ15N
TL
original
δ13C
corrected
δ13C
Tree Leaves
2
Mushroom
3
Worm
4.2
Centipede
8
Spider #1
5
Spider #2
10
Sparrow feather
8.5
Eagle feather
12
Corn
2
Grasshoppers (herbivores) 4.2
1.0
1.3
1.7
3.0
2.0
3.7
3.2
4.3
1.0
1.7
-27.0
-24.0
-26.0
-21.0
-24.0
-21.0
-23.0
-18.0
-13.0
-13.0
-27.0
-24.2
-26.4
-22.0
-24.5
-22.3
-24.1
-19.7
-13.0
-13.4
%
Corn
0
20
5
36
18
33
21
52
100
97
%
Tree Leaves
100
80
95
64
82
67
79
48
0
3
Step 1. Plotting the raw data. Figures A-D show 4 different ways to plot the data. Many
studies start with graphs that look like Figures. A and B. Figure A is not good because the
current convention is to use the carbon isotope data on the x-axis and the nitrogen isotope
data on the y-axis. One advantage of this convention is that higher 15N values along the
y-axis indicate higher trophic levels at higher positions in the graph, an intuitive result.
Figure B is not good because the symbols on the axes aren’t properly labeled. Figure C is
good, but the carbon units are given more weight than the nitrogen units (i.e., 1o/oo in N
units on the y-axis is only half as big as 1 o/oo in C units on the x-axis). Figure D is
probably best, giving the C and N units the same weight. (Note: Make sure your axes are
labeled correctly. With a word processing program, you can find the “” symbol used in
labeling the graph axes, by typing the letter “d”, highlighting it, then changing the font to
“symbol” - the greek letter “” should appear. Also, be sure to use a superscript for the 13
and 15 in 13C and 15N).
Overall, these initial data do show an increase in 15N expected when several TLs
are involved, and birds have the highest 15N values as expected for top predators. The
data shows a positive correlation between 13C and 15N, which would support the
interpretation that both 13C and 15N increase with increasing TL.
Step 2. Interpret your plot – trophic levels. The TL increases are usually much larger for
15N than 13C, 4-6 times larger. The actual o/oo increases per trophic level are estimated
at 2.2 -3.4o/oo for 15N and 0-1o/oo for 13C, or average values of about 3 and 0.5o/oo
respectively. Ecologists generally trust the 15N-based estimates of TL because of the
much stronger TL signal in the N isotopes than in the C isotopes. Also, source mixing
effects are usually much larger than TL effects for C than for N isotopes, so much so that
TL effects in the carbon data are obscured by source mixing.
Using the 15N data, the plant value at TL1 at the base of the food web is 2o/oo,
and counting upwards from that value with an increment of 3o/oo equaling one TL, the
highest calculated trophic level is 4.3 for the eagle. Using the formula
TL = 1 + (15NCONSUMER - 15NPLANT)/3
gives discrete estimates of TL for each sample (see data in Table A). There is one sample,
spider #1, whose TL seems too low at TL2, the herbivore level. Most spiders are
carnivores - you would have to check the species of this spider to see if it is really known
to be herbivorous.
Step 3. Interpret your plot – sources and 13C. There is a problem with the 13C data, and
here it is: If the animal data represent about 3.3 trophic levels above the plant base, and
13C increases 0.5o/oo per TL, then the total 13C increase from the -27o/oo leaves at the
base of the food web should be 3.3 x 0.5o/oo =1.65o/oo, or -27o/oo + 1.65o/oo = 25.35o/oo. This should be the value for the eagle, but we don’t get that value. Instead we
get the much higher value of -18o/oo. We have much too much 13C enrichment, and the
data look like a stairway that never quits rising (Fig. D).
In fact, this turned out to be a rather typical problem for isotope food web
research. When we asked a more experienced colleague about this result, we heard that
we might consider “inferring” another source to be present that had a much higher (less
negative) 13C value. To check this inference, we went back to the forest site of the
original sample collections. Nearby, we saw many cornfields which we realized also
might have provided food prey for the birds. So we collected corn plus grasshoppers.
After this nice day in the sun, we returned to the laboratory where we dried and ground
the samples, then sent them off for analysis. After a few weeks, the results come back as
these respective 15N and13C values: corn 2o/oo and -13o/oo, and grasshoppers 4.2o/oo
and -13o/oo.
When we add these data, we see the “mixing arch” typical of 2-source food webs
(Fig. E), with sources at either end. Values for predators plot in the top middle,
appropriate since they are the highest TL and integrate all the source inputs from both
sides of the 13C spectrum (Fig. E). With the new data, the increase in 13C at higher TLs
noted above in step 1 can now be re-interpreted in terms of source mixing, but there may
still be a component of TL that needs to be factored out of the 13C interpretations (see
next step). Generally tree leaves seem the most important food resource, but there are
also strong (>20%) contributions from corn for many consumers.
Step 4. 13C-based source assignments revisited and refined. Generally, sample 13C
values increase with increasing trophic level, because of incorporation of 13C-enriched
materials from the diet and isotope fractionation during metabolism (Fry and Sherr 1984,
Fry et al. 1984). Here we are interested in source contributions, so we first factor out
effects of fractionation by subtracting 0.5o/oo for each trophic level above plants.
Fractionation-related 13C corrections are sometimes made for lipid bias in food web
studies, but these further corrections are not included in this simple example.
Applying the trophic level corrections generally shifts the 13C data points
towards more negative values (Table A), indicating a stronger influence from tree leaves
and any other foods that share the -27o/oo carbon isotope value of tree leaves. When we
revisited the study site and collected corn, we noted some streams in the mixed forestcorn landscape, and stream algae can have these same -27o/oo 13C values.
Step 5. Calculate source contributions from corrected 13C values. This is straightforward
from the formula given in step 5 of the problem, and results are given in the Table A. The
tree leaf contributions increase slightly as a result of these corrections that shift 13C
values in a negative directions, towards the values of the tree leaves.
Step 6. Summary. We have worked through an example of how to interpret isotope data
for a food web, plotting the measured 15N and 13C values in a nicely-thought out graph
(Fig. E). We then recast our interpretation of this data in a second similar-but-notidentical graph in terms of trophic level and source contributions (Fig. F). The overall
results show 4.3 trophic levels and substantial influence of corn in this agricultural
landscape. We used %corn and TL as the respective x-axis and y-axis to preserve the
parallelism with the original 13C and15N data.
So, what have we learned beyond the mechanics of how to graph up the data?
Most importantly, we obtained the outlines of a food web with really very little effort
overall. Many animals spend >50% of their time in food-related activities, so focusing on
food webs is an important aspect of community ecology. Also, the food web integrates
many processes occurring across the landscape, drawing from both agricultural corn
fields and natural forests. Studying isotopes in food webs shows landscape and ecosystem
level connections. Lastly, it was interesting to use bird feathers – more and more bird
species are endangered, and it is good to have non-lethal samples such as feathers to help
indicate feeding habits and basic bird ecology.
One extra effort we made during this study was revisiting the field site and
sampling corn, finding a “missing link” or food source that we inferred must be there.
This inference and extra sampling is very often the case, because it is not always possible
to guess which foods are really most important sources in food webs.
There were also some puzzles in the data. For example, what kind of spider is it
that would be at trophic level 3.7, and is the mushroom in Table A really relying on 20%
corn? Some field work and literature review would be well-advised to help solve these
puzzles. Really, it is often better to start with a quick isotope diagram, then dig into the
actual food web with other eco-observations such as watching with binoculars,
performing lab experiments or examining gut contents under a microscope. This longer
eco-effort is usually needed to see the details of how the food web really fits together
under the isotope rainbow. Isotopes are just part of the picture, but especially good for
getting the overall picture straight in your mind, even if what’s actually happening in this
food web picture needs a lot more scrutiny to discern the details.
You might also think about your isotope results from two points of view. One
viewpoint identifies patterns in the overall distribution of isotopes you see when looking
at biplots of C vs. N isotopes. Multivariate statistics can help bring out the contrasts in
these distributions (Litvin and Weinstein 2004). Using patterns you can discuss whether
isotopes in one area/watershed/food web are different than in another area. This is a
classification problem, focusing on the differences between food webs. If there is a
reference area or food web, then this classification helps you see difference/divergence
from the reference, and is a strong use of isotopes (Moseman et al. 2004).
The second viewpoint is emphasized in the example above, calculating source
contributions. However, it is common to have too many sources and not enough tracers,
so that in the end, the source calculations become less exact minimum-maximum
(“minmax”) estimates. Point F below outlines this problem in detail. Calculating source
contributions is actually most useful in a negative sense, i.e., for identifying which
sources are unimportant. But when considered together, the positive identification of
strong patterns in the data (viewpoint 1 above) plus the negative rejection of unimportant
sources (viewpoint 2 above) make isotope analysis a powerful approach for investigating
food webs.
Lastly, there are several practical complications that often arise while working
with these isotope food web diagrams. Some common problems (A-F) are listed below,
along with some references and advice that will help you work through these
complications.
A) In these isotope diagrams, there are fractionation adjustments for trophic level
that apply to both N and C isotope data. The respective trophic enrichment factors of
3o/oo and 0.5o/oo for N and C isotope data used in this example are general averages,
and may be different for the animals or systems of most interest to you. You may want to
consult three references (Vander Zanden and Rasmussen 2001, Post 2002, McCutchan et
al. 2003) for more detail about the trophic level enrichment factors that are needed for
interpreting these isotope diagrams, e.g., you may want to consider the effects of using
enrichment factors of 0.0o/oo instead of 0.5o/oo for 13C and 2.2o/oo or 3.4o/oo instead
of 3o/oo for 15N.
B) Before making the source interpretations in step 4 of this example, also you
may need to consider other corrections. For example, you may want to add about 1o/oo to
13C values if samples have been preserved in formalin (Sarakinos et al. 2002), and add
0.5-3o/oo to 13C values for samples with high lipid contents, as determined by lipidextraction (Hobson et al. 1995) or C/N-based calculations (Fry 2002). However, if these
corrections are small for your samples, it may be better to not make the corrections, for
each correction you make also introduces another source of error.
C) The terrestrial example of this Appendix above has very few samples – just a
handful. How many more samples would really be enough in a food web study, and with
more samples, how can we estimate errors in the assignments of trophic level and source
contributions? (for help, see: Phillips 2001, Phillips and Gregg 2001, Phillips and Koch
2002).
D) Basal plant food resources often have different 15N values so that determining
the baseline value for trophic level 1 is not straightforward, complicating estimates of
trophic levels for consumers. Many TL estimates start at the herbivore rather than plants,
because plants vary too much or because the exact plant base is not always known.
Herbivores integrate and average out this variability present at the plant level (for help,
see: Vander Zanden and Rasmussen 2001, Post 2002). If you use an herbivore, the
equation for trophic levels starts counting at TL2 instead of TL1 and becomes:
TL = 2 + (15NCONSUMER - 15NHERBIVORE)/3
Also,13C values are sometimes used to help understand and model variations in
the15N baseline (Vander Zanden and Rasmussen 2001, Post 2002).
E) How do we recognize animals from a different region, animals that are
migrants or transients, versus the residents that belong with the food resources being
sampled locally? (for help, see: Caccamise et al. 2000, Fry et al. 2003).
F) There are not just 2 plant food resources in many food webs, but 3-10
potentially important plant foods. In these more complex cases, it is not clear which foods
support consumers, and only potential minmax contributions can be calculated for the
food resources (for help, see: Phillips and Gregg 2003).
To illustrate these minmax solutions, here is an example problem with too many
sources (3 sources) and not enough tracers (1 tracer). Given three sources with 15N
values of 5, 10 and 15o/oo, what are the source contributions to a sample whose isotope
value is 10o/oo? The models return the answer that on average, each source contributes
an equal one third to the sample. But inspection quickly shows that there are in fact an
infinite number of potential or feasible solutions to this problem, with percent
contributions of sources 1,2, and 3 feasibly (0,100,0), (50,0,50), (25,50,25), etc. No
solution is intrinsically more correct than the next one, and a model-reported average
value is just one more virtual estimate with equal standing to all the other feasible
solutions. In this case, a better viewpoint than emphasizing averages is that the data
provides a set of minmax estimates for each source. In this 3 source example, these
minmax estimates are 0-50% for source 1, 0-100% for source 2, and 0-50% for source 3.
Such min-max estimates reflect the true level of constraint provided by the data, without
an incorrect (but tempting) extrapolation to a unique solution.
To address this common problem of too many sources, Phillips and Gregg
developed IsoSource programming available on the web at
http://www.epa.gov/wed/pages/models/isosource/isosource.html. This programming
calculates contributions from multiple sources, typically starting from (13C, 15N) data.
Note that this web-based approach arose after Phillips (2001) discredited a published
intuitive approach to interpreting source contributions. The intuitive approach was based
on proximity of the sample isotope value to those of various sources when samples and
sources are plotted in a diagram of 15N vs. 13C (Ben-David and Schell 2001). But
sources far away from samples in these multi-source isotope diagrams can also contribute
strongly, so that this intuitive “near = important” model is flawed when many sources are
involved. Instead, mixing models should be based on mass balance principles outlined in
Section 5.4 of this book.
There are four important steps you need to think about when dealing with the
minmax IsoSource programming of Phillips and Gregg (2003).
1) Your goal is to estimate source contributions, so the first step is to factor out
any fractionation that may be occurring. For example, for a carnivore whose 15N value is
6o/oo, subtract 3o/oo to correct for fractionation to the herbivore level, and a further
3o/oo to get to the original plant source level, 0o/oo. Similar steps apply for any carbon
fractionations. For food web diagrams using (13C, 15N) data, you may want to rely on
general ecological estimates of trophic level when making your corrections, without
using 15N to estimate trophic level. Why not use 15N in these (13C, 15N) problems?
Because the 15N estimates of trophic level generally assume a starting source value, and
it would be circular reasoning to work forwards from the source 15N to estimate trophic
level, then work backwards from that value to re-estimate the source 15N. So, you need
to find another way to estimate trophic level if you want to use 15N as a source indicator,
and general estimates from feeding observations such as stomach content data may
suffice.
2) Plot your fractionation-corrected consumer isotope data along with your source
plant data in 13C vs. 15N biplots. Does the corrected consumer data fall within a
polygon you can make by connecting the points for the source plants? If not, you may be
missing a source. Collect more samples and consult the literature to see if you can add a
source point in the right place so that the polygon encloses all the consumer data.
3) When dealing with too many sources in isotope mixing diagrams, researchers
commonly face a decision about aggregating sources, whether to “lump” or “split”
sources. The usual case is that there are many, many food resources in nature, so the
researcher must make some decisions about what is important and what is not.
Mathematically, it is very useful to lump and aggregate sources, because with fewer
sources, often one can obtain exact solutions for the contributions of each source. But if
the number of sources exceeds 3 in your (13C, 15N) biplot, then only minmax estimates
can be obtained for the source contributions. This minmax information is often much less
conclusive.
There are five strategies to help work on this common problem of narrowing
down too many sources to just a few sources, using the IsoSource programming of
Phillips and Gregg (2003): i) Plot all the isotope data for the potential sources, and use
the visual plot to aggregate sources that have similar isotope values. In effect, nature has
pre-aggregated these sources anyway in terms of isotope mixing diagrams. ii) Is it
possible to aggregate foods by region, so that the food problem becomes a geographical
one? Often the net food resource in one area is quite different and distinct from that in
another area, so that that you can use aggregated “regional averages” rather than
considering all the individual foods themselves. iii) Use the minmax IsoSource
programming to calculate source contributions, and see if any source has typically small
contributions and can be ignored and dropped from consideration. iv) Is there any other
non-isotope information such as stomach content data that can constrain the source
contributions? Constraining any one of the source contributions will often remarkably
shrink the minmax ranges of all sources towards exact solutions. v) Lastly, realize that no
matter how you calculate the source contributions, exactly or as minmax estimates, that
both sets of estimates share an important similarity. This similarity is that all the
estimates let you exclude certain sources as unimportant. This is science at work,
excluding and falsifying hypothetical source contributions. However, when trying to
support (but still not prove) the importance of certain food resources, it is preferable to
have the exact estimates or minmax estimates that have narrow ranges. You will have to
work this out for yourself, balancing your desire for exactness against your biological
assessment of how many foods are likely to be important.
4) Once you have the source contributions, you can use a bar graph to think about
the minmax results (Fig. G). But how should you really think about these kinds of minmax data? You will have to decide for yourself what is important and how to present it,
but here is some of the logic. a) A low maximum value means you identify the food
source as unimportant (this is a strong use of isotopes, so perhaps you should just plot
maximum values, Fig. H). b) High maximum values are not very useful. c) Low
minimum values are not very useful. d) A high minimum value is useful, and supports or
“is consistent with” an important role for that food and is a fairly strong use of isotopes.
For this reason, you may choose to plot the minimum values (Fig. I). But high minimum
values still do not prove the importance of the food, especially since other unmeasured
foods may have been missed in the analysis. e) Large ranges between minmax estimates
are often not informative, unless the minimum is high (see previous point d). f) Small
minmax ranges are informative, narrowing towards exact values (but see also caveat for
point d). g) Working through the steps above, you may find that you can rank the
importance of sources from the minmax estimates, even if you cannot solve for average
contributions.
It is interesting that these steps for estimating source contributions apply not only
to food web isotope studies, but also much more widely. For example, the steps of
correcting for fractionation and aggregating sources figured prominently in a study that
estimated sources of atmospheric methane from isotope data (Snover et al. 2000).
In summary, working with isotope mixing diagrams takes some practice and has
some complications that need to be considered. Errors accumulate from several steps, and
it is good to try to keep these errors in mind when making final interpretations. Several
models help work through food web isotope problems (Phillips and Gregg 2003, HallAspland et al. 2004, Lebetkin and Simenstad 2004), but usually the data only support
minmax conclusions. So the closing advice is this. Use the models to look at a range of
feasible minmax solutions, and try to discern the common features of those solutions
(Benstead et al., in press). Those common features should be there because they are
supported by the data. Find those features and report those features.
Further Reading:
Caccamise, D.F., L.M. Reed, P.M. Castelli, S. Wainright and T.C. Nichols. 2000.
Distinguishing migratory and resident Canada geese using stable isotope analysis. Journal
of Wildlife Management 64:1084-1091.
Ben-David, M. and D.M. Schell. 2001. Mixing models in analyses of diet using multiple
stable isotopes: a response. Oecologia 127:180-184.
Benstead, J.P., J.G. March, B. Fry, K.C. Ewel and C.M. Pringle. In press. Trophic
support of inshore fisheries on a Pacific island: testing IsoSource in a multiple-source
stable isotope analysis. Ecology.
Finlay, J.C., S. Khandwala, and M.E. Power. 2002. Spatial scales of carbon flow in a
river food web. Ecology 83:1845-1859.
Fry, B. 1991. Stable isotope diagrams of freshwater food webs. Ecology 72:2293-2297.
Fry, B. 2002. Stable isotopic indicators of habitat use by Mississippi River fish. Journal
of the North American Benthological Society 21:676-685.
Fry, B., and E. Sherr. 1984. 13C measurements as indicators of carbon flow in marine
and freshwater ecosystems. Contributions in Marine Science 27:13-47.
Fry, B., R.K. Andersen, L. Entzeroth, J.L. Bird and P.L. Parker. 1984. 13C enrichment
and oceanic food web structure in the northwestern Gulf of Mexico. Contributions in
Marine Science 27:49-63.
Fry, B., D. Baltz, M. Benfield, J. Fleeger, A. Gace, H.A. Haas, and Z. Quinones. 2003.
Chemical indicators of movement and residency for brown shrimp (Farfantepenaeus
aztecus) in coastal Louisiana marshscapes. Estuaries 26:82-97.
Hall-Aspland, S.A., A.P. Hall and T.L. Rogers. 2004. A new approach to the solution of
the linear mixing model for a single isotope: application to the case of an opportunistic
predator. Oecologia DOI:10.1007/s00442-004-1783-0.
Hobson, K.A. and R.G. Clark. 1992. Assessing avian diets using stable isotopes II:
factors influencing diet-tissue fractionation. The Condor 94:189-197.
Hobson, K.A., W.G. Ambrose Jr., and P.E. Renaud. 1995. Sources of primary
production, benthic-pelagic coupling, and trophic relationships within the Northeast
Water Polynya: insights from 13C and 15N analysis. Marine Ecology Progress Series
128:1-10.
Litvin, S.Y. and M.P. Weinstein. 2004. Multivariate analysis of stable-isotope ratios to
infer movements and utilization of estuarine organic matter by juvenile weakfish
(Cynoscion regalis). Canadian Journal of Fisheries and Aquatic Sciences 61:1851-1861.
Lubetkin, S.C. and C.A. Simenstad. 2004. Multi-source mixing models to quantify food
web sources and pathways. Journal of Applied Ecology 41:996-1008.
McCutchan, J.H. Jr., W.M. Lewis Jr., C. Kendall and C.C. McGrath. 2003. Variation in
trophic shift for stable isotope ratios of carbon, nitrogen, and sulfur. Oikos 102:378-390.
Moseman S.M., L.A. Levin, C. Currin, and C. Forder. 2004. Colonization, succession,
and nutrition of macrobenthic assemblages in a restored wetland at Tijuana Estuary,
California. Estuarine Coastal and Shelf Science 60: 755-770.
Phillips D.L. 2001. Mixing models in analyses of diet using multiple stable isotopes: a
critique. Oecologia 127:166-170.
Phillips D.L. and J.W. Gregg. 2001. Uncertainty in source partitioning using stable
isotopes. Oecologia 127:171-179 (see also erratum, Oecologia 128: 204)
Phillips D.L. and P.L. Koch. 2002. Incorporating concentration dependence in stable
isotope mixing models. Oecologia 130:114-125.
Phillips D.L. and J.W. Gregg. 2003 Source partitioning using stable isotopes: coping with
too many sources. Oecologia 136:261-269.
Post, D.M. 2002. Using stable isotopes to estimate trophic position: models, methods and
assumptions. Ecology 83:703-718.
Sarakinos, H. C., M. L. Johnson and M. J. Vander Zanden. 2002. A synthesis of tissuepreservation effects on carbon and nitrogen stable isotope signatures. Canadian Journal of
Zoology 80: 381-387.
Snover, A.K., P.D. Quay, and W.M. Hao. 2000. The D/H content of methane emitted
from biomass burning. Global Biogeochemical Cycles 14:11-24.
Vander Zanden, J.M. and J.B. Rasmussen.  Variation in15N and 13C trophic
fractionation: implications for aquatic food web studies. Limnology and Oceanography
46:2061-2066.
Figure Legends
Fig. A. Preliminary isotope biplot, a common starting point in the graphic analysis of
stable isotope data.
Fig. B. As previous figure, but with carbon data on the x-axis, as per modern convention.
Fig. C. As previous figure, but with  symbols now correctly given, including
superscripts.
Fig. D. As previous figure, but the o/oo units on the x and y axes are now similar (i.e.,
spacing for a 1 o/oo interval on the x-axis equals the spacing for 1 o/oo on the y-axis).
Fig. E. As previous figure, but with added data from the second round of sampling.
Fig. F. As previous figure, but with axes relabeled to show interpretation of 13C results
in terms of sources (x-axis) and interpretation of 15N results in terms of trophic level (yaxis).
Fig. G. Minimum and maximum (“minmax”) contributions for a five-source mixing
problem in which there are too many sources and not enough tracers. There is no unique
average solution in these common cases, only min-max range estimates for each source.
Fig. H. As previous figure, but only maximum contributions.
Fig. I. As previous figure, but only minimum contributions.
Do you have what it takes to become an isotope sourcerer?