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Converting Isotope Ratios to Diet Composition: The Use of Mixing Models
Donald L. Phillips U.S. Environmental Protection Agency,
Corvallis, OR
Merav Ben-David University of Wyoming, Laramie, WY
Jillian W. Gregg Oregon State University, Corvallis, OR
Isotopically, “You are what you eat”
Concept of isotopic mass balance
Isotopic signature of consumer’s tissue reflects signatures of food sources proportional to their dietary contribution
Assimilated diet, not necessarily ingested diet
Must adjust for tissue-diet discrimination
Standard linear mixing model (2 source)
1 isotopic ratio, e.g., 13C 2 sources, e.g., foods X and Y
System of 2 equations in 2 unknowns (fX , fY )
gives contributions of foods X and Y to diet
13 13 13
1consumer X X Y Y
X Y
C f C f C
ff
Mixing diagram (2 source)
C3 plants bison C4 plants
X Y -25 -21 -15
13C (l)
-21 = 0.6 (-25) + 0.4 (-15)
fX = 0.6, fY = 0.4 Bison’s assimilated diet is 60% C3 and 40% C4
plants
Standard linear mixing model (3 source)
2 isotopic ratios, e.g., 13C and 15N 3 sources, e.g., foods X, Y, and Z
System of 3 equations in 3 unknowns (fX , fY , f Z)
gives contributions of foods X,Y, and Z to diet
13 13 13 13
15 15 15 15
1
consumer X X Y Y Z Z
consumer X X Y Y Z Z
X Y Z
C f C f C f C
N f N f N f N
ff f
Mixing diagram (3 source)
Consumer falls inside polygon bounded by food sources
In this example: fX = 0.38, fY = 0.24, fZ = 0.38
So, consumer’s assimilated diet is:
38% X 24% Y 38% Z
0
2
4
6
8
10
12
14
16
18
-26 -24 -22 -20 -18 -16 -14
13C (l )
15 N
(l
)
X
Y
Zconsumer
Uncertainty
Isotopic signatures for consumer and food sources have some variability Population variability Measurement error
How does this affect estimated proportions?
Uncertainty
0
2
4
6
8
10
12
14
16
18
-28 -26 -24 -22 -20 -18 -16 -14
13C (l )
15 N
(l
)
0
2
4
6
8
10
12
14
16
18
-28 -26 -24 -22 -20 -18 -16 -14
13C (l )
15 N
(l
)
using mean values using mean + SE values
X
X
Y
Y
Z
Z
X
X
Y
Y
Z
Z38%38%
24%
36%
17%
47%
Units shaded cells:isotopic signature - consumer l -21.0 bisonisotopic signature - source X l -25.0 C3 plantsisotopic signature - source Y l -15.0 C4 plantsno. of samples - consumer unitless 10 bisonno. of samples - source X unitless 10 C3 plantsno. of samples - source Y unitless 10 C4 plantsSD of isotopic signature - consumer l 1.0 bisonSD of isotopic signature - source X l 1.0 C3 plantsSD of isotopic signature - source Y l 1.0 C4 plants
lower 95% mean / SE upper 95%proportion of diet - source X (C3) 0.52 0.60 0.68
0.04proportion of diet - source Y (C4) 0.32 0.40 0.48
0.04
Uncertainty: IsoError spreadsheet (Excel)
www.epa.gov/wed/pages/models.htm
Enter:
isotopic signatures
# of samples
std. deviations
Calculates for each food source’s dietary contribution:
mean, std. error,
95% conf. interval
Too many sources
What if there are more food sources? If # sources > # isotopic signatures + 1,
then no unique source contribution solution e.g.: 7 food sources, 2 isotopic signatures
3 equations in 7 unknowns, many solutions Can still use mixing models
find all combinations of 7 food sources that give observed consumer signatures
this defines the range of possible contributions for each food source
Too many sources: IsoSource softwarewww.epa.gov/wed/pages/models.htm
Mink Dietary Proportions, Ben-David et al. (1997)
1.00 .1 .2 .3 .4 .5 .6 .7 .8 .9
15N
(‰
)
7
8
9
10
11
12
13
14
15
16
17
18
-28 -26 -24 -22 -20 -18 -16 -14 -12 -10
13C (‰)
0 .1 .2 .3 .4 .5
Duck 0 - 7% Fish
46 - 68%
0 .1 .2 .3 .4 .5
Crab 12 - 45%
0 .1 .2 .3 .4 .5
Mussel 0 - 19%
0 .1 .2 .3 .4 .5
Rodent 0 - 6%
M
Amphipod 0 - 12%
0 .1 .2 .3 .4 .5
0 .1 .2 .3 .4 .5
Shrimp 0 - 29%
Shrimp 0 - 21%
Mink
Rodent 0 - 4%
Duck 0 - 5%
Amphipod 0 - 12%
Mussel 0 - 14%
Crab 19 - 42%
Fish 49 - 63%
M
15 N
(‰
)
a
b
c
de
f
g
Too many sources: mink example (Ben-David et al., 1997)
Concentration effects
Assumption: % food source contribution is the same for all elements examined (e.g., C & N)
What if [C] and [N] vary widely?
High [N] sources probably contribute more N relative to C than do low [N] sources
Concentration dependent mixing model
Solves for food source contributions using: isotopic ratios (e.g., 13C and 15N ) weighted by elemental concentrations (e.g., [C],
[N])
Separate results for dietary contributions of: biomass C N
Concentration: IsoConc spreadsheet (Excel)www.epa.gov/wed/pages/models.htm
13C 15N [C] [N] biomass C N(l ) (l ) (%) (%) fraction fraction fraction
source X -20 16 50 12 0.14 0.14 0.17source Y -16 8 50 12 0.43 0.43 0.55source Z -24 3 50 6 0.43 0.43 0.28consumer -20 8
blue = isotopic & conc. data entered red = dietary contributions
Food source Z: lower [N] than other food sources lower contribution of N to consumer than C or biomass
Mixing model assumptions
model assumption--------------------------------------------------------------------------------------------all models Mixture of assimilated diet, not ingested diet standard Source contribution same for biomass & all elements (e.g.
C, N)
conc. dep. Source element contribution biomass * conc (e.g. C, N)
Need to use assimilated conc’s, not ingested conc’s
Thus, must consider digestibility of different foods
(Robbins, Hilderbrand, & Farley 2002)
Other digestive complexities
All mixing models assume complete mixing of prey tissues consumer’s tissues
May be preferential routing of material, e.g.: lipid C lipid C protein C protein C
May affect apparent dietary contributions
Physiological routing effects are confounded with concentration effects in standard model
New approaches
Concentration effects Concentration dependent model can separate
these from physiological routing effects If digestibility data are available
Physiological routing Compound-specific isotopic analysis
e.g., essential fatty acids (lipid), amino acids (protein)
May require further development of mixing models to accommodate this new information
Resources and References
www.epa.gov/wed/pages/models.htm - download software and papers:
IsoError (Excel) Phillips DL, Gregg JW (2001) Uncertainty in source partitioning
using stable isotopes. Oecologia 127: 171-179 (erratum 128: 304) IsoSource (Visual Basic)
Phillips DL, Gregg JW (2003) Source partitioning using stable isotopes: coping with too many sources. Oecologia 136: 261-269.
IsoConc (Excel) Phillips DL, Koch PW (2002) Incorporating concentration
dependence in stable isotope mixing models. Oecologia 130: 114-125.
Robbins, Hilderbrand, & Farley (2002) comment paper Koch & Phillips (2002) reply paper