Converting Isotope Ratios to Diet Composition: The Use of Mixing Models Donald L. Phillips U.S. Environmental Protection Agency, Corvallis, OR Merav Ben-David.

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