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., d13C 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

Mixing diagram (2 source) C3 plants bison C4 plants X Y -25 -21 -15 d13C (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., d13C and d15N 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

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 Y consumer Z X

Uncertainty Isotopic signatures for consumer and food sources have some variability Population variability Measurement error How does this affect estimated proportions?

Uncertainty using mean values using mean + SE values Y Y 38% 47% 38% Z X Z X 36% Y Y 24% 17% Z Z X X using mean values using mean + SE values

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 software www.epa.gov/wed/pages/models.htm

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., d13C and d15N ) weighted by elemental concentrations (e.g., [C], [N]) Separate results for dietary contributions of: biomass C N

Concentration: IsoConc spreadsheet (Excel) www. epa Concentration: IsoConc spreadsheet (Excel) www.epa.gov/wed/pages/models.htm 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 -------------------------------------------------------------------------------------------- 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 Physiological routing 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