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Converting Isotope Ratios to Diet Composition: The Use of Mixing Models

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.

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Converting Isotope Ratios to Diet Composition: The Use of Mixing Models

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  1. 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

  2. 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

  3. 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

  4. Mixing diagram (2 source) C3 plants bison C4 plants XY -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

  5. 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

  6. 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

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

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

  9. 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

  10. 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

  11. Too many sources: IsoSource softwarewww.epa.gov/wed/pages/models.htm

  12. Too many sources: mink example (Ben-David et al., 1997)

  13. 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

  14. 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

  15. 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

  16. 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)

  17. 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

  18. 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

  19. 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

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