Incorporating concentration dependence in stable isotope mixing models: a reply to Robbins, Hilderbrand and Farley (2002)

In Phillips and Koch (2002), we presented an isotopic mixing model for use in cases where elemental concentration differs greatly among potential contributors to the mixture. Our primary goal was to present the mathematics of this system for two isotopes and three sources, noting that it was generalizable to n isotopes and n+1 sources. To illustrate the magnitude of the differences that might result if elemental concentrations differed greatly among possible sources, we performed model sensitivity tests and examined examples involving mixing of different food sources in the diets of captive mink and wild bears. The response by Robbins et al. (2002) deals largely with our bear example and it makes five points we will address. First, Robbins et al. (2002) argue that our example involving bears from the Kenai Pennisula, Alaska, which used data from their previously published work (Hilderbrand et al. 1996; Jacoby et al. 1999), is unrealistic in several ways, and therefore, that our results should not be used to make management decisions. We agree completely. We did not attempt to present a rigorous re-analysis of isotopic constraints on Kenai bear diets. Our only goal with the illustrative examples was to alert workers to an important complication that could crop up in dietary (and other) isotope analyses, and to offer a tool for addressing this complication in a quantitative manner. Second, in addition to their concerns about our results for the coastal Kenai bears, Robbins et al. (2002) take issue with the single sentence in our paper on inland bear populations. We suggested that standard linear mixing "may be overestimating the amount of meat in bear diets simply because bear tissue 615N values will strongly resemble those of terrestrial meat once this Nrich source makes up more than 10 or 20% of assimilated biomass". Robbins et al. (2002) find this suggestion "baseless", citing data from a subset of the inland populations with isotopic data suggesting nearly 100% plant diets. Yet these populations have no access to salmon and little access to large ungulates and, therefore, it is not especially surprising that they are essentially herbivorous. The existence of entirely herbivorous bear populations does not address the point we were raising. There are populations of brown (Ursus arctos) and black (U. americanus) bears that have access to terrestrial meat and apparently eat it. For the Greater Yellowstone ecosystem, Jacoby et al. (1999) used standard linear mixing and estimated that brown bears have a mean of 58% terrestrial meat in their diets, whereas black bears average 48% (all data from their Table 1). Likewise, brown bears from the southwestern United States have 88% terrestrial meat in their diets; black bears average 39%. Brown bears from the Blackfeet and Flathead Indian Reservations in Montana have estimated meat intakes of 69%. Clearly it is only for these populations, where there is a mixture of meat and plants in the diet, that our comments about biases in isotope mixing are relevant. Indeed, Jacoby et al. (1999) were surprised by the high dietary meat estimate for southwestern United States bears, and devoted two paragraphs to attempts to explain the result. We stand by our suggestion that concentration differences among leafy plants, nuts, and terrestrial meat should be investigated as a potential contributor to high dietary meat estimates. Third, Robbins et al. (2002) present a strong case demonstrating that Kenai bears consume leafy plants rather than fruit, and argue that our model might yield different results with a more realistic leafy plant diet. They note that leafy plants tend to have higher N concentrations ([N]) and lower C:N ratios than fruit. And because plant protein digestion is efficient, whereas digestion of structural carbohydrates in leafy plants is not, the C:N ratio of assimilated leafy plant biomass may be P.L. Koch (E) Department of Earth Sciences, University of California, 1156 High St., Santa Cruz, CA 95064, USA e-mail: pkoch@es.ucsc.edu Fax: +1-831-4593074