Incorporating concentration dependence in stable isotope mixing models: a response to Phillips and Koch (2002).

Phillips and Koch (2002) suggested that the standard, linear mixing model used to estimate assimilated diets may produce inaccurate results when animals consume foods that vary markedly in their C:N ratios and elemental concentrations. They presented a concentration-dependent model and used published values on captive and freeranging bears to illustrate theoretical shortcomings of earlier, concentration-independent models. The assimilated diet estimates for Alaskan bears on the Kenai Peninsula using their concentration-dependent model differed markedly from previously published results (Jacoby et al. 1999). For example, the importance of salmon to brown bears (Ursus arctos) decreased from 50% to 26% of the assimilated diet and for black bears (Ursus americanus) allopatric to brown bears from 53% to zero. Estimating the importance of salmon to bears has profound conservation implications as salmon stocks become increasingly depleted by human activities. Brown bear populations with significant access to salmon are up to 50 times denser, adult females are twice as heavy, and litter sizes are 25% larger than in salmon-deprived populations (Hilderbrand et al. 1999c). Recently, brown bears have been identified as major conveyors of the marinederived nutrients in salmon to Alaskan riparian forests (Hilderbrand et al. 1999a; Helfield and Naiman 2001). Thus, the validity of the Phillips and Koch (2002) estimates must be evaluated as they note that incorrect assumptions in mixing models "may produce misleading results with major ramifications on assessments of feeding ecology and management strategies". The original dietary estimates of the importance of salmon by Jacoby et al. (1999) and Hilderbrand et al. (1999b, c) used a bear-specific, carbon-enrichment, linear mixing model (Hilderbrand et al. 1996) to separate marine (salmon) from terrestrial carbon sources. This approach is the most direct of all the models, has the fewest assumptions as fractionation effects related to digestion and substrate routing are part of the feeding trial results used to generate the original regression, and has been used previously to estimate the importance of salmon to earlier humans (Chisholm et al. 1982; Taylor et al. 1998). Phillips and Koch (2002) also used a concentration-independent mixing model to simultaneously estimate assimilated dietary salmon, terrestrial meat, and terrestrial plant content and "reached roughly the same conclusions" as Jacoby et al. (1999) and Hilderbrand et al. (1999b, c). Even though the above two estimates are in agreement and are derived from markedly different models and assumptions, Phillips and Koch (2002) insisted that the very different values generated by their concentration-dependent model that requires more inputs and assumptions are the correct values. The estimates from the Phillips and Koch (2002) concentration-dependent model are driven by the composition and C:N concentrations of the hypothesized assimilated diet, particularly the plant portion of the diet that was composed of equal parts apples (Malus sylvestris), blackberries (Rubus sp.), domestic cranberries (Vaccinium macrocarpon) and raspberries (Rubus sp.), and rhubarb stems (Rheum rhabarbarum). Despite extensive literature on the diets of bears, Phillips and Koch (2002) clearly made no effort to mimic a realistic plant diet in their modeling efforts as no Alaskan bear consumes their hypothetical diet. Although the actual plant names are irrelevant in illustrating their model, outputs of the model, comparisons to previous estimates, and management implications do depend on the diet chosen. The lack of realistic diet inputs in their example poses serious scientific and conservation concerns. The plant component of their hypothetical diet has a gross C:N ratio of 44:1 as compared to 4.6:1 and 3.7:1 for salmon and terrestrial meat (Table 1 in Phillips and Koch C.T. Robbins (X) School of Biological Sciences and Department of Natural Resource Sciences, Washington State University, Pullman, WA 99164-4236, USA e-mail: ctrobbins@wsu.edu Tel.: +1-509-3351119, Fax: +1-509-3353184