Phillips Donald L, Koch Paul L
Office of Research and Development, National Health and Environmental Effects Research Laboratory, Western Ecology Division, U.S. Environmental Protection Agency, 200 SW 35th Street, 97333, Corvallis, OR, USA.
Department of Earth Sciences, University of California, 1156 High Street, 95064, Santa Cruz, CA, USA.
Oecologia. 2002 Jan;130(1):114-125. doi: 10.1007/s004420100786. Epub 2002 Jan 1.
Stable isotopes are often used as natural labels to quantify the contributions of multiple sources to a mixture. For example, C and N isotopic signatures can be used to determine the fraction of three food sources in a consumer's diet. The standard dual isotope, three source linear mixing model assumes that the proportional contribution of a source to a mixture is the same for both elements (e.g., C, N). This may be a reasonable assumption if the concentrations are similar among all sources. However, one source is often particularly rich or poor in one element (e.g., N), which logically leads to a proportionate increase or decrease in the contribution of that source to the mixture for that element relative to the other element (e.g., C). We have developed a concentration-weighted linear mixing model, which assumes that for each element, a source's contribution is proportional to the contributed mass times the elemental concentration in that source. The model is outlined for two elements and three sources, but can be generalized to n elements and n+1 sources. Sensitivity analyses for C and N in three sources indicated that varying the N concentration of just one source had large and differing effects on the estimated source contributions of mass, C, and N. The same was true for a case study of bears feeding on salmon, moose, and N-poor plants. In this example, the estimated biomass contribution of salmon from the concentration-weighted model was markedly less than the standard model estimate. Application of the model to a captive feeding study of captive mink fed on salmon, lean beef, and C-rich, N-poor beef fat reproduced very closely the known dietary proportions, whereas the standard model failed to yield a set of positive source proportions. Use of this concentration-weighted model is recommended whenever the elemental concentrations vary substantially among the sources, which may occur in a variety of ecological and geochemical applications of stable isotope analysis. Possible examples besides dietary and food web studies include stable isotope analysis of water sources in soils, plants, or water bodies; geological sources for soils or marine systems; decomposition and soil organic matter dynamics, and tracing animal migration patterns. A spreadsheet for performing the calculations for this model is available at http://www.epa.gov/wed/pages/models.htm.
稳定同位素常被用作天然标记物，以量化多种来源对混合物的贡献。例如，碳（C）和氮（N）同位素特征可用于确定消费者饮食中三种食物来源的占比。标准的双同位素、三源线性混合模型假定，对于两种元素（如C、N）而言，某一来源对混合物的比例贡献是相同的。如果所有来源中的浓度相似，这可能是一个合理的假设。然而，某一来源在一种元素（如N）上往往特别丰富或匮乏，这在逻辑上会导致该来源对该元素混合物的贡献相对于另一元素（如C）成比例地增加或减少。我们开发了一种浓度加权线性混合模型，该模型假定对于每种元素，某一来源的贡献与贡献的质量乘以该来源中的元素浓度成正比。该模型针对两种元素和三个来源进行了概述，但可推广到n种元素和n + 1个来源。对三个来源中的C和N进行的敏感性分析表明，仅改变一个来源的N浓度，对质量、C和N的估计来源贡献会产生巨大且不同的影响。以熊捕食鲑鱼、驼鹿和低氮植物为例的案例研究也是如此。在此示例中，浓度加权模型估计的鲑鱼生物量贡献明显低于标准模型的估计值。将该模型应用于以鲑鱼、瘦牛肉以及富含C、低含N的牛肉脂肪喂养圈养水貂的圈养喂养研究中，非常精确地再现了已知的饮食比例，而标准模型未能得出一组正的来源比例。每当各来源之间的元素浓度差异很大时，建议使用这种浓度加权模型，这可能出现在稳定同位素分析的各种生态和地球化学应用中。除了饮食和食物网研究之外，可能的例子还包括对土壤、植物或水体中的水源进行稳定同位素分析；土壤或海洋系统的地质来源；分解和土壤有机质动态，以及追踪动物迁徙模式。可在http://www.epa.gov/wed/pages/models.htm获取用于执行此模型计算的电子表格。
