An assessment of assumptions and uncertainty in deuterium-based estimates of terrestrial subsidies to aquatic consumers MICHAEL T. BRETT , 1,3 GORDON W. HOLTGRIEVE, 2 AND DANIEL E. SCHINDLER 2 1 Department of Civil and Environmental Engineering, University of Washington, Seattle, Washington 98105 USA 2 School of Aquatic and Fishery Sciences, University of Washington, Seattle, Washington 98105 USA Abstract. The deuterium ratio ( 2 H/ 1 H) in tissue is often used to estimate terrestrial subsidies to aquatic consumers because of strongly differentiated values between terrestrial and aquatic primary producers. However, quantitative deuterium-based analyses of terrestrial resource assimilation are highly dependent on several poorly defined assumptions. We explored the sensitivityof these estimates to assumptions regarding environmental water contributions to consumer deuterium content (x) and algal photosynthetic hydrogen discrimination (e H ). We also tested whether 13 C/ 12 C and 2 H/ 1 H-based estimates of terrestrial resource assimilation give similaroutcomes. The average of the 12 experiments that have directly estimated proportional contributions of environmental water to consumer tissue 2 H/ 1 H was 0.27  0.11 (mean  SD), with similar values for invertebrates and fish. Conversely, of the 28 field studies that have used 2 H/ 1 H to characterize aquatic food webs, all but one assume a value that is less than our current best estimate, usually substantially less. A reanalysis of the raw data from four recent case studies indicates the calculated terrestrial contribution to aquatic consumers is extremely sensitive to this assumption. When the authors’ original assumptions were used (i.e., x = 0.16  0.05), the estimated proportional contribution of terrestrial resources to aquatic con- sumers (h T ) averaged 29  17%, and when x = 0.27 was used the average estimated assimilation of allochthonous resources was 0.00. A compilation of published photosynthetic hydrogen discrimina- tion values for microalgae averaged e H = 150  27& (SD, n = 99), and a sensitivity analysis showed the outcomes of these calculations were also strongly influenced by uncertainty in e H . There was no statistical association between 13 C/ 12 C and 2 H/ 1 H-based estimates of terrestrial subsidies (r = 0.12, n = 274). This analysis indicates that the assumptions in deuterium-based estimates of terrestrial resource assimilation are highly influential but poorly constrained; therefore, the impact of these assumptions on calculated outputs must be carefully assessed and thoroughly reported. Due to the highly uncertain assumptions inherent in deuterium-based analyses, we urge much more caution when using this approach to estimate terrestrial subsidies to consumers in aquatic ecosystems. Key words: algal photosynthetic hydrogen discrimination; allochthonous subsidies; deuterium; environmental water; lakes; mixing models; phytoplankton; s isotopes; terrestrial; uncertainty; zooplankton. INTRODUCTION A longstanding theme in ecology has been the transfer of energy across habitats or ecosystem boundaries; so-called cross-system interactions or subsidies (Lindeman 1942, Polis et al. 1997). Given that carbon is typically the largest mass fraction and structural backbone of organic tissues, the tracking of carbon between ecosystems is frequently, and reasonably, used to infer energy transfers among habitats. However, the tracking of carbon directly using isotopic or other tracers can be problematic, often because of complex chemical and metabolic processes that lead to overlapping isotopic signatures and multiple fractionating pathways. This has led researchers to seek other chemical tracers to quantify cross-system interactions. For recent attempts to study the transfer of energy from terrestrial ecosystems to aquatic consumers, a tracer of choice has been the bulk 2 H/ 1 H ratio in tissues (Doucett et al. 2007, Solomon et al. 2009, Cole et al. 2011). Hydro- gen isotope ratios have the advantage of large differences between terrestrial and aquatic producers (averaging 40& to 80&); terrestrial plants are enriched with deuterium because they preferentially transpire “lighter” water (i.e., water mole- cules that do not contain deuterium), whereas aquatic algae preferentially use lighter water for biosynthetic processes (Doucett et al. 2007). In contrast to analyses based on stable isotopes of carbon and nitrogen, hydrogen-based analyses are complicated by hydrogen exchange and environmental water contributions to consumer hydrogen content (x; Van- der Zanden et al. 2016). Much of the oxygen and hydrogen in animal tissues exchanges with environmental water during normal metabolic processes (Vander Zanden et al. 2016). This exchange has long been used in terrestrial ecology to trace the provenance of migratory animals (Hobson 1999, Soto et al. 2013) and is also the basis for hydrogen labeling techniques to characterize protein and lipid synthesis (Hob- son et al. 1999). The analytical literature distinguishes exchangeable and nonexchangeable hydrogen (Schimmelmann 1991), which can create the impression that hydrogen exchange can be classified into binary categories. This may be true enough in metabolically inactive organic matter such as feathers, hair, nails, chitin, and dead tissue. For example, the hydrogen contained in acid bonds in organic matter exchanges freely Manuscript received 13 July 2017; revised 20 November 2017; accepted 7 December 2017. Corresponding Editor: Kirk O. Winemiller. 3 E-mail: mtbrett@uw.edu 1073 Ecology , 99(5), 2018, pp. 1073–1088 © 2018 by the Ecological Society of America