Responses of phytoplankton to excessive nutrients in rivers cause many ecological problems, including harmful algal blooms, hypoxia and even food web collapse, posing serious risks to fish and human health. Successful remediation requires identification of the types and sources of the problem nutrients. Multi-isotopic approaches are powerful tools for solving such problems because water samples can be easily collected from water quality monitoring programs and analyzed for nutrient isotopes and organic matter (OM) isotopes, as well as various chemical measurements. Nutrient and phytoplankton isotopic compositions can be compared to determine seasonal and spatial changes in the dominant source of nutrient for phytoplankton production. Particulate OM (POM) samples are easily collected, which contain both phytoplankton and terrestrial OM. However, physical isolation of phytoplankton is often challenging. Hence, methods are needed to calculate the isotopic values of bulk phytoplankton, particularly δ13C and δ15N, from the isotopic values of bulk POM and other associated chemical data.
We reviewed several recent proposed methods to calculate phytoplankton δ13C and δ15N based on isotopic and chemical data for POM and its terrestrial OM component, where POM is treated as a two-source mixture of terrestrial OM and phytoplankton. We found problems with these methods that include: (a) the untenable assumption that C, N, and H all partition the same way even though C:N may vary widely between the two components; (b) the need to incorporate an arbitrary adjustment factor to account for this; or (c) the inappropriate use of non-linear C:N ratios in linear mixing models. We derived a set of equations for phytoplankton δ13C and δ15N that avoids these issues. First, for POM and each of its two components, the C:N data are linearized by computing the C and N fractions of the total C+N mass. The fractions of C and N in POM that come from terrestrial OM are then calculated separately. Separate estimations avoid the assumption that C and N assort the same between the components of POM, which is not true when their C:N ratios are not equal. These separate calculations also forgo the need for an additional adjustment factor to account for differences in C:N ratios. The δ13C and δ15N values for phytoplankton can then be calculated by a two-source mixing model. Finally, this method was applied to multi-year POM sampling data from the San Joaquin River and its tributaries.