Modeling the irradiance dependency of the quantum efficiency of photosynthesis

Measures of the quantum efficiency of photosynthesis (phi(PSII)) across an irradiance (E) gradient are an increasingly common physiological assay and alternative to traditional photosynthetic-irradiance (PE) assays. Routinely, the analysis and interpretation of these data are analogous to PE measurements. Relative electron transport rates (rETR = E x phi(PSII)) are computed and fit to a PE curve to retrieve physiologically meaningful PE parameters. This widespread approach is statistically flawed as the response variable (rETR) is explicitly dependent on the predictor variable (E). Alternatively the E-dependency of phi(PSII) can be modeled directly while retaining the desired PE parameters by normalizing a given PE model to E. This manuscript presents a robust analysis in support of this alternative procedure. First, we demonstrate that scaling phi(PSII) to rETR unnecessarily amplifies the measurement error of phi(PSII) and using a Monte-Carlo analysis on synthetic data induces significantly higher uncertainty in computed PE parameters relative to modeling the E-dependency of phi(PSII) directly. Next a large dataset is simultaneously fitted to four PE models implemented in their original and E-normalized forms. Four statistical criteria used to evaluate the efficacy of nonlinear models demonstrate improved model fits and more precise PE parameters when data are modeled as E-dependent changes in phi(PSII). The analysis presented in this manuscript clearly demonstrates that modeling the E-dependency of phi(PSII) directly should be the norm for interpreting active fluorescence measures.