Bayesian change point quantile regression approach to enhance the understanding of shifting phytoplankton-dimethyl sulfide relationships in aquatic ecosystems

Abstract

Dimethyl sulfide (DMS) serves as an anti-greenhouse gas, plays multiple roles 7 in aquatic ecosystems, and contributes to the global sulfur cycle. The chlorophyll 8 a (CHL, an indicator of phytoplankton biomass)-DMS relationship is critical for 9 estimating DMS emissions from aquatic ecosystems. Importantly, recent research has 10 identified that the CHL-DMS relationship has a breakpoint, where the relationship 11 is positive below a CHL threshold and negative at higher CHL concentrations. 12 Conventionally, mean regression methods are employed to characterize the CHL-DMS 13 relationship. However, these approaches focus on the response of mean conditions 14 and cannot illustrate responses of other parts of the DMS distribution, which could 15 be important in order to obtain a complete view of the CHL-DMS relationship. In 16 this study, for the first time, we proposed a novel Bayesian change point quantile 17 regression (BCPQR) model that integrates and inherits advantages of Bayesian change 18 point models and Bayesian quantile regression models. Our objective was to examine 19 whether or not the BCPQR approach could enhance the understanding of shifting 20 CHL-DMS relationships in aquatic ecosystems. We fitted BCPQR models at five 21 regression quantiles for freshwater lakes and for seas. We found that BCPQR models 22 could provide a relatively complete view on the CHL-DMS relationship. In particular, 23 it quantified the upper boundary of the relationship, representing the limiting effect of 24 CHL on DMS. Based on the results of paired parameter comparisons, we revealed the 25 inequality of regression slopes in BCPQR models for seas, indicating that applying 26 the mean regression method to develop the CHL-DMS relationship in seas might not 27 be appropriate. We also confirmed relationship differences between lakes and seas at 28 multiple regression quantiles. Further, by introducing the concept of DMS emission 29 potential, we found that pH was not likely a key factor leading to the change of the 30 CHL-DMS relationship in lakes. These findings cannot be revealed using piecewise 31 linear regression. We thereby concluded that the BCPQR model does indeed enhance 32 the understanding of shifting CHL-DMS relationships in aquatic ecosystems and is 33 expected to benefit efforts aimed at estimating DMS emissions. Considering that 34 shifting (threshold) relationships are not rare and that the BCPQR model can easily 35 be adapted to different systems, the BCPQR approach is expected to have great 36 potential for generalization in other environmental and ecological studies.