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

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.