Approaching the upper boundary of driver-response relationships: identifying factors using a novel framework integrating quantile regression with interpretable machine learning

Highlights

● A novel framework integrating quantile regression with machine learning is proposed.

● It aims to identify factors driving observations to upper boundary of relationship.

● Increasing N:P and TN concentration help fulfill the effect of TP on CHL.

● Wetter and warmer decrease potential and increase eutrophication control difficulty.

● The framework advances applications of quantile regression and machine learning.

Abstract

The identification of factors that may be forcing ecological observations to approach the upper boundary provides insight into potential mechanisms affecting driver-response relationships, and can help inform ecosystem management, but has rarely been explored. In this study, we propose a novel framework integrating quantile regression with interpretable machine learning. In the first stage of the framework, we estimate the upper boundary of a driver-response relationship using quantile regression. Next, we calculate “potentials” of the response variable depending on the driver, which are defined as vertical distances from the estimated upper boundary of the relationship to observations in the driver-response variable scatter plot. Finally, we identify key factors impacting the potential using a machine learning model. We illustrate the necessary steps to implement the framework using the total phosphorus (TP)-Chlorophyll a (CHL) relationship in lakes across the continental US. We found that the nitrogen to phosphorus ratio (N׃P), annual average precipitation, total nitrogen (TN), and summer average air temperature were key factors impacting the potential of CHL depending on TP. We further revealed important implications of our findings for lake eutrophication management. The important role of N׃P and TN on the potential highlights the co-limitation of phosphorus and nitrogen and indicates the need for dual nutrient criteria. Future wetter and/or warmer climate scenarios can decrease the potential which may reduce the efficacy of lake eutrophication management. The novel framework advances the application of quantile regression to identify factors driving observations to approach the upper boundary of driver-response relationships.

Graphical abstract

Keywords

Driver-response / Upper boundary of relationship / Interpretable machine learning / Quantile regression / Total phosphorus / Chlorophyll a

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Acknowledgements

This research was funded by the National Natural Science Foundation of China (Nos. 71761147001 and 42030707), the International Partnership Program by the Chinese Academy of Sciences (No. 121311KYSB20190029), the Fundamental Research Fund for the Central Universities (No. 20720210083), and the National Science Foundation (Nos. EF-1638679, EF-1638554, EF-1638539, and EF-1638550). Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the US Government.

Data Accessibility Statement

The data supporting the findings of this study are available within the article and its supplementary materials. The code that support the findings of this study are available from the first author (Z. Liang, [e-mail]), upon reasonable request.

Electronic Supplementary Material

Supplementary material is available in the online version of this article at https://doi.org/10.1007/s11783-023-1676-2 and is accessible for authorized users.

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