Linking intrinsic and apparent relationships betweenphytoplankton and environmental forcings using machinelearning d What are the challenges

Abstract. Controls on phytoplankton growth are typically determined in two ways: by varying one driver of growth at a time such as nutrient or light in a controlled laboratory setting (intrinsic relationships) or by observing the emergence of relationships in the environment (apparent relationships). However, challenges remain when trying to take the intrinsic relationships found in a lab and scaling them up to the size of ecosystems (i.e., linking intrinsic relationships in the lab to apparent relationships in large ecosystems). We investigated whether machine learning (ML) techniques could help bridge this gap. ML methods have many benefits, including the ability to accurately predict outcomes in complex systems without prior knowledge. Although previous studies have found that ML can find apparent relationships, there has yet to be a systematic study that has examined when and why these apparent relationships will diverge from the underlying intrinsic relationships. To investigate this question, we created three scenarios: one where the intrinsic and apparent relationships operate on the same time and spatial scale, another model where the intrinsic and apparent relationships have different timescales but the same spatial scale, and finally one in which we apply ML to actual ESM output. Our results demonstrated that when intrinsic and apparent relationships are closely related and operate on the same spatial and temporal timescale, ML is able to extract the intrinsic relationships when only provided information about the apparent relationships. However, when the intrinsic and apparent relationships operated on different timescales (as little separation as hourly to daily), the ML methods underestimated the biomass in the intrinsic relationships. This was largely attributable to the decline in the variation of the measurements; the hourly time series had higher variability than the daily, weekly, and monthly-averaged time series. Although the limitations found by ML were overestimated, they were able to produce more realistic shapes of the actual relationships compared to MLR. Future research may use this type of information to investigate which nutrients affect the biomass most when values of the other nutrients change. From our study, it appears that ML can extract useful information from ESM output and could likely do so for observational datasets as well.