Abstract. A key challenge for biological oceanography is relating the physiological mechanisms controlling phytoplankton growth to the spatial distribution of those phytoplankton. Physiological mechanisms are often isolated by varying one driver of growth, such as nutrient or light, in a controlled laboratory setting producing what we call “intrinsic relationships”. We contrast these with the “apparent relationships” which emerge in the environment in climatological data. Although previous studies have found machine learning (ML) can find apparent relationships, there has yet to be a systematic study examining when and why these apparent relationships diverge from the underlying intrinsic relationships found in the lab and how and why this may depend on the method applied. Here we conduct a proof-of-concept study with three scenarios in which biomass is by construction a function of time-averaged phytoplankton growth rate. In the first scenario, the inputs and outputs of the intrinsic and apparent relationships vary over the same monthly timescales. In the second, the intrinsic relationships relate averages of drivers that vary on hourly timescales to biomass, but the apparent relationships are sought between monthly averages of these inputs and monthly-averaged output. In the third scenario we apply ML to the output of an actual Earth system model (ESM). Our results demonstrated that when intrinsic and apparent relationships operate on the same spatial and temporal timescale, neural network ensembles (NNEs) were able to extract the intrinsic relationships when only provided information about the apparent relationships, while colimitation and its inability to extrapolate resulted in random forests (RFs) diverging from the true response. When intrinsic and apparent relationships operated on different timescales (as little separation as hourly versus daily), NNEs fed with apparent relationships in time-averaged data produced responses with the right shape but underestimated the biomass. This was because when the intrinsic relationship was nonlinear, the response to a time-averaged input differed systematically from the time-averaged response. Although the limitations found by NNEs were overestimated, they were able to produce more realistic shapes of the actual relationships compared to multiple linear regression. Additionally, NNEs were able to model the interactions between predictors and their effects on biomass, allowing for a qualitative assessment of the colimitation patterns and the nutrient causing the most limitation. Future research may be able to use this type of analysis for observational datasets and other ESMs to identify apparent relationships between biogeochemical variables (rather than spatiotemporal distributions only) and identify interactions and colimitations without having to perform (or at least performing fewer) growth experiments in a lab. From our study, it appears that ML can extract useful information from ESM output and could likely do so for observational datasets as well.

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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.

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