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Bayesian two-part modeling of phytoplankton biomass and occurrence

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Abstract

Phytoplankton biomass data often involve zero outcomes preventing a description by continuous distributions with positive support such as the lognormal distribution commonly used to describe ecological data. Two usual solutions: ignoring the zeroes and adding a small positive number to all outcomes, induce bias and reduce predictive power. To address these shortcomings, we design a Bayesian two-part model with a binary component for presence or absence and a continuous component involving a lognormal model for non-zero biomass. We specify two equations relating species-specific occurrence probabilities and expected log-biomasses when present to potential covariates, with spike-and-slab priors imposed on linear effects to selectively discard the irrelevant predictors. We analyze the biomass data of 74 phytoplankton (57 diatoms and 17 dinoflagellates) recorded weekly at Station L4 (Western English Channel, UK) between April 2003 and December 2009, along with measurements of abiotic covariates. Our results disclose different combinations of environmental predictors for the occurrence and the biomass of individual species. Overall, the occurrence of dinoflagellates is associated with higher temperature and irradiance levels compared to diatoms, with virtually no dependence on nutrient concentrations. Irradiance emerges as the key predictor of biomass when species are present. Optimum temperatures for biomass accumulation and temperature sensitivities vary widely among and within functional types. Compared to one-stage models based on usual zero-handling approaches, our two-part model stands out with higher prediction accuracy. The two-part modeling approach provides a valuable framework for decoupling the predictors of species occurrence and abundance from observational data.

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Data availability

Source data were obtained from and are available from the Western Channel Observatory www.westernchannelobservatory.org.uk. The L4 environmental data are available at the British Oceanographic Data Centre https://www.bodc.ac.uk/ (doi: https://doi.org/10.5285/f1968a39-26bf-55fe-e044-000b5de50f38).

Code availability

The OpenBUGS code used to fit the model to data is available in the Online Supplementary Materials.

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Acknowledgements

This work was supported by the Simons Collaboration on Computational Biogeochemical Modeling of Marine Ecosystems/CBIOMES (Grant ID: 549935, AJI). C.E.W. was funded through the UK Natural Environment Research Council’s National Capability Long-term Single Centre Science Programme, “Climate Linked Atlantic Sector Science”, Grant No. NE/R015953/1, and is a contribution to Theme 1.3—Biological Dynamics. Phytoplankton biomass and environmental data were provided by the Plymouth Marine Laboratory’s Western Channel Observatory www.westernchannelobservatory.org.uk, which was funded as part of the UK’s Natural Environmental Research Council’s National Capability.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada

    Crispin M. Mutshinda & Andrew J. Irwin

  2. Flatiron Institute, Simons Foundation, New York, NY, 10010, USA

    Aditya Mishra

  3. Department of Oceanography, Dalhousie University, Halifax, NS, Canada

    Zoe V. Finkel

  4. Plymouth Marine Laboratory, Prospect Place, Plymouth, PL1 3DH, UK

    Claire E. Widdicombe

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  1. Crispin M. Mutshinda
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Correspondence to Crispin M. Mutshinda.

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Mutshinda, C.M., Mishra, A., Finkel, Z.V. et al. Bayesian two-part modeling of phytoplankton biomass and occurrence. Hydrobiologia 849, 1287–1300 (2022). https://doi.org/10.1007/s10750-021-04789-2

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  • DOI: https://doi.org/10.1007/s10750-021-04789-2

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