Predicting cyanobacterial biovolume from water temperature and conductivity using a Bayesian compound Poisson-Gamma model

Abstract

Eutrophication and climate change scenarios engender the need to develop good predictive models for harmful cyanobacterial blooms (CyanoHABs). Nevertheless, modeling cyanobacterial biomass is a challenging task due to strongly skewed distributions that include many absences as well as extreme values (dense blooms). Most modeling approaches alter the natural distribution of the data by splitting them into zeros (absences) and positive values, assuming that different processes underlie these two components. Our objectives were (1) to develop a probabilistic model relating cyanobacterial biovolume to environmental variables in the Río de la Plata Estuary (35°S, 56°W, n = 205 observations) considering all biovolume values (zeros and positive biomass) as part of the same process; and (2) to use the model to predict cyanobacterial biovolume under different risk level scenarios using water temperature and conductivity as explanatory variables. We developed a compound Poisson-Gamma (CPG) regression model, an approach that has not previously been used for modeling phytoplankton biovolume, within a Bayesian hierarchical framework. Posterior predictive checks showed that the fitted model had a good overall fit to the observed cyanobacterial biovolume and to more specific features of the data, such as the proportion of samples crossing three threshold risk levels (0.2, 1 and 2 mm³ L^-1) at different water temperatures and conductivities. The CPG model highlights the strong control of cyanobacterial biovolume by nonlinear and interactive effects of water temperature and conductivity. The highest probability of crossing the three biovolume levels occurred at 22.2 °C and at the lowest observed conductivity (∼0.1 mS cm^-1). Cross-validation of the fitted model using out-of-sample observations (n = 72) showed the model's potential to be used in situ, as it enabled prediction of cyanobacterial biomass based on two readily measured variables (temperature and conductivity), making it an interesting tool for early alert systems and management strategies. Furthermore, this novel application demonstrates the potential of the Bayesian CPG approach for predicting cyanobacterial dynamics in response to environmental change.

Keywords: Alert levels; Bayesian modeling; Brackish ecosystems; HAB management; Risk thresholds; Salinity.