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.

中文翻译：

---

使用贝叶斯化合物Poisson-Gamma模型从水温和电导率预测蓝细菌的生物量。

富营养化和气候变化情景导致需要为有害的蓝藻水华（CyanoHAB）开发良好的预测模型。然而，由于严重偏斜的分布（包括许多缺失和极值（密集开花）），对蓝细菌生物质进行建模是一项艰巨的任务。大多数建模方法都将数据分为零（缺失）和正值，从而改变了数据的自然分布，前提是这两个组成部分的基础是不同的过程。我们的目标是（1）考虑到所有生物量值（零和正生物量），开发一个概率模型，将蓝细菌的生物量与Ríode la Plata河口（35°S，56°W，n = 205个观测值）中的环境变量相关联具有相同的过程；（2）以水温和电导率为解释变量，使用该模型预测不同风险水平情景下的蓝细菌生物量。我们开发了复合的泊松-伽玛（CPG）回归模型，该方法以前在贝叶斯层次结构框架内尚未用于对浮游植物生物量进行建模。后验预测表明，拟合模型对观察到的蓝细菌生物量和数据的更特定特征具有良好的总体拟合，例如在三个阈值风险水平（0.2、1和2mm³L-1）上越过样品的比例不同的水温和电导率。CPG模型强调了水温和电导率的非线性和交互作用对蓝细菌生物量的强力控制。跨越三个生物体积水平的最高可能性发生在22.2°C，而观察到的电导率最低（〜0.1 mS cm-1）。使用样本外观察值（n = 72）对拟合模型进行交叉验证，表明该模型具有就地使用的潜力，因为它可以基于两个易于测量的变量（温度和电导率）预测蓝细菌的生物量，从而使其成为可能早期警报系统和管理策略的有趣工具。此外，该新颖的应用证明了贝叶斯CPG方法在预测响应环境变化的蓝细菌动力学方面的潜力。由于可以基于两个易于测量的变量（温度和电导率）预测蓝细菌的生物量，因此具有就地使用的潜力，这使其成为用于预警系统和管理策略的有趣工具。此外，该新颖的应用证明了贝叶斯CPG方法在预测响应环境变化的蓝细菌动力学方面的潜力。由于可以基于两个易于测量的变量（温度和电导率）预测蓝细菌的生物量，因此具有就地使用的潜力，这使其成为用于预警系统和管理策略的有趣工具。此外，该新颖的应用证明了贝叶斯CPG方法在预测响应环境变化的蓝细菌动力学方面的潜力。