Blooms of filamentous cyanobacteria occur regularly in the Baltic Sea during summer (Kahru et al., 2020; Kahru and Elmgren, 2014; Karlson et al., 2022), mainly from end of June until August, and are dominated by the diazotrophic filamentous cyanobacterial species Nodularia spumigena, Aphanizomenon flos-aquae, and Dolichospermum spp. (Carlsson and Rita, 2019; Klawonn et al., 2016; Olofsson et al., 2020a). The toxicity of these blooms is mainly attributed to the hepatotoxin nodularin, produced by N. spumigena. The chemical structure and toxicity of nodularin is similar to microcystin (Lundholm et al., 2009). The toxicity of cyanobacterial blooms is known to cause economic losses to the surrounding societies of the Baltic Sea (Jonasson et al., 2008) with negative effects on the food chain dynamics on several trophic levels (Karjalainen et al., 2007). How cyanobacteria and their toxins respond to the ongoing and future climate change in the Baltic Sea is, however, not well known. Therefore, an understanding of what influences and predicts the spatial occurrence of cyanobacteria and related toxins is needed for efficient management of the Baltic Sea.

The spatial and temporal distribution of cyanobacteria in the Baltic Sea area has been investigated using several different approaches. Monitoring data based on microscope analyses (Karlson et al., 2022; Olofsson et al., 2020a), satellite remote sensing of ocean color where high reflectance at wavelengths in the red part of the spectrum is indicative of near surface accumulations of filamentous cyanobacteria (Hansson and Hakansson, 2007; Kahru and Elmgren, 2014; Karlson et al., 2022), and several modeling approaches have been applied to describe the blooms (Hense et al., 2013; Hieronymus et al., 2021; Löptien and Dietze, 2022; Munkes et al., 2021). From these, several hypotheses have developed for what could influence the expansion and increase the occurrence of filamentous cyanobacterial blooms. For instance, availability of inorganic nitrogen and phosphorus (Andersen et al., 2020; Carpenter, 2005; Lu et al., 2019; Paerl et al., 2018; Wurtsbaugh et al., 2019; Yang et al., 2008), the ratio of inorganic nitrogen to phosphorus (Burford et al., 2023; Pliński et al., 2007), chlorophyll a concentration (Budakoti, 2024), salinity (Lehtimäki et al., 1994; Moisander et al., 2002; Silveira and Odebrecht, 2019), temperature (Stal, 2009; Walls et al., 2018), and also a combination of salinity and temperature (Olofsson et al., 2020a). In addition to promoting cyanobacterial growth, environmental drivers such as temperature, light, and nutrient availability can also modulate the production of cyanotoxins. For instance, nodularin production in Baltic Sea species has been shown to vary with nitrogen availability and physiological state (Lehtimaki et al., 1997). Similarly, oxidative stress conditions have been linked to microcystin release, potentially as part of a programmed cell death response (Ross et al., 2006). These findings suggest that bloom toxicity is not solely a function of biomass, but also of stress-related cellular responses. Despite the available knowledge on cyanobacterial blooms, little is known regarding what factors control spatial occurrence of N. spumigena and nodularin across the Baltic Sea. There are several factors that may limit the proper spatial estimation of nodularin occurrence across the Baltic Sea. Such factors include sampling difficulty due to spatial variability of nodularin concentrations and the large spatial scale of the area. In addition, seasonal variability of nodularin concentrations poses a sampling challenge due to the short period of time when the toxin nodularin is produced, mainly in the late summer. Moreover, limited, infrequent, and sparse monitoring, especially in the open sea, can lead to underreporting or missing peak toxin periods. The fact that nodularin cannot be directly measured by satellite and remote sensing along with lack of standardized modeling approaches poses great challenges to make predictions about current and future occurrence of nodularin in the Baltic Sea. Additionally, it has been shown that filamentous cyanobacteria over longer time scales are not so common in Bothnian Bay (Olofsson et al., 2021) nor in Kattegat (Olofsson et al., 2020b). Furthermore, future prediction of nodularin occurrence under climate change is a modeling challenge, especially in the long-term time frame when the worst-case climate scenario is projected to occur in the Baltic Sea. For instance, climate scenario SSP5-8.5 for 2100 is critical for the Baltic Sea with projected surface temperature increases up to 3.2 °C (Meier et al., 2022). This scenario is combined with increased runoff, accelerated oxygen depletion, decreased salinity, and worsened algal blooms (Friedland et al., 2012; Meier, 2006). All these factors, together with lack of proper modeling approach, make the current and future prediction of nodularin a methodological challenge.

To mitigate this methodological gap we integrated the results of a geostatistical interpolation method, the Empirical Bayesian Kriging (EBK) regression prediction (Gribov and Krivoruchko, 2020), and ensemble learning algorithms (Dietterich, 2000), to predict and interpret the spatial distribution of nodularin occurrence across the Baltic Sea. Kriging algorithms in EBK regression prediction are advanced geostatistical prediction methods and known as best linear unbiased estimators producing robust estimates at unsampled locations (Goovaerts, 1997; Krivoruchko and Gribov, 2019). EBK regression prediction methods are also known to generate robust and better accuracy than other kriging techniques both for small datasets and even when data is locally moderately non-stationary (Gribov and Krivoruchko, 2020; Krivoruchko, 2012). In the case of small dataset and clustered sampling points, kriging algorithm allows quantifying the spatial autocorrelation by determining the range or the distance within which points are correlated, and the sampling error or fine-scale variation called “nugget”. Moreover, kriging assigns weights to neighboring points based on their spatial correlation, meaning that kriging firsthand considers the autocorrelation of points, not just their physical distance (Antonakos and Lambrakis, 2021; Chilès and Delfiner, 1999). By utilizing autocorrelation, kriging removes spatially correlated noise and creates a fine and less smeared kriged map. Kriging also ensures that the final residuals are not autocorrelated by modeling the main predictors and creating the best linear unbiased predictions (Chilès and Delfiner, 1999; Fotheringham and Rogerson, 2009). The relationships between explanatory and dependent variables could alter in several locations; yet the EBK regression prediction is able to accurately simulate these regional variations and takes regional influences into consideration (Deutsch and Journel, 1992; Gribov and Krivoruchko, 2020; Krivoruchko and Gribov, 2019; Pyrcz and Deutsch, 2014).

There are also cases where the spatial estimation of continuous variables could be a challenging task when EBK regression prediction does not determine the relevance of the explanatory variables that affect the predictive variables or the independent variables that are highly correlated with the response variables (Olea, 1999; Wang et al., 2019). This could be because the phenomenon being sampled, may be produced by nonlinear processes, and the data may exhibit complex multivariate features, non-Gaussianity, and non-stationarity. In such a situation, the power of machine-learning algorithms in ensemble modeling allows identification of patterns in the complex datasets and to make estimation and prediction with no requirement for rigid statistical assumptions, such as stationarity and linearity (Ghannam and Techtmann, 2021; Sathya and Abraham, 2013). Machine-learning algorithms also allow the inclusion of multiple variables, coping with missing values, and being able to reveal the hidden relationships between predictors (Abdelgadir et al., 2023, 2025; Beery et al., 2021; Jiang et al., 2022; Thompson et al., 2019). Using Ensemble Learning (multiple models instead of single model) is known to quantify uncertainty in long-term projections (Álvarez Fanjul et al., 2025; Eyring et al., 2024a, b). In addition, using climate change scenarios coupled with real-time monitoring data from satellite imagery altogether allows for long-term trends to be estimated (Eyring et al., 2024a, b). It is also shown that combining the in-situ data with real-time monitoring data can further improves the accuracy of models (Wang, 2023; Yang et al., 2016). This altogether could possibility reveals uncertainty in long-term projections regardless of how long the period is (Eyring et al., 2024a, b; Parker, 2013). Previous studies demonstrated the difficulty and the uncertainty of resolving species composition changes under impacts of global change, particularly species known to be sensitive to change (Thuiller, 2004; Thuiller et al., 2009, 2019). However, it has been shown that using ensemble modeling combined with Stacked Species Distribution Models SSDM (Schmitt et al., 2017) and climate scenarios, allows for predicting shifts in habitat suitability, species richness, and assemblage structure (Abdelgadir et al., 2025; Brandt et al., 2017; Khan and Verma, 2022; Moullec et al., 2022). Therefore, using multi-model approach may provide a robust method to mitigate the uncertainties of species forecasting.

Algorithms in ensemble learning can resolve the issues concerning autocorrelation, clustered samples, small datasets, and unsampled sites across the study area. Algorithms overcome the overfitting by generating what are called “pseudo-absence data points” (Hysen et al., 2022), which represent those unsampled sites across the study area and in a way compare the observed environment (represented by the presence) against what is available. Algorithms also avoid overfitting by dividing the data into training and testing sets, which allows the model to learn on one subset of the data (training set) and evaluate its performance on another subset (testing set). All these procedures together ensure that the model generalizes well to new data, making it more robust and reliable. In addition, stacked species distribution modeling SSDM (Schmitt et al., 2017) is an advanced approach combining several ensemble outputs to model species assemblages into one forecast.

Herein we integrated the results of the EBK regression prediction, ensemble learning algorithms, and SSDM, using 139 nodularin concentration measurements, abundance of the cyanobacteria N. spumigena, and model-based raster layers on environmental and geographical variables to predict and interpret the spatial occurrence of nodularin across the Baltic Sea. Using integrated results of the above methods, the study aim was to understand what factors drive the spatial occurrence of nodularin, and how the spatial occurrence of this cyanotoxin will be affected by the projected climate change scenarios in the year 2100 across the Baltic Sea. This setup may act as proof of concept and can be applied when data is limited, and large sampling campaigns are challenging.

Blooms of toxic cyanobacteria are a global issue, and it's challenging to make predictions of toxin occurrence as the connection to organism abundance is not straightforward (Huisman et al., 2018; Ibelings et al., 2021). Therefore, understanding bloom formation and toxicity of cyanobacterial blooms in the Baltic Sea is difficult using observational data alone. Here, models can be very effective in increasing spatial and temporal resolution and the interconnection between abundance and toxicity. As a proof of concept, we integrated and compared the results of two different modeling approaches to understand and interpret the current and future spatial expansion of nodularin occurrence across the Baltic Sea. Although there are no expectations on substantial variations in degree of accuracy between geostatistical and ML-based predictions, there has in recent years been a general move from geostatistics to machine learning (Veronesi and Schillaci, 2019). According to the same study, the number of documents mentioning ML algorithms-based predictions has rapidly increased, surpassing kriging-based algorithms in the last decade. Our findings suggest the efficiency of both kriging and ML algorithms given that the overall geographical estimations and maps produced by the kriging and ensemble-based models in this study are aligned despite the differences of approaches. Findings suggest that the model generated by the integrated method is yielded by using advantages of both methods, which in turn increase prediction accuracy and performance.

Several abiotic variables, such as PO₄, NO₃, sea surface temperature, and salinity, are known to directly or indirectly affect and control the abundance of cyanobacteria (Almroth-Rosell et al., 2016; Andersen et al., 2020; Karlson et al., 2010; Lips and Lips, 2008; Lu et al., 2019; Olofsson et al., 2020a; Stal, 2009; Unger et al., 2013; Wurtsbaugh et al., 2019; Yang et al., 2008), and therefore we also included many environmental factors. Considering the importance of abiotic variables in modeling cyanobacterial abundance, the corresponding general ocean circulation models GCMs require adequate horizontal and vertical resolution and trustworthy boundary conditions. An earlier study by Reissmann et al. (2009) showed that variations in GCMs are likely to affect the simulation of cyanobacteria (see also Munkes et al., 2021). Therefore, we employed different GCMs to reduce possible errors that could arise from abiotic variables of different ocean models. Our simulation showed that there were conformities in predicted distribution of nodularin despite the different GCMs used in this study. Although each one of the combined approaches has different working procedures, each model effectively yielded similar performance observed in the predicted distribution of nodularin occurrence across the Baltic Sea. This finding indicates that both kriging and ML-based algorithms, the ensemble, can capture the differences in abiotic variables of different GCMs. The findings also suggest that the approach could help resolve the error arising from great divergence between general circulation models (GCMs) when used for predicting the presence or occurrence of cyanotoxins.

Using our conceptual model-setup we were able to locate areas with high predicted nodularin concentrations in response to current environmental variables and projected future changes of the same variables. These areas were the Eastern and Western Gotland Sea, the Northern Baltic Proper, southern parts of the Bothnian Sea, and the Arkona basin, corresponding to the effects and interactions between temperature, PO₄, NO₃ : PO₄, salinity, and distance to shore. The effects of temperature, PO₄ and NO₃ : PO₄ are aligned with previous studies by Deng et al. (2022); Lürling et al. (2017), and Olofsson et al. (2016), documenting that water temperature increase is associated with higher nutrient loads and phosphate release from sediments, all of which could have an impact on cyanobacterial biomass increase. Rising temperature is also associated with terrestrial runoff of organic matter but also causes a decrease in salinity in the northern Baltic Proper, northern parts of the Bothnian Sea, Bothnian Bay, and southward to the Arkona basin (see Andersson et al., 2013, 2015). Moreover, the increase in the abundance of cyanobacteria may also be associated with basin-specific decreases in salinity (Kuosa et al., 2017; Olofsson et al., 2020a; Suikkanen et al., 2007), which could highlight the area increase of nodularin predicted in the Arkona basin.

To further investigate whether nodularin accumulates closer to or far from the shoreline, we included the geographical variable “distance to shore” as a predictor. Results of Bayesian regression show that distance to shore, surprisingly, appears to have significant positive direct and interaction effects together with other variables on the predicted area increase of nodularin. Our findings show that predicted sites with high nodularin concentration are located further offshore. Considering the differences in biogeochemical characteristics between coastal and offshore waters (Vigouroux et al., 2021) and that offshore waters are generally more nutrient-depleted than waters closer to the coast (see Löptien and Dietze, 2022), our results, in contrast to common assumption, suggest that predicted occurrence of nodularin is not only driven by nutrient concentrations like PO₄ and NO₃. However, the predicted occurrence of nodularin in nutrient-depleted areas could be attributed to the limitation of model-based projection of nutrient load scenarios, which do not differentiate between dissolved inorganic phosphorus stored by cyanobacteria and dissolved organic phosphorus. The fact that cyanobacteria can utilize dissolved organic phosphorus under nutrient-depleted conditions (see Caille et al., 2024; Rabouille et al., 2022) could explain the observed and predicted occurrence of nodularin. Our model finding suggests the importance of including distance to shore as a geographical variable in future modeling of cyanobacteria and cyanotoxin, particularly in nutrient-depleted areas across the Baltic Sea.

To explore what drives predicted area distribution of nodularin, we analyzed the interaction effect of the selected predictors. Results of Bayesian linear regression show that there were variations in the interaction effects between different variables of ERGOM and NODC on the predicted occurrence of nodularin, with a relatively low coefficient of determination R2≤0.25. This statistical observation can be attributed to the differences in resolutions of variables measured by GCM of different origins (see e.g., Dietze and Löptien, 2016; Löptien and Dietze, 2022; Meier et al., 2011; Meier and Kauker, 2003; Munkes et al., 2021; Schrum and Backhaus, 2002). However, these statistical observations are not great enough to offset the spatial regression observed in the regression function R2≥0.7 and the detrimental and significant effects of other variables with p<0.001, 0.01 and 0.05 observed, e.g., in salinity, temperature, PO₄, distance to shore, and their interaction effects. Despite the statistical results of Bayesian linear regression, our model finding suggests that the spatial regression function produced by the kriging algorithm is useful to interpret the drivers of the predicted occurrences of nodularin.

Future increased occurrence of nodularin was predicted for the Eastern Gotland Sea, Northern Baltic Proper, the Bothnian Sea, the Quark, and Arkona Basin in response to overall projected changes in environmental variables, particularly the NO₃ concentration and temperature. Earlier studies demonstrated that cyanobacterial taxa, such as Nodularia spumigena and Aphanizomenon spp., will benefit from climate change due to increased stratification by higher temperatures and that the growth and nitrogen fixation are favored by rising temperatures (Karlberg and Wulff, 2013; Munkes et al., 2021; Paerl and Otten, 2013; Visser et al., 2016). Furthermore, it has been shown that the effects of climate change under different scenarios are smaller than the effects of considered nutrient load changes (Saraiva et al., 2019). Taken together, our model findings suggest that reducing nutrient load could lead to improved future environmental conditions in the Baltic Sea, which in turn could reduce future area distribution of nodularin.

Results of the LMG based on ERGOM and NODC data, where N. spumigena leads the importance ranking is biologically intuitive: toxin concentration is closely tied to the abundance of the toxin-producing organism itself. Contribution of salinity (15.2, 24 %) and chlorophyll a (12.8, 12 %) indicate that both ionic conditions and overall phytoplankton biomass modulate nodularin concentrations. Nutrient availability (NO₃, PO₄ and N : P jointly contribute ∼ 24.2 %) is the next most influential factor especially NO₃, all reflecting that N supply often governs cyanobacterial growth and secondary metabolite production. Temperature (18.5, 10 %) is environmental modulator that further tunes metabolic rates and community composition. Furthermore, distance to shore (9.3, 1.0 %) as proximity to the shore possibly reflects nutrient loading or mixing regimes, which in turn affect nodularin levels. These findings suggest that while biological factors (Nodularia abundance and chlorophyll) and temperature are dominant, both physicochemical conditions (salinity, nutrients, and distance to shore) play appreciable roles in explaining variation in nodularin. The two full models explain about 78 % and 72 % of the total variance in nodularin, suggesting that more variables can be included to further reveal conditions under which toxin-producing blooms thrive.

Given the great divergence and large spread between findings of other models projecting cyanobacterial bloom (e.g., Hense et al., 2013; Meier et al., 2012, 2019; Munkes et al., 2021; Neumann, 2010; Saraiva et al., 2019), the variation in GCMs, and that cyanotoxins cannot be directly measured by satellite and remote sensing, our modeling approach that combines geostatistical and ML algorithms could help mitigate this methodological gap. The approach used here shows that while geostatistical methods were able to analyze small spatially correlated datasets to predict values at unsampled locations, the ML algorithms were able to handle complex and non-linear relationships in data that geostatistical models might miss. Model prediction of both EBK regression and ensemble learning provided useful and conformable spatial estimation of nodularin occurrence, suggesting that combining results of geostatistical interpolation and ML-based modeling could serve as a promising future approach for cyanotoxin investigation. Both models, for example, can use the advantages of both techniques to produce predictions that are more accurate than those made by any one model alone. This approach could also help mitigate future expansion of nodularin by detecting and predicting possible hotspot occurrences that could arise due to different future climatic scenarios across the Baltic Sea. Despite the model's accuracy and performance, care should be taken when interpreting the model findings, given that there was limited data availability that covers both nodularin concentration and abundance of N. spumigena in corresponding samples and that the sampling period of the study was conducted only during the summer and in one year. The risk of overfitting due to data limitations is still very high, regardless of using ensemble and model accuracy observed in this study. Although the study integrates different downscaled datasets from global and regional models, a careful inspection should be given to harmonize the datasets, calibrate regional projections using global boundary conditions, align the differing resolutions, and quantify uncertainty. It is also worth mentioning that, despite many efforts made, predicting Nodularia sp. blooms from the environmental factors remains challenging (Kahru et al., 2020; Karlson et al., 2010). Moreover, the integrated model must be carefully inspected to ensure that it is still interpretable and computationally practical, providing that model success and performance are strongly reliant on the quality of the input data.

Our proof-of-concept model combination setup used herein demonstrates the need to integrate geostatistical interpolation and machine-learning-based modeling to monitor and mitigate spatial expansion of nodularin across the Baltic Sea and to enhance decision-making strategies in this area. Improved model accuracy using combined approaches may enable more precise recommendations that could help mitigate future expansion of cyanotoxins in the Baltic Sea. Our model combination can be a useful tool to generate spatial estimates of nodularin occurrence at unsampled locations and temporal occurrence when sampling efforts are challenging. We show evidence that the predicted area distribution of nodularin is a result of several interacting environmental variables together with a geographical factor of distance to shore that could further help explain increased expansion into different areas in the future, which is also beneficial from a management perspective. Furthermore, the combined approaches presented in this study could be crucial for effective management applied for nutrient reduction and predicting future climate change impacts, as cyanobacteria can exacerbate eutrophication, affect water quality, and pose health risks. If used carefully, these approaches could help prioritize surveillance and implement earlier sampling efforts in areas predicted to have high and/or increasing cyanotoxin concentration.