Harmful algal bloom (HAB) is an international term adopted by the Intergovernmental Oceanographic Commission (ICO) of the United Nations Educational, Scientific and Cultural Organization (UNESCO) to refer to any proliferation of microalgae (regardless of the density) perceived as harmful owing to its negative impact on public health, aquaculture, the environment and/or recreational activities (Kudela et al., 2015; Reguera et al., 2016; FAO, 2023). HABs constitute a serious threat to public health as well as sustainable coastal and marine development worldwide. HABs cannot easily be eliminated or prevented, but the potentially negative consequences can be managed and mitigated (FAO, 2023). Adopting an adequate suit of actions in due time is particularly relevant for aquaculture production systems. Among the most problematic HAB events are those associated with proliferations of Dinophysis species, mainly D. acuminata and D. acuta, which, even at low cell densities, cause Diarrheic Shellfish Poisoning (DSP) events. These marine mixotrophic dinoflagellates are producers of different analogues of the okadaic acid group of toxins and the main cause of shellfish harvesting closures in boundary upwelling systems (Trainer et al., 2010) as in the eastern Atlantic coasts of Europe (Reguera et al., 2014; Swan et al., 2018), particularly in the Iberian Peninsula (Vale et al., 2008; Fernández et al., 2019). Here, D. acuminata is the dominant species and it blooms (10² – 10⁴ cells·L^-1) mainly from April to October, coinciding with the upwelling season. Environmental factors are known to shape the proliferation and distribution of Dinophysis species (Díaz et al., 2013, 2016; Fernández et al., 2019; Lima et al., 2022). As a consequence, considerable effort has been devoted to understanding the ecophysiology, population dynamics and bloom development of D. acuminata over the past two decades (Smayda, 1997; Anschütz et al., 2022; Lima et al., 2022; FAO, 2023).

The development of sustainable shellfish aquaculture is highly dependent on the provision of reliable monitoring and predictive information on the occurrence of HABs. To assist the day-to-day management activities, it is fundamental to disclose regular information on HAB and biotoxins risk to end-users. Around the world, HAB alert bulletins and warning systems vary in complexity and can be delivered by a range of platforms using traditional environmental data or based on purely computational methods (Anderson et al., 2015; Lima et al., 2022; Wang et al., 2022; FAO, 2023). Reports rely on field observations, ocean colour satellite imagery, models, historical trends, public health reports, buoy data and forecasts of potential bloom progression (e.g. bulletins from NOAA, EUA; Marine Institute, Ireland; INTECMAR, Galicia; IPMA, Portugal). Multiple methods exist for monitoring algal densities and signalling the presence of algal blooms (Anderson, 2009; Stumpf et al., 2009, 2010, FAO, 2023). In situ species-specific cell counts have the highest confidence but the spatial and temporal resolution of the sampling is generally limited. In this regard, the Portuguese Institute for Sea and Atmosphere (IPMA), which is the national government agency responsible for shellfish toxicity monitoring, uses two thresholds of Dinophysis cell density: 200 cells·L^-1 to publicly emit a HAB warning alert and 500 cells·L^-1 to propose a DSP precautionary closure of shellfish harvesting.

Remote sensing has the advantage of providing large spatial coverage and with finer resolutions, although temporal frequency can be limited by clouds. Remote sensing of the coastal ocean is intricate. Satellite imagery of coastal and inland waters require atmospheric correction algorithms (Zhang et al., 2014; Fan et al., 2017; Lu et al., 2018; Ilori et al., 2019). Near-coast processes as daily winds, river run-off or coastal upwelling can also bias data from satellite imagery, especially due to their impact on ocean colour and plankton assemblages, and the high spatial and temporal resolutions of their dynamics (Shen et al., 2012; Smith and Bernard, 2020). Operational models allow near real-time forecasting and can be used to calculate the temporal and spatial coverage of phytoplankton distribution and chlorophyll-a. Data sampling schemes (spatial and temporal) have great influence on the accuracy of the forecasts (Stumpf et al., 2009, 2010).

In this work, we propose a demographic model of D. acuminata as a tool for forecasting its blooms and help decision making. The model is applied separately to distinct regions of the Portuguese coast with the goals of anticipating two operational thresholds concentration of 200 and 500 cells·L^-1. For that, we assess the set of environmental variables governing D. acuminata growth.

The study was conducted along the Portuguese continental coast, which together with Galicia, comprise the west coast of Iberia, constituting the northern limit of the northeast Atlantic upwelling system ( Figure 1 ) (Ambar and Dias, 2008; Alvarez et al., 2010). Usually, upwelling occurs from late Spring to early Autumn. Along the western coast, it is driven by northerly winds, while along the southern margin, although not as frequent or intense, these events are mainly due to westerly winds. During upwelling, the shelf circulation is characterized by alongshore flows roughly aligned with the wind direction. This means that during the summer months, the water transport is mainly southward and eastward, respectively, along the west and south coasts of the study area. During winter the winds relax, with intermittent periods of both upwelling- and downwelling-favourable winds (Ambar and Dias, 2008; Alvarez et al., 2010; Leitão et al., 2019), inducing local inversion in coastal shelf currents.

The thickness of the upper ocean mixed layer and seasonal thermocline, also varies widely according to the season: in winter, vertical stratification is low, with homogeneous mixed layer depths (MLD) reaching about 200 meters, while during the summer upwelling season, the water column is highly stratified, with MLD typically narrower than 20 meters.

The coastal area studied is also under the influence of several rivers, where fresh water run-offs also impact the inner shore stratification pattern (Cunha, 2001). The main rivers flowing into the shelf are highlighted in Figure 1 . Along the western margin, among all the rivers depicted in this figure, the Minho, Douro, Tagus, and Sado rivers stand out as a the most significant freshwater sources to the shelf, while on the southern coast, the Guadiana detaches as the most important one. This fresh-water outflows, can generate lenses of low buoyancy water that can spread offshore, with variable seasonal distances, occasionally exhibiting a persistent signature throughout the year. This is the case of the Western Iberia Buoyant Plume (WIBP), first identified by Peliz et al. (2002), which extends meridionally from approximately 40°N, to the Galician coast, in the northern region of the study area. It results from the outflow of several regional rivers, from which the Minho and Douro are the main contributors (Otero et al., 2008). The WIBP maintains a year-round presence in the area and significantly impacts both the structure of upwelling and the expected vertical stratification pattern along the inner shelf.

Our results suggest that D. acuminata thrives under the combination of high PAR and cool seawater. Given spring-summer light conditions, D. acuminata blooms with SST below 18°C. On the other hand, with SST above 20°C D. acuminata cannot bloom. These results fit the niche envelop previously reported for D. acuminata (e.g. Anschütz et al., 2022) as well as other Dinoflagellate species causing HABs in the North Atlantic (Gianella et al., 2021; Lima et al., 2022). These favourable conditions correspond to the spring-summer upwelling regime characterized by bright sunny days and nutrient-rich cold waters, typical to the Iberian and Morocco coastal ocean (Ambar and Dias, 2008; Alvarez et al., 2010; Díaz et al., 2013, 2016; Moita et al., 2016; Leitão et al., 2019; Danchenko et al., 2022). In other locations on the North Atlantic, namely along the Bay of Biscay, British Isles and British Channel, the water is cold enough due to its higher latitude. Consequently, the summer is the typical season for HAB of D. acuminata as well as other Dinoflagellate species in the North Atlantic (Smayda and Trainer, 2010; Díaz et al., 2013, 2016; Moita et al., 2016; Swan et al., 2018; Fernández et al., 2019; Gianella et al., 2021; Danchenko et al., 2022; Lima et al., 2022).

Despite the environmental conditions favouring HABs being already reasonably understood, attempts to systematically forecast them have underachieve. Often, these attempts considered the modelling of HABs as a strictly statistical problem requiring a strictly statistical solution. Consequently, statistical tools were applied to produce empirical models forecasting the population size from environmental predictors. By doing so, these attempts incurred in two flaws: first, to choose population size as response variable when the correct choice should be the population growth rate; second, neglecting the fundamental factor in demographic forecasting that is “how much was there to start with?” i.e., the initial population size. It is known that numerous phytoplankton species can double their population in 12h under good environmental conditions (e.g. Smayda, 1997); if there is 1 cell to start with, the day after we have 4 cells. But if there are 1000 cells to start with, the day after we have 4000 cells. Our simulations with D. acuminata illustrated well these aspects and the results are evidence that forecasting HABs is a problem of population dynamics/demography. Hence, the solution must come from population dynamics/demography theory and respective mechanistic models. These say that environmental factors set the population growth rate and the maximum sustainable population size, also known as “carrying capacity”. Hence, in the simplest approach possible, the correct choice for response variable is the population growth rate. In a more elaborate approach, as we did in this work, the environmental predictors affect the population growth rate dependency from current population size i.e., how the initially exponential growth dampens as the population approaches its carrying capacity. It is only at this stage (i.e., once the core model has been established from population dynamics/demography theory) that statistics steps in to fit the dependency of demographic parameters from environmental predictors; and for that fit there are many viable statistical alternatives.

Like many dinoflagellates (see Smayda, 1997), D. acuminata is a mixotrophic species (Anschütz et al., 2022): a phagotroph acquiring phototrophy from the Mesodinium it preys upon, in its turn acquiring phototrophy from the Teleaulax it preys upon. This sequence is known as the Teleaulax-Mesodinium-Dinophysis-Complex. Given the D. acuminata sensibility to the light environment and its phototrophy being acquired from its prey, demographic models shall predict better D. acuminata growth if they also take into consideration the availability of Mesodinium. The fact that the niche envelops of both predator and prey are similar (see Anschütz et al., 2022) facilitates this task. Nevertheless, the onset of the right environmental conditions should not immediately trigger a D. acuminata bloom as a prior bloom of Mesodinium is likely required (see Moita et al., 2016). Unfortunately, weekly data on Teleaulax and Mesodinium are not available in the study area. Hence, we could not include them in our modelling. Still, we recognize that these predator-prey dynamics and the time-lag between prey bloom and the following predator bloom may justify why the D. acuminata growth was better forecasted from the environmental data relative to the previous 5 days, rather than from the simultaneous data. Once the monitoring constrains by us identified are solved, modelling the Teleaulax-Mesodinium-Dinophysis-Complex will become the fundamental development for accurate forecasting of D. acuminata blooms.

This work identified the necessary knowledge about D. acuminata ecology and population dynamics so that this is no longer a limitation to forecasting its blooms. The results also indicate that for this knowledge to be effective it must be applied to input data with better resolution. While this is not improved, forecasts will continue limited and attempts to develop better models are probably futile. The first key issues lessening the adequacy of the input data was the census intervals of 7 days that proved to be too wide to monitor D. acuminata populations when environmental conditions were favourable for their growth ( Figures 2 , 3 , 7 ). Even starting from low numbers, after 7 days of favourable growth their populations can overshoot the 500 cell·L^-1 threshold representing a harmful abundances for shellfish toxification. Knowing D. acuminata has relatively low inherent growth rates compared to many other HAB species, our results quantitatively confirm the severe insufficiency of 7-day census for most microbiological processes. When modelling population growth, the simulations may overshoot reality, and even became unstable or chaotic, because a continuous process was modelled as being discrete and with too large time intervals (Akçakaya et al., 1999; Caswell, 2001). The importance of monitoring and modelling HABs with time resolutions shorter than 7 days was actually demonstrated by the significant improvements in south Florida’s operational monitoring program when the monitoring was performed twice-daily and in the operational forecast system when the model was run twice-weekly (Stumpf et al., 2009). The second key issue lessening the adequacy of the input data was the laboratory detection limit of 20 cells·L^-1. Our work proved this limit to be too coarse to monitor D. acuminata populations when environmental conditions were favourable for their growth. Below the detection limit, the actual in situ population numbers were unknown, with 0 or 19 cell·L^-1 being equally likely yet producing opposing results ( Figure 10 ). Starting the model with 1 or 19 cells can result after 7 days in an incipient population or an overshoot of the HAB alarm threshold (200 cell·L^-1), which is problematic for an operational shellfish toxicity monitoring program that needs to communicate accurate information.

Even good demographic models applied to high resolution data underachieve forecasting HABs if they do not take into account the motion of the ocean water with the consequent advection and diffusion of the phytoplankton cells. For this reason, the state-of-the-art in forecasting HABs use hydrodynamic simulations to force Lagrangian simulations of phytoplankton dispersion. Such are the cases of HABs forecasting in the North Atlantic, namely along the Iberian shelf, Bay of Biscay, British Isles and British Channel (Bedington et al., 2022; Hariri et al., 2022). Cell multiplication is the fundamental determinant of HABs during their earlier stages. However, when populations have already achieved densities that are high and/or harmful, their transport and dispersion gain importance for the accuracy of the forecasts (Bedington et al., 2022). A significant portion of the lack of accuracy in our modelling efforts resulted from the lack of hydrodynamics in our model and this was exacerbated by a too wide census/projection interval. Over the course of 7 days, advective transportation could carry D. acuminata cells towards or away from each of census location whereas diffusion processes and/or sinking losses could locally alter its cell density in a specific volume of water. This was challenging both for monitoring and for forecasting. In the case of monitoring, it brought great uncertainty about how much of the change in the observed population numbers resulted from its “local” biology and how much resulted from larger scale hydrodynamics. Given this uncertainty, it was very hard to estimate model coefficients with confidence. In the case of forecasting, even if we had a perfect demographic model to forecast cell multiplication, not knowing where those cells headed turned very difficult to produce accurate forecasts.

The too wide census/projection intervals, the coarse detection limit and the neglection of hydrodynamics are probably behind the unexpected surge in D. acuminata numbers following situations of perceived absence. Improving these aspects demands substantial increase in the sampling logistics, laboratory methods and modelling efforts, which is difficult if the resources of any given HAB monitoring program are not increased. For future work in this field, we suggest two solutions. One, is to use image acquisition systems (both in situ and laboratory hardware units) with machine learning software to automate the counting of phytoplankton cells and therefore increase sample processing and lower the detection limit. The other is to intensify the seawater collection effort only when conditions are favourable for any given HAB species. Considering D. acuminata, this sampling intensification should take place during the upwelling regime that takes place along the western Iberian shelf mainly during the summer season (Ambar and Dias, 2008; Alvarez et al., 2010; Leitão et al., 2019; Danchenko et al., 2022). Hence, weather forecasts of incoming north winds leading to upwelling, and the subsequent cooling of SST, may be used as triggers (in some semi-automatic way) to intensify the sampling effort, as well as to relax the remaining time. A time-variable monitoring programme maybe the key to optimize the prediction of D. acuminata blooms, as well as other HAB species, and obtain forecasts of the highest quality, helping effective management measures for the shellfish industry.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

VV: Software, Methodology, Investigation, Formal analysis, Writing – original draft, Visualization, Validation. TLR: Writing – review & editing, Resources, Methodology, Investigation, Data curation, Conceptualization. LS-G: Writing – review & editing, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Data curation, Conceptualization. MM: Writing – review & editing, Resources, Project administration, Funding acquisition. BM: Writing – review & editing, Resources, Methodology, Formal analysis, Data curation, Conceptualization.