During the PROTEVSMED-SWOT campaign May 2018, south of the Balearic Islands,, we implemented a sampling strategy to cross a frontal zone separating two distinct water masses several times, with a North-South, “hippodrome” shaped route (hereinafter NS-Hippodrome, Fig. ) . High-resolution physical and biological surface measurements were collected using a CTD sensor mounted on a towed vehicle, a thermosalinograph (TSG) and an automated flow cytometer installed on the surface water intake of the TSG circuit. By employing an adaptive Lagrangian sampling strategy, we tracked physical and biological structures in both space and time, identifying a fine-scale frontal zone separating the two water masses A and B, each characterized by contrasting abundances of nine phytoplankton groups defined by flow cytometry . To capture the phytoplankton diel cycle, both water masses were continuously sampled along the NS-Hippodrome from 11 to 13 May, 2018. This approach allowed us to capture the diel cycle in both A and B similarly, reducing biases from cell size and division. As a result, any differences in cell abundance between the A and B water masses are not related to diel cycle variations, making the observations independent and identically distributed (hereafter i.i.d.).

Based on extensive analysis of temperature and salinity in the water column and across the zone, characterized the frontal area around 38.32° N. They stated that surface salinity was a good marker for the water masses in the visited area (Fig. c). The salinity gradient during the cruise (see Fig. ) indicates that water mass A is characterized by a salinity ≥ 37.6 gkg-1, and water mass B by a salinity ≤ 37.3 gkg-1. The front F lies between these two isohalines. The frontal zone definition also followed a geographic criteria, 38.36° N ≥ Latitude ≥ 38.30° N, corresponding to the measurement locations . To focus on the frontal zone, measurement points that lay within the salinity range of the front but outside of its geographical boundaries were considered as part of a transitional zone (T) and were not used for the data analysis. In total, 30 samples were collected in A, 44 in B, 11 in F and 17 in T.

Automated flow cytometry enables high-frequency seawater sampling and analysis to identify phytoplankton groups based on their optical scattering and fluorescence properties . The CytoSense flow cytometer (Cytobuoy b.v., Netherlands) uses a sheath fluid of 0.1 µm filtered seawater to align and guide individual particles (cells) through a 488 nm laser beam. As cells interact with the laser beam, multiple optical signals are simultaneously recorded for each particle (cell).

First, forward scatter (FWS) and sideward scatter (SWS) are measured, providing insights into particle size, shape, and granularity. Second, fluorescence signals from photosynthetic pigments are also detected using photomultiplier tubes: red fluorescence (FLR) from chlorophyll and orange (FLO) fluorescence from phycoerythrin. Sequential protocols are run sequentially every 30 min, to analyse samples by phytoplankton size class. The first protocol (FLR6) had a FLR trigger threshold fixed at 6 mV and could analyze a volume of 1.5 cm3. It was dedicated to the analysis of the picophytoplankton (< 2 µm). The second protocol (FLR25) targeted nanophytoplankton and microphytoplankton (> 2 µm) with a FLR trigger level set at 25 mV and an analysed volume of 4 cm3.

Data acquisition was performed using CytoUSB software (Cytobuoy) and analyzed with CytoClus (Cytobuoy). The cytometer produces 2D cytograms, graphical representations that plot individual particles according to their optical signals, highlighting distinct populations based on scattering and fluorescence properties. Within these dot clouds, we manually identified clusters that serve as proxies for functional phytoplankton group . CytoClus provides cell abundances (cellscm-3) and mean optical signal intensities for each phytoplankton group.

Nine phytoplankton groups were identified : one cyanobacterial group, Synechococcus (Syne, 1,µm); four picoeukaryote groups (Pico1, Pico2, Pico3, PicoHFLR, 0.2–2 µm); two nanoplankton groups (SNano, RNano, 2–20 µm), cryptophytes (Crypto, 10–50 µm); and one microphytoplankton group (Micro, 20–200 µm). Abundances (number of cells) are converted into carbon biomass (mmolCm-3) using allometric relationships described in and . Importantly, there are huge size, biomass and abundance contrasts between the nine phytoplankton groups (Figs.  and ).

We denote by Com the random vector characterizing a community. It is composed of the biomass of the 9 phytoplankton groups described previously. We assume that the biomass distribution of the community in the front, denoted by ComF, is mathematically described as a finite discrete mixture of three random components corresponding, respectively, to the communities of water masses A (ComA) and B (ComB) and an unknown community (ComC), as follows: 1ComF=IU=AComA+IU=BComB+IU=CComC, where, for any generic condition T, the indicator function is defined as: 2IT=1if condition T is satisfied,0otherwise

Here, U is an unobserved categorical random variable taking values in the set {A,B,C}, with the following probabilities: 3P(U=A)=λA,P(U=B)=λB,P(U=C)=λC, with λA+λB+λC=1.

Each observation is thus assumed to originate from one of the three communities A, B, or C, with respective weights λA, λB, and λC. The case where λC is significantly different from 0 indicates the presence of the new community C, while λC→0 corresponds to a mixture involving only communities A and B.

The collected observations (i.i.d., cf. Sect. 2.1) of ComF is a table of dimension n × m, where n=11 biomass measurements and m=9 phytoplankton groups.

Multivariate normal distribution of A, B, F and T were assessed with the Henze–Zirkler's test . Except for A, the empirical biomass distribution in B, F and T revealed non-Gaussian shapes associated with high variability for each phytoplankton group (see Fig. ), suggesting underlying mixture structures of Gaussian distributions. Given this, we proposed that ComA, ComB and ComC, are themselves issued from a mixture of, respectively, j, k and l multivariate Gaussian components, which model potential sub-communities within A, B and C as follows: 4ComA∼∑r=1jαAr⋅N(μAr,ΣAr),5ComB∼∑s=1kαBs⋅N(μBs,ΣBs),6ComC∼∑t=1lαCt⋅N(μCt,ΣCt), where α denote the mixture weights (summing to 1 in each case), and μ∈Rm, Σ∈Rm×m are the mean vectors and covariance matrices of the respective multivariate Gaussian components.

To estimate parameters μ, Σ, α and λ, and the number of components j, k and l in ComA, ComB and ComC, respectively, we combined two estimation strategies: (i) an Expectation–Maximization (EM) algorithm ; and (ii) a two step Bayesian approach.

Communities A and B were, respectively estimated using in situ samples using large dataset from water mass A and water mass B (step 1 in Table ). We considered varying numbers of components j,k∈{1,…,10}.

The potential community C cannot be directly observed in the front (due to the limited number of observations). Thus, we estimated the Gaussian parameters of likely communities to be in C from the larger dataset of the rest of the cruise, hereafter the outside dataset, which consists of 461 observations (black dots on Fig. b). The limitations of this approach are discussed in more detail in the Discussion section. We assumed that the community in the outside dataset denoted by Com^C′ is a mixture of sub-communities, large enough to represent the latent community ComC. In other terms, we considered ComC to be a subset of Com^C′. Here, we considered varying numbers of components l′∈{1,…,20} to be able to propose several candidates for C (step 2 in Table ).

For all combinations j,k∈{1,…,10} and l′∈{1,…,20}, the EM algorithm explored 14 models, each corresponding to a different structure of the covariance matrix Σ, ranging from diagonal to fully parameterized. Diagonal matrices imply no interaction between phytoplankton groups, while off-diagonal terms capture inter-group correlations.

Model selection was guided by the Integrated Completed Likelihood (ICL) criterion , which penalizes model complexity and cluster overlap. First, optimal values of j, k and l′ were chosen by averaging ICL values across covariance structures. Then, the best covariance model was selected for parameter estimation. In addition to μ and Σ values, the EM algorithm estimated the α weights for ComA and ComB. Note that for Com^C′, only the μC′ and ΣC′ values were used. The weights of the candidates for ComC, αC, will be further estimated by the Bayesian model (see step 3 and 4 in Table ). The R package mclust was used to estimate the Gaussian parameters.

Since very few observations were collected in the frontal region (n=11), a Bayesian approach was used to estimate the weights of components λA, λB, λC, see Eq. (), and the sub components weights αC1,…, αCl, see Eq. (). Dirichlet distributions, which represent a distribution over probability distributions often used to model multivariate proportions, were used here to represent the component weights. These distributions were parameterized by a vector of positive real numbers and we proposed a non-informative prior, as follow: 7λA,λB,λC∼Dirichlet(1,1,1)8αC1,…,αCl∼Dirichlet(1,…,1), assigning the same weight to all coefficients. The Hierarchical Bayesian Model is decomposed in two steps. In the exploratory model (Step 3, Table ), the l′ candidate components identified in Com^C′ via EM were used to estimate their associated weights αC1,…,αCl′ in Eq. (). This step allowed to select only the most significant components among them, i.e. the l components with the highest posterior αC values, to define ComC. In the final model (Step 4, Table ), we estimated the weights of the components λA, λB, λC, see Eq. (), and the sub-components weights αC1,…,αCl, see Eq. (), with the selected l components in C.

A sensitivity analysis was performed to test the robustness of the Bayesian inference. In particular, the sensitivity analysis aimed at assessing the robustness of the model according to the number of observations in the front, and the robustness of the model to false positive detection (i.e. detecting a new community when no communities are present in the data). For this, numerical sampling of “known” frontal community were done in two cases. First, we considered the case where front observations are only a mixture of ComA and ComB (i.e. simulations do not include the component ComC, λC=0). Five scenarios were assessed : (1) λA=λB=0.5; (2) λA=0.4 and λB=0.6; (3) λA=0.6 and λB=0.4; (4) λA=0.7 and λB=0.3; (5) λA=0.3 and λB=0.7. Second, we considered the case where a new community exists, i.e. simulations include the component ComC, λC≠0. Here the λ values used are the same as observed in the in situ dataset (see the results Sect. 4.2), and with proportion λA=0.45 , λB=0.2 and λC=0.35. In all cases, 5, 10, 20, 30 and 50 frontal observations were simulated 10 times. Then the Bayesian model was computed to estimate the λ values of the known communities from the simulated datasets. In addition a comparison test for equal distribution between transitional waters T and front F was performed .

The posterior probability distribution sampling was computed with STAN's Hamiltonian Monte Carlo (HMC) algorithm. For all the models (i.e. exploratory and final models and sensitivity analysis) we performed four chains of 11 000 iterations to study the convergence. The first 10 000 draws of each chain were discarded (i.e. burn-in) to avoid initial sample bias. Thus, the last 1000 iterations of the four chains were used for analysis of the posterior probability distribution. Convergence was assessed with R^ statistic and effective sample size. The models were computed in R by means of the rstan package as interface with STAN .

According to the mean ICL criterion, one component, A1, is enough to model ComA (Fig. a), while two components (hereafter B1 and B2) are necessary to model ComB (Fig. b). The weights of B1 and B2 are, respectively αB1=0.47 and αB2=0.53. In the outside dataset, 12 candidates components were selected (Fig. c).

Figure  shows that the estimated parameters of the multivariate Gaussian fitted well to the observed phytoplankton biomass in water mass A (Fig. a) and water mass B (Fig. b). The mixture of two components in ComB allows to model complex biomass distributions, for e.g. skewed distribution for Crypto, Pico1, Pico3, SNano, RNano or PicoHFLR, compared with ComA.

The exploratory model was performed with 12 candidates components, denoted C′ as they were estimated from the outside dataset community, to describe ComC (see step 2 in Table ). Using the proposed candidates, the exploratory model (whose trajectories and values of R^ and effective sample size are consistent with those of a converged chain, see Fig.  and Table ) was used to estimate the weights αC and λA,λB and λC in the mixture (Fig. a and b). Among the three communities, ComC has a higher weight (λ) in the mixture (0.787, quantile 2.5 % = 0.123, quantile 97.5 % = 0.902), followed by ComA (0.203, quantile 2.5 % = 0.051, quantile 975 % = 0.459) and ComB (0.065, quantile 2.5 % = 0.002, quantile 97.5 % = 0.127) (Fig. a and Table ). Among the 12 candidates components in ComC (Fig. b), components C′8 and C′10 present the highest weight, α, approx. 0.2, and to a lesser extent C′5 and C′6 with weights reaching 0.1. The weights of the other 8 components are below 0.05 (see Table  for quantiles values of the posterior distribution for each components). For the final model, performed with the most significant components, only C′8 and C′10 were used in ComC as they display the highest weight. We considered C′8 and C′10, the most significant components in the exploratory model, as the two components of the community C, ComC, which we call hereafter C1 and C2, respectively. The number of components in ComC was chosen to be the most parsimonious possible. For the sake of simplicity, the components C′5 and C′6 were not used in the final model as they did not show strong differences relative to using only C′8 and C′10 in ComC.

In the final model (that converged, see Fig.  for the trajectories, and Table  for convergence metrics), the estimations of λA,λB and λC did not vary drastically – 0.203 (quantile 2.5 % = 0.057, quantile 97.5 % = 0.467) for ComA, 0.06 (quantile 2.5 % = 0.003, quantile 97.5 % = 0.281) for ComB and 0.714 (quantile 2.5 % = 0.439, quantile 97.5 % = 0.901) for ComC, Fig. c – relative to those observed before in the model with 12 components. In this second model, the weights of C1 (αC1=0.55, quantile 2.5 % = 0.258, quantile 97.5 % = 0.823) and C2 (αC2=0.45, quantile 2.5 % = 0.177, quantile 97.5 % = 0.742) were almost equivalent in the mixture (Fig. d and Table ).

Figure  shows how the final model fits the observed data in the front. As expected when looking at the weight λB (0.06, see in Fig. c), components B1 (dark blue curve) and B2 (light blue curve) contribute little to the global mixture (black lines), which is mostly driven by components A1 (light green curve), C1 (dark orange curve), and C2 (orange curve). Overall, the mixture of these five components captures the phytoplankton groups biomass distribution well. In some cases, the biomass distribution is bimodal (for Syne, Pico2, RNano) or skewed (for Pico1, Micro). For Pico3 and RNano a difference remained between the estimated density and the observed biomass in the front (Fig. ). For Pico3, the μ values for C1 and C2 are the lowest (see Table ). However due to high variance in Σ matrices the mode around 0.14–0.16 is not captured by the model.

The parameters of the multivariate Gaussian estimated by the EM algorithm are referenced in Table  for μ parameters and in Tables – for Σ covariance matrices. The μ values and the variances in the diagonal of the Σ matrices of SNano, RNano and Pico3 are the highest. These results highlight the dominance and a large variability in biomass of these phytoplankton groups during the cruise.

In ComB, the covariance matrices ΣB1 and ΣB2 are diagonal. This suggests that the addition of interactions between phytoplankton groups would not have improved the modeling of ComB. By contrast, for ComA and ComC, the covariance matrices is not diagonal which allow to model positive or negative interactions between each phytoplankton group. The covariances matrices ΣC1 and ΣC2 present similar patterns and highlight mostly the positive interactions of SNano and RNano with most of the phytoplankton groups, except for Pico3. In these two communities Pico3 and Pico2 have a negative interaction. ΣA1 presents similar pattern than in ΣC1 and ΣC2, but the main differences are negative interactions of Syne and Crypto with SNano, RNano, Micro and PicoHFLR, and strong interactions between Pico3 and Crypto (positive) and PicoHFLR (negative).

Overall, the relative biomass (i.e. calculated from μ and α values) of the phytoplankton groups of ComC is intermediate between ComA and ComB. However, RNano and Pico3 in ComC show a relative biomass that is higher and lower, respectively than in ComA and ComB (Fig. a). This pattern is clearly observed when looking at the relative biomass at the sub-component scale (Fig. b). Where the relative biomass in C1 and C2 for RNano and Pico3 are, respectively higher and lower than in the other three components.Nevertheless, Fig. b, shows that two sub-components of the same community show different patterns for the same phytoplankton group. This is the case of C1 and C2 for Syne, which reach their lowest and highest relative biomass, respectively for these components.

Figure  shows the results of the sensitivity analysis performed on simulated data. The posterior distribution obtained from the Bayesian inference showed satisfactory mean estimation of the unknown parameters, leading to close estimates compared to the true values independently of the number of simulated observations. Note that while the average values of the posterior distributions of estimated parameters are reliable even for the lowest number of observations, increasing the number of simulated data lead to a decrease in the standard deviation of the posterior distribution (see in Fig. ). In the case that the simulated data is only coming from a mixture of components ComA and ComB (λC=0), the sensitivity test shows that the estimated values of λC are very close to 0, meaning that this component is not important in the mixture (comparing to the cases where λ≠0) (Fig. ). In addition, the model can detect slight changes in the proportions of components even in the case that the simulated data is coming from a mixture of the three components ComA, ComB and ComC. Overall, the sensitivity analysis highlighted the robustness of the approach, even with fewer observations than the actual number of observations in the in situ data. Finally, the comparison test for equal distribution between transitional waters and front rejected the H0 hypothesis (H0:T=dF, p value < 0.05), which suggests that frontal and transitional water communities are different.

We developed a statistical approach to address key challenges in detecting and confirming fine-scale frontal-adapted phytoplankton communities, despite the limited and highly variable data from an oceanographic campaign. We represented the phytoplankton biomass distribution across and within a frontal region – reflecting the phytoplankton community composition – using a multivariate Gaussian mixture of distinct sub-communities. The critical objective was to determine which community and sub-community has the highest weight within the front. Here, we combined two approaches, Expectation–Maximization (EM) algorithm and Bayesian modelling, to characterize the nature of frontal phytoplankton communities from sparse in situ data. The EM algorithm allowed us to estimate parameters (μ and Σ) of Gaussian distributions and identify the number of communities and sub-communities (from relatively large datasets), while the Bayesian approach, known to be robust even with few observations, enabled us to determine their relative weights (λ and α) within the frontal community. Sensitivity analysis (Fig. ) confirmed that the Bayesian inference was robust even for fewer observation (here down to 5) than the actual in situ frontal dataset (i.e. 11 observations).

The parameters μ (average biomass) and Σ (variance and covariance) provided a realistic overview of the phytoplankton community composition (PCC), highlighting the global dominance of two nanophytoplankton groups (SNano, RNano) and the largest picoeukaryote (Pico3), as well as the interactions between these groups that shape specific PCC (Tables , , , and ). In the Mediterranean Sea, Synechococcus species (Syne) are the most dominant group of phytoplankton in abundance . However, certain physical forcings, such as frontal structuring, may alter their presence by locally modifying environmental conditions (e.g., nutrient inputs), which can favor larger cells . In frontal zones, different types of interactions between plankton organisms, such as shading or shared predation, can lead to distinct community structures . Notably, the differences observed between the covariance matrices (i.e. ΣA1, ΣC1, and ΣC2) suggest that interactions between phytoplankton are different within distinct communities (Tables , , and ). Estimated values of parameters λ corresponding to the weight of communities within the front and its adjacent water masses provided information to answer our questions: “What is the structure of the community that might be formed at the front? Is the frontal community a mixture, where the expected community results from the combination of the adjacent water communities, or is there another community resulting from intrinsic frontal characteristics?”. In particular, λC (0.714 in the final model, Fig. c) represents the proportion of the frontal community attributed to ComC. Since λC>0, our results suggest that the phytoplankton frontal community is not a mixture of adjacent communities, but instead is a specific frontal-adapted community. More precisely, λC indicates that ComC represents more than 70 % of the frontal community ComF (Fig. c).

Figure  shows the spatial projection of each sample point, with shapes and colors representing their community and sub-community classification, identified as the dominant component and sub-component of the Gaussian mixtures (highest λ and α). We reach two key conclusions. First, our approach successfully reconstructed the initial pattern observed by , characterized by a distribution of two communities on either side of the frontal region (here identified as ComA and ComB). A notable refinement was the identification of two sub-communities within ComB (B1 and B2), which could be attributed to significant fine-scale meandering activity in the southern part of the front (i.e., within the Algerian Basin) . We hypothesize that such dynamics could lead to a closer cohabitation of different sub-communities. Second, our approach appeared to successfully detect the presence of the unknown ComC located within the frontal community (ComF).

Our findings suggest that the frontal region acted as a selective environment, structuring phytoplankton communities by promoting certain phytoplankton groups while disadvantaging others (Fig. ). According to our results, the frontal zone during PROTEVSMED-SWOT represented a narrow habitat for communities C1 and C2.

described the impact of frontal responses of plankton groups using the terms “winners” and “losers”. In the Californian Current Ecosystem, larger phytoplankton (e.g., microphytoplankton, diatoms) were classified as “winners” (increased abundance within fronts) and smaller picophytoplankton as “losers” (decreased abundance within fronts). Taking into account the whole ComC, our result showed that RNano was clearly a “winner” and Pico3 was a “loser” within the front (Fig. ). However, at a smaller scale, we showed that even within a same community, phytoplankton assemblage were different. For example, this was the case of Synechococcus (Syne) that, respectively showed the lowest and highest μ values with C1 and C2 (Fig. b). This suggests that Syne can simultaneously be both “winner” and “loser”, depending on local conditions. This pattern may result from differences in the origins of C1 and C2 communities, driven by advection or stirring of distinct water masses, or from biological interactions that either favored or hindered Syne . highlighted that different plankton communities can be observed at a smaller scale (1–5 km) than the width of the front scale (10–30 km).

The strong assumption that the potential front-adapted community existed within the outside dataset implies two limitations. On the one hand, the outside dataset is not an exhaustive dataset of the region. Actually, phytoplankton communities of the southern water masses may not be efficiently represented in the outside dataset, since the water masses off the Algerian coast (south of the sampling area) were not sampled. In addition, the inclusion of the stations close to the Balearic coasts might have led to an over-representation of coastal phytoplankton communities (different than the one observed in the open sea). But excluding coastal stations and selecting only data near the NS-Hippodrome transect (e.g., between 38–39° N and 3–5° E) did not drastically affect our results. On the other hand, frontal conditions could be unique in both space and time and might have not been sampled elsewhere than in the NS-Hippodrome transect. Actually, the communities identified in ComC, C1 and C2, were mostly observed in stations in the same range of temperature and salinity that were close to the studied front, to the east, and were sampled a few days before the NS-Hippodrome transect sampling (Fig. ). Hydrodynamic circulation across the frontal area was eastward . This suggests that the communities observed at these sites in the outside dataset may have been advected from the front.

As Fig.  shows, our approach may not precisely capture the biomass distribution of certain phytoplankton groups (e.g. Pico3 and RNano). This is certainly because no biomass distributions that better fit the frontal data were observed in the “outside” dataset for these two groups. A more flexible option would be to estimate all parameters using a full Bayesian approach (i.e. the number of Gaussian components, μ, α, Σ and λ). However, as the number of parameters to be estimated far exceeded the actual number of observations at the front (number of observations = 11; number of parameters = 458), we opted to “fix” certain parameters (i.e. μ and Σ) using existing data (adjacent water masses and outside dataset). Nevertheless, the sensitivity analysis demonstrated the robustness of our approach, showing that the new components C1 and C2 in ComC helped to model the community in the front more accurately, revealing the existence of a new frontal community.