# Performance of a multimetric index based on phytoplankton to evaluate the ecological quality of French large rivers: The IPHYGE index

Albin Meyer, Emilie Prygiel, Christophe Laplace-Treyture

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## To cite this version:

Albin Meyer, Emilie Prygiel, Christophe Laplace-Treyture. Performance of a multimetric index based on phytoplankton to evaluate the ecological quality of French large rivers: The IPHYGE index. Ecological Indicators, 2024, 166, pp.112303. 10.1016/j.ecolind.2024.112303. hal-04789085

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Submitted on 18 Nov 2024

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# Performance of a multimetric index based on phytoplankton to evaluate the ecological quality of French large rivers: The IPHYGE index

Albin Meyer<sup>a, c, *</sup>, Emilie Prygiel<sup>b</sup>, Christophe Laplace-Treyture<sup>a, c, *</sup>

## ARTICLE INFO

**Keywords:**
Trophic indices
Eutrophication
WFD
Chlorophyll a

## ABSTRACT

Large rivers around the world are impacted by human activities. Such activities can lead to the eutrophication of these water bodies, and consequently to potentially harmful algal blooms. In this study, we describe the development of a phytoplankton-based multimetric index used for the biomonitoring of the ecological quality of large rivers located in metropolitan France, as advocated by the European Water Framework Directive. Using a dataset containing phytoplanktonic surveys sampled over the 2010–2021 period for a total of 963 station-years, we calculated biomass-based and trophic metrics. We then selected the best biomass-based metric and several trophic metrics based on their ability to highlight situations impaired by eutrophication and/or algal blooms and well correlated to pressure gradients (i.e. using coefficients of determination). The best biomass-based metric was calculated from both the seasonal average and maximal concentrations of chlorophyll-a. Three trophic metrics, created using the Weighted Average – Partial Least-Squares method, were included in the multimetric index. Each metric is correlated with one parameter of interest, namely with total phosphorus, Kjeldahl nitrogen and nitrates. The values of the biomass metric and the three trophic metrics were aggregated to calculate the final value of the IPHYGE index (“Indice Phytoplancton pour les Grands cours d’Eau”; phytoplankton index for large rivers) in order to obtain the best relationship with the eutrophication pressure. Ecological quality classes derived from the index values were well related to gradients of parameters linked to eutrophication, for example total phosphorus and nitrogen compounds.

## 1. Introduction

Large rivers around the world are impacted by human activities, such as navigation, alteration of their hydromorphology (damming, channelization) and chemical pollution (Nilsson, 2005). Furthermore, they are integrative and representative of the anthropogenic activities located in their watershed (Carone et al., 2009). In the last decades (more than 20 years) many restoration works have been set up in order to reduce and/or reverse the impacts of such activities on the normal functioning of large rivers and their ecosystems (Buijse et al., 2005; Meyer et al., 2021a). The integral part of restoration process is dependent on monitoring tools allowing for the evaluation of the ecological status of large rivers, especially in order to identify whether or not such rivers are impacted by anthropogenic activities and, if needed, which ones.

In Europe, the Water Framework Directive (WFD) provides a legal framework ensuring that water bodies found in Europe reach a good ecological quality class (European Council, 2000). The ecological status is defined through the use of hydromorphological and physicochemical indicators and through the use of biotic indices (e.g., Hering et al., 2006), based on pertinent biological components, depending on the type of water bodies. For rivers, these biological components (also known as biological quality elements in the WFD) are fishes (e.g., Pont et al., 2007), benthic macroinvertebrates (e.g., Mondy et al., 2012; Meyer et al., 2020), benthic diatoms (e.g., Coste et al., 2007), macrophytes (e.g., Haury et al., 2006) and phytoplankton (e.g., Borics et al., 2007; Mischke et al., 2011).

Phytoplankton communities are known to respond to physical and chemical environmental factors (Pathak et al., 2021). Such responses can be used for the development of phytoplankton-based indices. Among

<footnote><sup>a</sup> INRAE, UR EABX, F-33612 Cestas, France</footnote>

<footnote><sup>b</sup> Cerema, ER TEAM, F-02100 Saint-Quentin, France</footnote>

<footnote><sup>c</sup> Pôle R&D ECLA Ecosystemes Lacustres, France</footnote>

<footnote>* Corresponding authors.
E-mail addresses: albmey@hotmail.com (A. Meyer), christophe.laplace-treyture@inrae.fr (C. Laplace-Treyture).</footnote>
these responses, phytoplankton is usually used as a good bioindicator of eutrophication. Phytoplankton biomass are driven by many environmental factors, among them nutrient concentrations (such as phosphorus and nitrogen), water temperature and water residence time (Giblin and Gerrish, 2020; Pathak et al., 2021). Eutrophic conditions can lead to the development of algal blooms, which can be harmful if the blooming species (e.g., Cyanobacteria) release toxins in the environment (Graham et al., 2020).

Thus, phytoplankton-based bioindication methods are usually used to indicate algal blooms and eutrophication conditions (driven by total phosphorus), for either lakes or large rivers (Phillips et al., 2012, 2013; Mischke et al., 2016). In order to highlight such conditions, the methods are frequently based on multimetric indices, usually coupling one or two biomass-based metrics with one or multiple other metrics (e.g., Wu et al., 2014).

Usually, the biomass-based metrics are calculated from chlorophyll-a concentrations (frequently log-transformed), but they can also be calculated from total abundance or biovolume (e.g., Mischke et al., 2016). The main objective of such a metric is to highlight potential algal blooms. Concentrations of chlorophyll-a are also frequently and highly correlated to nutrient concentrations in the water (Stow and Cha, 2013; Canfield et al., 2019).

The other metrics can be of various types:

(i) they can be based on Zelinka and Marvan's formula (Zelinka and Marvan, 1961), i.e. an average of the trophic scores of specific taxa present in a given phytoplankton community, double-weighted by their abundance (or their biovolume) and by another weighting factor, frequently indicating, for example, their ecological valence towards the trophic score. For large rivers, such a metric can be found for the German PhytoFluss method (i.e. the Type-specific Index Potamoplankton metric; Mischke et al., 2011) and Polish IFPL method (Indeksu Fito-planktonowego; Picińska-Faltynowicz and Blachuta, 2012). For lakes, such a metric is used in France (Indice Phytoplancton Lacustre [IPLAC]; Laplace-Treyture and Feret, 2016), in Austria (the Brettum index; Brettum, 1989; Wolfram et al., 2014), in Germany (the Phytoplankton-Taxa-Seen-Index, Mischke et al., 2008) and in Italy (the Phytoplankton Trophic Index; see Phillips et al., 2013);

(ii) they can be based on the phytoplankton community structure, highlighting the diversity, richness and/or relative importance of the whole community or of relevant bioindicative taxonomic groups, such as Bacillariophyceae, Cyanobacteria or Chlorophyceae (e.g., the Romanian method, as described in Mischke et al., 2016; the Portuguese method, Penha et al., 2021; the Czech method, Opatřilová et al., 2011);

(iii) they can be based on the phytoplankton taxa traits. For example, the Hungarian method (Hungarian River Phytoplankton Index; Borics et al., 2007) includes a metric based on functional groups, the metric Q. Using Reynolds et al. (2002) as a basis, Borics et al. (2007) further identified functional groups of phytoplankton species. The Q metric is the biovolume-weighted average of each group score, which shows if their presences were indicative of desirable conditions (oligotrophic, lotic conditions, among others).

In this study we describe the development of a phytoplankton-based index for the biomonitoring of French continental natural large rivers. Until now, no such method was available for French large rivers. Its development was constrained by the WFD. Namely, the inclusion of a biomass-based metric in the index was required. We chose to develop a multimetric index, combining both a biomass-based metric and trophic metrics, in order to (i) obtain an index whose values would reflect the main anthropogenic pressures impacting the phytoplankton communities (mainly eutrophication), and (ii) increase the robustness of the

developed index (Wu et al., 2014; Vadas et al., 2022).

For the biomass-based metric we explored how using either total biovolume or concentrations of chlorophyll-a, as a basis for its value, would allow for a better modeling of the anthropogenic pressures impacting phytoplankton communities. In addition, we opted to develop several trophic metrics, based on Zelinka and Marvan's formula (1961), as it was shown that it could be used to develop robust and efficient methods for highlighting anthropogenic pressures (e.g., Haury et al., 2006; Mischke et al., 2011).

## 2. Material and methods

### 2.1. Dataset

In order to develop this new index we first created a dataset compiling the results of the routine monitoring over the period 2010–2021 of the phytoplankton communities found in French natural or heavily modified large rivers, belonging to 28 different French river types (Wasson et al., 2002, 2006). Data from heavily-modified large rivers were included in our study in order to improve the description of the gradient of eutrophication observed in French large rivers, as it allowed us to include in our dataset several rivers with higher trophic levels (mainly total phosphorus concentrations). Phytoplankton sampling and identification followed a standard adapted for the monitoring of large rivers (Laplace-Treyture et al., 2010). All sampling events occurred during the growing season, i.e. between March and October. Although the sampling standard indicates that six samplings should be performed per year for a given station, the yearly sampling frequency varied a lot between stations due to variations of regional management. Frequencies varied between 4 and 17 sampling events per year (mean = 6.1 sampling events). Nevertheless, we kept all these sampling events in our development dataset in order to conserve a relatively good national coverage of all river types found in France (Wasson et al., 2002, 2006) (Fig. 1).

Phytoplanktonic data were complemented with water physical and chemical data (Fig. 2). Concentration values were retrieved for 198 parameters from the national and open French database compiling all routine water quality monitoring (Naïades; accessed in 2022; https://naïades.eaufrance.fr/). Two different datasets were created from these data: the first dataset containing the average concentrations of each parameter over the seven days preceding each sampling events (hypothesizing that the most recent conditions would be best linked with the observed phytoplanktonic communities; e.g., Crossetti et al., 2013), and the second dataset containing the yearly average values for each station-year.

We used the yearly dataset to describe the anthropogenic pressures and their impacts on the monitored stations, following a procedure described in Alric et al. (2021). We described impact levels for a total of 11 pressure categories related to water quality: "Acidification", "Poly-cyclic Aromatic Hydrocarbons", "Suspended particles", "Nitrates", "Nitrogen compounds (except Nitrates)", "PolyChlorinated Biphenyls", "Organic matter", "Phosphorous compounds", "Mineral micro-pollutants", "Organic micropollutants" and "Pesticides". We used the "One out, All out" approach to assign to a given pressure category the worst chemical quality class allocated by its individual parameters. From worst to best, chemical quality classes were either "Bad", "Poor", "Moderate", "Good" or "High", and they were defined by using concentration thresholds used in the French water quality assessment system and specific to each parameter (SEQ-Eau Version 2; Oudin and Maupas, 2003).

In order to also investigate the ability of the developed method to highlight algal blooms, we described an additional and simplified "pressure category" called "Bloom". This "Bloom" pressure category used a simple characterization approach: if for a given station-year at least one bloom has been observed during the year, the station-year has been considered "impaired" by blooms. Such an information was not
<figure><img src="image_4.png" /><figcaption>Fig. 1. Location of the sampled stations in France (one station = one dot; N = 160). Reference stations, which exhibited least disturbed conditions, are colored in green, whereas the other stations are in red. Blue lines indicate the main rivers.</figcaption></figure>

available for all station-years in our dataset and impaired station-years remained limited (only N = 38 station-years “impaired” by blooms).

The final dataset was split in two datasets: the first one, containing all data acquired from 2010 to 2019, for a total of 963 station-years, was used for the development of the method, whereas the second dataset, containing 168 station-years monitored in 2020 and 2021, was used to validate the performances of the metrics and of the developed index. The development dataset thus comprised phytoplanktonic data for 160 sampling stations, for a total of 6283 sampling events.

## 2.2. Least disturbed conditions

As stated in the WFD, the ecological status of monitored rivers has to be defined in a comparison with reference conditions (European Council, 2000). Real reference conditions are rare for large rivers, as they are integrative of the anthropogenic pressures observed at the watershed scale. We thus chose to identify station-years with the least disturbed conditions (Least Impaired River Reaches = LIRR; e.g., Statzner et al., 2005), based on the described levels of anthropogenic pressures.

Preliminary analyses of the response of chlorophyll-a concentrations to pressure levels (Fig. A.1 and Table A.1 in the Supplementary data) allowed us to highlight that concentrations of chlorophyll-a mainly (and quite expectedly) responded to pressure categories linked to eutrophication, i.e. for “Nitrates”, “Nitrogen compounds (except Nitrates)”, “Organic matter”, and “Phosphorous compounds”. Moreover, these pressure categories were available for the entirety of our dataset (i.e. for all station-years), whereas other pressure categories were, sometimes, not accessible: for the other seven pressure categories, data availability

varied between 44.0 and 100.0 %, with a mean equal to 75.6 % (Fig. A.1 in the Supplementary data). Consequently, we decided to identify the LIRR based on the four pressure categories linked to eutrophication, using the following criterion: a LIRR should exhibit at least three such pressure categories with “High” chemical quality classes, with the remaining one being at least in a “Good” chemical quality class, i.e. with low to no impact for all four pressure categories. We selected this criterion to be both sufficiently severe, while still keeping a relatively good distribution of LIRR situations at the national scale. All remaining station-years which would not verify this criterion had been considered as Impaired River Reaches (IRR). We identified 82 LIRR and 881 IRR. The locations and “reference” status of all stations can be seen on Fig. 1.

## 2.3. Combined Stressor index

In additions to the other chemical parameters, we also chose to calculate a synthetic stressor index, a Combined Stressor Index (CSI), which has been developed for the inter-comparison of European phytoplankton-based methods for large rivers (Mischke et al., 2016). Mischke et al. (2016) used boosted regression tree models in order to identify the main chemical drivers of concentrations of chlorophyll-a measured in European large rivers. Three parameters were thus identified: total phosphorus, total nitrogen and log₁₀-transformed chlorides. The Combined Stressor Index (Eq. (1)) is equal to the sum of the normalized yearly average of the concentrations of these three parameters:

$$ \text{CSI} = \text{TP}_{\text{norm}} + \text{TN}_{\text{norm}} + \text{CL}_{\text{norm}} \quad (1) $$
<figure><img src="image_5.png" /><figcaption>Fig. 2. Synthesis of the main workflow followed for the development of the IPHYGE. occ. — occurrences, LIRR — Least Impaired River Reaches (i.e. reference conditions), IRR — Impaired River Reaches, TP — total phosphorus, NKJ — Kjeldahl nitrogen.</figcaption></figure>

Normalized values were obtained by dividing the concentrations of each parameter by the “worst” value (actually the 90th percentile) observed in the dataset used for the European intercalibration exercise. Worst values were equal to 0.194 mg/L(P), 5.000 mg/L(N) and 2.870 for respectively total phosphorus, total nitrogen and log₁₀-transformed chlorides. After this normalization step, values higher than 1 were made equal to 1. CSI values were thus comprised in between 0 and 3.

For the development of the biomass metrics, we chose to also work with a second version of the CSI adapted to the French dataset (CSI<sub>FR</sub>). Indeed, the first version of the CSI, presented above, did not allow for a good description of the pressure gradients as observed in our stations, especially for total nitrogen (truncated distributions of the normalized values were observed) (Meyer et al., 2021b, 2023). Therefore, we decided (i) to replace total nitrogen with Kjeldahl nitrogen in the formula, as we observed that this parameter was a better driver of chlorophyll-a concentrations (Table A.1 in the Supplementary data), and (ii) to use the 95th percentile of the distribution of the concentrations of each parameter in our dataset as “worst” values. The formula for the “French” version of the CSI is the following one (Eq. (2)):

$$ \text{CSI}_{\text{FR}} = \text{TP}_{\text{norm}} + \text{NKJ}_{\text{norm}} + \text{CL}_{\text{norm}} \quad (2) $$

Worst values were equal to 0.246 mg/L(P), 1.303 mg/L(N) and 1.969 for respectively total phosphorus, Kjeldahl nitrogen and log₁₀-transformed chlorides.

## 2.4. Biomass metrics

Biomass metrics (BM) are simple metrics whose values are derived

from biomass proxies, either total biovolumes or chlorophyll-a concentrations (Eq. (3)). We chose to work with simple linear transformations, using either or both the seasonal average and maximal values of the proxies:

$$ \text{BM} = a_1 \cdot \log(\text{proxy}) + b \quad (3a) $$

$$ \text{BM} = a_1 \cdot \log(\max(\text{proxy})) + b \quad (3b) $$

$$ \text{BM} = a_1 \cdot \log(\text{proxy}) + a_2 \cdot \log(\max(\text{proxy})) + b \quad (3c) $$

with proxy the seasonal average value of total biovolumes or concentrations of chlorophyll-a, max(proxy) its maximal value over the growing season period, a₁ and a₂ the slope coefficients, and b the intercept. Formula parameters a₁, a₂ and b were determined by using results from (multiple) linear regressions between the proxy values and CSI<sub>FR</sub>. Proxy values and their maximal values were log-transformed as it allowed for a better model of CSI<sub>FR</sub> values. Using all three described equations and both biomass proxies allowed us to generate six different biomass metrics.

## 2.5. Trophic metrics

We calculated trophic metrics for three nutrient parameters of interest, namely total phosphorus, Kjeldahl nitrogen and nitrates (Fig. 2). We used Zelinka and Marvan's formula (1961) as a basis for calculations of all trophic metrics (TM; Eq. (4)):

$$ \text{TM}_s = \frac{\sum_i (\text{TS}_i \times \text{SC}_i \times \text{BV}_{i,s})}{\sum_i (\text{SC}_i \times \text{BV}_{i,s})} \quad (4) $$
with TM_s the value of a trophic metric for a given sampling event s, TS_i the trophic score of taxon i, SC_i a weighting factor for taxon i (here, SC for stenoecy coefficient) and BV_{i,s} the biovolume of taxon i for the same sampling event s.

The stenoecy coefficients (SC_i) were equal to the inverse of the square-root of the unbiased weighted variance of a given taxon i for a given parameter (Eq. (5)):

$$SC_i = 1/\sigma_i \qquad (5)$$

The unbiased weighted variance of a given taxon i ($\sigma_i^2$) for a given nutrient parameter x was calculated using the following formula (Eq. (6)):

$$\sigma_i^2 = \frac{\sum BV_{i,s}}{\left(\sum BV_{i,s}\right)^2 - \sum BV_{i,s}^2} \times \sum BV_{i,s} \times (x_{i,s} - \mu)^2 \qquad (6)$$

with BV_{i,s} the biovolume of taxon i in the stations where it can be observed, x_{i,s} the concentration of nutrient parameter x in the stations where taxon i can be observed, and μ the biovolumes-weighted average of the concentrations of nutrient parameter x in the stations where taxon i can be observed.

SC_i values were transformed in order to be expressed in a scale ranging from 0 (for euryecious taxa) to 3 (stenoeicious taxa), in order to stay coherent with other French methods using trophic metrics (e.g., Lenoir and Coste, 1996; Haury et al., 2006; Coste et al., 2007; Laplace-Treyture and Feret, 2016).

We explored how different ways of calculating the trophic scores of the taxa (TS_i) would influence the performances of the different trophic metrics. Namely, we explored the following two methods of calculations, for a given nutrient parameter of interest:

(i) using the weighted average of the concentrations of the nutrient parameter in the stations where taxa can be observed (ter Braak and van Dam, 1989);

(ii) using the WA-PLS method (Weighted Averaging Partial Least-Squares regression), described by ter Braak and Juggins in 1993, and more recently used by Liu et al. in 2020 (also see Pajunen et al., 2016). The standard approach using weighted averaging (ter Braak and van Dam, 1989) can lead to a compression of the distribution of the calculated trophic metric values in the middle of the observed range of concentrations of the nutrient parameter (Liu et al., 2020). The WA-PLS method tries to overcome such a limitation by iterating over the trophic scores of all taxa in order to better generate a distribution of trophic metric values similar to the observed one. The WA-PLS generates successive and iterative components allowing for a refinement of the trophic scores of the taxa by using the model residuals of the previous step. Nevertheless, such a method can lead to overfitting to the peculiarities of the training dataset and thus to low performances for the test dataset. Thus, a cross-validation step allows for the identification of the optimal number of components (ter Braak and Juggins, 1993).

Trophic scores (TS_i) were actually calculated from two different datasets: one with biovolumes at the species level (excluding rare taxa, with less than 5 occurrences) and another one with biovolumes aggregated at the genus level (also excluding rare taxa, with less than 20 occurrences) (Fig. 2). Occurrence thresholds were defined in order to avoid rare taxa resulting of misidentifications and to obtain more robust data as done in other indices (Coste et al., 2009; Marchetto et al., 2009; Laplace-Treyture and Feret, 2016). Moreover, we also explored if calculating the trophic scores at the sample scale (i.e. using all concentrations and biovolumes measured for all sampling events) or at the station-year scale (i.e. using yearly average of concentrations and biovolumes) would influence the performances of the trophic metrics. Last, we also tested if using the trophic scores obtained at the station-year

scale (instead of the corresponding one obtained at the sample scale) would improve the performances of the trophic metrics calculated at the sample scale.

## 2.6. Ecological quality ratio

As constrained by the WFD, the values of the metrics (i.e. biomass and trophic ones) were expressed as Ecological Quality Ratio (EQR), i.e. their values were expressed as a ratio of values observed in reference conditions (here, least disturbed conditions). We used the following formula (Eq. (7)) to express all metric values as EQR:

$$MET_{EQR,m} = (MET_{OBS,m} - worst_m)/(best_m - worst_m) \qquad (7)$$

with MET_{EQR,m} the value of the metric m expressed as EQR and MET_{OBS,m} its original value. For a given metric m, the parameter worst_m corresponds to either the maximal (for the biomass metrics) or the minimal (for the trophic metrics) observed value in the entire dataset. The best_m values were calculated from the distribution of the metric values in the least disturbed conditions (the LIRR). The best_m values were defined as the value of either the 3rd quartile (for the biomass metrics) or the 1st quartile (for the trophic metrics) of the distribution of the values of the metric m in the LIRR.

## 2.7. Metric performances

In order to identify the best biomass and trophic metrics, we evaluated their link with the concentrations or values of multiple parameters of interest, namely the concentrations of total phosphorus, Kjeldahl nitrogen, nitrates, and chlorides, and the CSI values in its European version. We performed linear regressions between the EQR values of the metrics and the concentrations/values of the parameters of interest. Adjusted R² obtained with the linear models were used to sort the metrics.

We also checked the ability of each metric to discriminate between the LIRR and the IRR by the four pressure categories linked to eutrophication and the “Bloom” pressure category. Thus, we calculated discrimination efficiencies (DE) for each of these pressure categories. For a given metric and a given pressure category, the DE value is the proportion of station-years impaired by this specific pressure category (i. e. with a chemical quality class either “Moderate”, “Poor” or “Bad”) and which exhibited values lower than the first quartile of the distribution of the given metric in the LIRR.

## 2.8. The IPHYGE index

The final value of the IPHYGE index is the weighted average of the values of four chosen metrics: one biomass-based metric and three trophic metrics, one per parameter of interest (i.e. total phosphorus, Kjeldahl nitrogen and nitrates). Those metrics were selected based on their performances for the station-years included in the development dataset (cf. previous section). We used the following equation (Eq. (8)):

$$IPHYGE = (w_1 \times BM + w_2 \times TM_{TP} + w_3 \times TM_{KN} + w_4 \times TM_N)/(w_1 + w_2 + w_3 + w_4) \qquad (8)$$

with w_1, w_2, w_3 and w_4 the weights of the four metrics, and BM, TM_{TP}, TM_{KN} and TM_N the values expressed as EQR of, respectively, the biomass-based metric (BM) and the trophic metrics related to total phosphorus (TM_{TP}), Kjeldahl nitrogen (TM_{KN}) and nitrates (TM_N).

We tested three different weighting sets, and thus three different potential indices. The first weighting set was characterized by an equal weight for all four metrics (w_1 = w_2 = w_3 = w_4 = 1). The second weighting set was characterized by a lower weight (w_1 = 0.5 instead of 1) for the biomass-based metric, as the development of this metric highlighted that the metric performances could be lower than the ones of the trophic metrics. The third and last weighting set was characterized
by both a lower weight for the biomass-based metric and by a higher weight ($w_2 = 2$ instead of 1) for the trophic metric modeling total phosphorus, as this parameter was deemed to be the main driver of phytoplankton communities.

## 2.9. Ecological quality classes

In order to assign an ecological quality class (among the five ecological quality classes used in the WFD, i.e. “Bad”, “Poor”, “Moderate”, “Good” and “High”) to each station-year, we defined boundary values based on the distribution of the IPHYGE in the LIRR. The selected way to calculate the boundary values is presented in Fig. 3. We firstly defined the Good-Moderate boundary value as the first quartile of the IPHYGE distribution in the LIRR, before dividing both remaining range of values in order to obtain the other boundary values: the range of values comprised between the Good-Moderate boundary value and 1 was equally divided in two in order to obtain the High-Good boundary value, whereas the range of values comprised between the Good-Moderate boundary value and 0 was equally divided in three in order to obtain both the Moderate-Poor and Poor-Bad boundary values.

<figure><img src="image_6.png" /><figcaption>Fig. 3. Boxplots of the distribution of the IPHYGE in Impaired River Reaches (IRR) and in the Least Impaired River Reaches (LIRR). Boundary values were defined based on the distribution of the IPHYGE in the LIRR. Each boxplot represents the minimum/Q25/median/Q75/maximum values, respectively. Outliers (open circles) are outside the 1.5 interquartile range of the corresponding IPHYGE distribution. H = High, G = Good, M = Moderate, P = Poor and B = Bad. N = 963 station-years, with 881 IRR and 82 LIRR.</figcaption></figure>

### Table 1

Performances of the biomass-based metrics (BM). Metric values were either based on chlorophyll-a concentrations ([chlo-a]) or total biovolume as proxies of the phytoplanktonic biomass, and they were calculated by using either or both the seasonal average (avg) or maximal (max) values. $DE_{avg}$ = mean discrimination efficiency for four pressure categories linked to eutrophication and the “Bloom” pressure category (cf. §2.1.). CSI = Combined Stressor Index (cf. §2.3.). In bold are the results of the best biomass metric.

<table><thead><tr><th rowspan="2">Code</th><th rowspan="2">Biomass proxy</th><th rowspan="2">Formula</th><th rowspan="2">DE<sub>avg</sub></th><th colspan="5">Adjusted R<sup>2</sup></th></tr><tr><th>Total phosphorus</th><th>Kjeldahl nitrogen</th><th>Nitrates</th><th>Chlorides</th><th>CSI</th></tr></thead><tbody><tr><td>BM1</td><td>[chlo-a]</td><td>avg</td><td>0.748</td><td>0.132</td><td>0.226</td><td>0.001</td><td>0.058</td><td>0.221</td></tr><tr><td>BM2</td><td>[chlo-a]</td><td>max</td><td>0.653</td><td>0.102</td><td>0.176</td><td>0.001</td><td>0.054</td><td>0.173</td></tr><tr><td>BM3</td><td>[chlo-a]</td><td>avg + max</td><td><strong>0.828</strong></td><td><strong>0.145</strong></td><td><strong>0.246</strong></td><td><strong>0.002</strong></td><td><strong>0.055</strong></td><td><strong>0.240</strong></td></tr><tr><td>BM4</td><td>Total biovolume</td><td>avg</td><td>0.725</td><td>0.089</td><td>0.155</td><td>-0.001</td><td>0.036</td><td>0.112</td></tr><tr><td>BM5</td><td>Total biovolume</td><td>max</td><td>0.565</td><td>0.076</td><td>0.136</td><td>-0.001</td><td>0.033</td><td>0.103</td></tr><tr><td>BM6</td><td>Total biovolume</td><td>avg + max</td><td>0.724</td><td>0.099</td><td>0.154</td><td>-0.001</td><td>0.045</td><td>0.121</td></tr></tbody></table>

## 2.10. Statistical analyses

All statistical analyses were performed with R (v.4.2.1; R Core Team, 2022). The following libraries were used to generate the trophic metrics: SDMTools (VanDerWal et al., 2019) and fxtWAPLS (Liu et al., 2020). Linear regressions were done using the function lm() in base R, and conditions of normality and homogeneity of variance were verified. Comparisons of value distributions, either between IPHYGE values and chemical quality classes, or between stressor values and IPHYGE ecological quality classes, were done with Kruskal-Wallis tests, followed by a post-hoc multiple comparison test (Conover's test) when significant, using the PMCMRplus package (Pohlert, 2022). For statistical significance, alpha was set at 0.05.

# 3. Results

## 3.1. Performances of the biomass-based metrics

Results of the linear regressions for the potential biomass-based metrics highlighted that the chlorophyll-a concentrations allowed for better modeling the values of all five parameters of interest, compared to total biovolumes (Table 1). The adjusted R² values for chlorophyll-a metrics were correct for Kjeldahl nitrogen and CSI, with values ranging between 0.173 (biomass-based metric BM2 vs CSI) and 0.246 (BM3 vs Kjeldahl nitrogen). Concerning total phosphorus, the performances of the chlorophyll-a metrics were lower, with adjusted R² values varying between 0.102 (BM2) and 0.145 (BM3). Whatever the proxy used for biomass, performances were null for nitrates and limited for chlorides, with adjusted R² values close to 0.05. Average DE values ranged from 0.565 (BM5) to 0.828 (BM3).

Overall, the best metric was BM3, which exhibited the highest adjusted R² values and the highest average DE (0.828) over all six tested metrics. Thus, we selected this metric as the first constituent metric of the IPHYGE index and we named it MBP, for phytoplanktonic biomass metric (“Métrique de Biomasse Phytoplanktonique”). Its detailed formula is given in the Supplementary data. The MBP metric performances were confirmed on the validation dataset, with similar adjusted R² and linear trends observed for this dataset (Fig. 4).

## 3.2. Contributive taxa for trophic metrics

After excluding rare taxa, trophic scores and stenoecy coefficients were calculated for 355 species and for 301 genera which cover the whole taxonomic diversity we observed in French large rivers (Tables A.2 and A.3 in the Supplementary data). Frequencies of algal groups for both dataset (at the species or genus level) were quite similar. In decreasing order of importance, the contributive species mainly belonged to: chlorophytes (40.8 % of the species), diatoms (33.0 %), cyanobacteria (10.1 %), ochrophytes (7.3 %) and euglenophytes (2.0 %).
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Linear regressions between the EQR values of the selected biomass-based metric (called MBP) and the values of the total phosphorus (TP), CSI, nitrates and Kjeldahl nitrogen, for the dataset used in the index development (in black; N = 963 station-years) and for the validation dataset (in blue; N = 168 station-years). Dotted lines correspond to the regression lines.</figcaption></figure>

**Table 2**

Performances of the trophic metrics calculated using concentrations of total phosphorus. Metric values were based on biovolumes aggregated either at the genus or at the species level. W-AVG = weighted average method and WA-PLS = Weighted Average – Partial Least-Squares regression method. DE<sub>avg</sub> = mean discrimination efficiency for four pressure categories linked to eutrophication and the “Bloom” pressure category (cf. §2.1.). CSI = Combined Stressor Index (cf. §2.3.). Results are sorted based on adjusted R<sup>2</sup> values for total phosphorus, in decreasing order.

<table><thead><tr><th rowspan="2">Method</th><th rowspan="2">Taxonomic level</th><th rowspan="2">Scale for calculations of taxa scores</th><th rowspan="2">Scale for calculations of metric values</th><th rowspan="2">DE<sub>avg</sub></th><th colspan="5">Adjusted R<sup>2</sup></th></tr><tr><th>Total phosphorus</th><th>Kjeldahl nitrogen</th><th>Nitrates</th><th>Chlorides</th><th>CSI</th></tr></thead><tbody><tr><td>WA-PLS</td><td>genus</td><td>station-year</td><td>sample</td><td>0.914</td><td>0.469</td><td>0.344</td><td>0.040</td><td>0.077</td><td>0.472</td></tr><tr><td>WA-PLS</td><td>genus</td><td>station-year</td><td>station-year</td><td>0.906</td><td>0.429</td><td>0.291</td><td>0.044</td><td>0.068</td><td>0.433</td></tr><tr><td>WA-PLS</td><td>genus</td><td>sample</td><td>sample</td><td>0.918</td><td>0.403</td><td>0.323</td><td>0.055</td><td>0.065</td><td>0.477</td></tr><tr><td>WA-PLS</td><td>species</td><td>station-year</td><td>sample</td><td>0.919</td><td>0.400</td><td>0.281</td><td>0.060</td><td>0.049</td><td>0.468</td></tr><tr><td>WA-PLS</td><td>species</td><td>station-year</td><td>station-year</td><td>0.928</td><td>0.400</td><td>0.268</td><td>0.053</td><td>0.051</td><td>0.456</td></tr><tr><td>WA-PLS</td><td>species</td><td>sample</td><td>sample</td><td>0.910</td><td>0.366</td><td>0.288</td><td>0.069</td><td>0.053</td><td>0.482</td></tr><tr><td>W-AVG</td><td>species</td><td>station-year</td><td>sample</td><td>0.896</td><td>0.313</td><td>0.283</td><td>0.065</td><td>0.027</td><td>0.416</td></tr><tr><td>W-AVG</td><td>species</td><td>station-year</td><td>station-year</td><td>0.909</td><td>0.293</td><td>0.285</td><td>0.060</td><td>0.029</td><td>0.391</td></tr><tr><td>W-AVG</td><td>genus</td><td>station-year</td><td>sample</td><td>0.866</td><td>0.293</td><td>0.291</td><td>0.037</td><td>0.058</td><td>0.390</td></tr><tr><td>W-AVG</td><td>genus</td><td>station-year</td><td>station-year</td><td>0.858</td><td>0.262</td><td>0.281</td><td>0.047</td><td>0.050</td><td>0.359</td></tr><tr><td>W-AVG</td><td>species</td><td>sample</td><td>sample</td><td>0.900</td><td>0.257</td><td>0.247</td><td>0.067</td><td>0.019</td><td>0.358</td></tr><tr><td>W-AVG</td><td>genus</td><td>sample</td><td>sample</td><td>0.905</td><td>0.246</td><td>0.268</td><td>0.035</td><td>0.051</td><td>0.336</td></tr></tbody></table>
‰). For genera, the contributive taxa mainly belonged to: chlorophytes (38.9 % of the genera), diatoms (24.6 %), cyanobacteria (14.3 %), ochrophytes (10.0 %) and euglenophytes (2.7 %).

### 3.3. Performances of the trophic metrics based on total phosphorus

Results of the linear regressions for the trophic metrics based on total phosphorus highlighted that the WA-PLS method allowed for overall better performances compared to the standard weighted average results (Table 2). Of note, the WA-PLS method led to better results when working at the genus level, whereas for the weighted average method, the best results were observed at the species level.

Adjusted R² values for total phosphorus varied between 0.246 and 0.469. Adjusted R² values were even a little bit higher for the CSI, with values ranging from 0.336 to 0.477. Results for Kjeldahl nitrogen were also correct, with adjusted R² values comprised between 0.247 and 0.344. Results for both nitrates and chlorides were limited, with all adjusted R² values lower than 0.100. Average DE values were quite high, compared to what was observed for the biomass-based metrics (Table 1), with values comprised between 0.858 and 0.928 (Table 2).

The best performing metric, i.e. with the highest adjusted R² value for total phosphorus, was selected as a constituent metric for the IPHYGE index. We named this metric MG-P, for generic composition metric for total phosphorus ("Métrique de composition au Genre –

Phosphore total"). The trophic scores and stenoey coefficients of the 301 genera contained in the MG-P are given in Table A.2, in the *Supplementary data*. The performances of the MG-P metric were confirmed on the validation dataset, with similar adjusted R² and linear trends observed for this dataset (Fig. 5).

### 3.4. Performances of the trophic metrics based on Kjeldahl nitrogen

Similarly to what was observed for total phosphorus in the previous section, results of the linear regressions for the trophic metrics based on Kjeldahl nitrogen highlighted that the WA-PLS method allowed for overall better performances compared to the standard weighted average results (Table 3). Also, results were better at the genus and at the species levels for the WA-PLS and weighted average methods, respectively.

Adjusted R² values for Kjeldahl nitrogen were comprised between 0.247 and 0.453. Values were similar for CSI, albeit a little lower, with adjusted R² values ranging from 0.196 to 0.413. Results for total phosphorus were also correct, with values varying between 0.118 and 0.310. Similarly to what was observed for the trophic metric based on total phosphorus (Table 2), adjusted R² values were really low for nitrates and chlorides, with all values lower than 0.050 (Table 3). The range of average DE values was similar to what was observed for the previous trophic metric (Table 2), with values comprised between 0.833 and 0.906 (Table 3).

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Linear regressions between the EQR values of the selected trophic metric based on total phosphorus (MG-P) and the values of the total phosphorus (TP), CSI, nitrates and Kjeldahl nitrogen, for the dataset used in the index development (in black; N = 963 station-years) and for the validation dataset (in blue; N = 168 station-years). Dotted lines correspond to the regression lines.</figcaption></figure>
<caption>**Table 3**</caption>

Performances of the trophic metrics calculated using concentrations of Kjeldahl nitrogen. Metric values were based on biovolumes aggregated either at the genus or at the species level. W-AVG = weighted average method and WA-PLS = Weighted Average – Partial Least-Squares regression method. DE<sub>avg</sub> = mean discrimination efficiency for four pressure categories linked to eutrophication and the “Bloom” pressure category (cf. §2.1.). CSI = Combined Stressor Index (cf. §2.3.). Results are sorted based on adjusted R<sup>2</sup> values for Kjeldahl nitrogen, in decreasing order.

<table><thead><tr><th rowspan="2">Method</th><th rowspan="2">Taxonomic level</th><th rowspan="2">Scale for calculations of taxa scores</th><th rowspan="2">Scale for calculations of metric values</th><th rowspan="2">DE<sub>avg</sub></th><th colspan="5">Adjusted R<sup>2</sup></th></tr><tr><th>Total phosphorus</th><th>Kjeldahl nitrogen</th><th>Nitrates</th><th>Chlorides</th><th>CSI</th></tr></thead><tbody><tr><td>WA-PLS</td><td>genus</td><td>station-year</td><td>sample</td><td>0.900</td><td>0.310</td><td>0.453</td><td>0.022</td><td>0.045</td><td>0.394</td></tr><tr><td>WA-PLS</td><td>genus</td><td>station-year</td><td>station-year</td><td>0.871</td><td>0.267</td><td>0.432</td><td>0.024</td><td>0.046</td><td>0.351</td></tr><tr><td>WA-PLS</td><td>species</td><td>station-year</td><td>station-year</td><td>0.906</td><td>0.266</td><td>0.419</td><td>0.037</td><td>0.040</td><td>0.375</td></tr><tr><td>WA-PLS</td><td>genus</td><td>sample</td><td>sample</td><td>0.877</td><td>0.294</td><td>0.405</td><td>0.034</td><td>0.043</td><td>0.413</td></tr><tr><td>WA-PLS</td><td>species</td><td>station-year</td><td>sample</td><td>0.904</td><td>0.267</td><td>0.403</td><td>0.041</td><td>0.031</td><td>0.380</td></tr><tr><td>WA-PLS</td><td>species</td><td>sample</td><td>sample</td><td>0.891</td><td>0.242</td><td>0.388</td><td>0.050</td><td>0.030</td><td>0.388</td></tr><tr><td>W-AVG</td><td>species</td><td>station-year</td><td>station-year</td><td>0.885</td><td>0.169</td><td>0.333</td><td>0.038</td><td>0.021</td><td>0.283</td></tr><tr><td>W-AVG</td><td>species</td><td>station-year</td><td>sample</td><td>0.896</td><td>0.196</td><td>0.326</td><td>0.047</td><td>0.022</td><td>0.341</td></tr><tr><td>W-AVG</td><td>genus</td><td>station-year</td><td>station-year</td><td>0.833</td><td>0.158</td><td>0.315</td><td>0.024</td><td>0.029</td><td>0.256</td></tr><tr><td>W-AVG</td><td>genus</td><td>station-year</td><td>sample</td><td>0.860</td><td>0.199</td><td>0.312</td><td>0.022</td><td>0.040</td><td>0.320</td></tr><tr><td>W-AVG</td><td>species</td><td>sample</td><td>sample</td><td>0.892</td><td>0.146</td><td>0.310</td><td>0.035</td><td>0.018</td><td>0.268</td></tr><tr><td>W-AVG</td><td>genus</td><td>sample</td><td>sample</td><td>0.866</td><td>0.118</td><td>0.247</td><td>0.011</td><td>0.024</td><td>0.196</td></tr></tbody></table>

The best performing metric, i.e. with the highest adjusted R<sup>2</sup> value for Kjeldahl nitrogen (Table 3), was selected as a constituent metric for the IPHYGE index. We named this metric MG-A, for generic composition metric for Kjeldahl nitrogen (“Métrique de composition au Genre –

Azote Kjeldahl”). The trophic scores and stenoecy coefficients of the 300 genera contained in the metric MG-A are given in Table A.2, in the Supplementary data. The performances of the MG-A metric were confirmed on the 2020–2021 dataset, with in general similar adjusted R<sup>2</sup>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Linear regressions between the EQR values of the selected trophic metric based on Kjeldahl nitrogen (MG-A) and the values of the total phosphorus (TP), CSI, nitrates and Kjeldahl nitrogen, for the dataset used in the index development (in black; N = 963 station-years) and for the validation dataset (in blue; N = 168 station-years). Dotted lines correspond to the regression lines.</figcaption></figure>
and linear trends observed for this dataset (Fig. 6). Nevertheless, a small loss of performance was observed for Kjeldahl nitrogen, with adjusted R² going from 0.453 on the development dataset to a lower value for the validation dataset, with a value equal to 0.313.

### 3.5. Performances of the trophic metrics based on nitrates

Once again, the WA-PLS method allowed for overall better model performance, compared to results obtained with the weighted average

<caption>**Table 4**</caption>

Performances of the trophic metrics calculated using concentrations of nitrates. Metric values were based on biovolumes aggregated either at the genus or at the species level. W-AVG = weighted average method and WA-PLS = Weighted Average – Partial Least-Squares regression method. DE<sub>avg</sub> = mean discrimination efficiency for four pressure categories linked to eutrophication and the “Bloom” pressure category (cf. §2.3.). CSI = Combined Stressor Index (cf. §2.1.). Results are sorted based on adjusted R² values for nitrates, in decreasing order.

<table><thead><tr><th rowspan="2">Method</th><th rowspan="2">Taxonomic level</th><th rowspan="2">Scale for calculations of taxa scores</th><th rowspan="2">Scale for calculations of metric values</th><th rowspan="2">DE<sub>avg</sub></th><th colspan="5">Adjusted R<sup>2</sup></th></tr><tr><th>Total phosphorus</th><th>Kjeldahl nitrogen</th><th>Nitrates</th><th>Chlorides</th><th>CSI</th></tr></thead><tbody><tr><td>WA-PLS</td><td>species</td><td>station-year</td><td>sample</td><td>0.844</td><td>0.040</td><td>0.013</td><td>0.378</td><td>-0.001</td><td>0.229</td></tr><tr><td>WA-PLS</td><td>species</td><td>sample</td><td>sample</td><td>0.760</td><td>0.045</td><td>0.025</td><td>0.369</td><td>0.010</td><td>0.205</td></tr><tr><td>WA-PLS</td><td>species</td><td>station-year</td><td>station-year</td><td>0.776</td><td>0.032</td><td>0.009</td><td>0.360</td><td>0.005</td><td>0.196</td></tr><tr><td>WA-PLS</td><td>genus</td><td>station-year</td><td>sample</td><td>0.614</td><td>0.048</td><td>0.010</td><td>0.289</td><td>0.000</td><td>0.175</td></tr><tr><td>WA-PLS</td><td>genus</td><td>station-year</td><td>station-year</td><td>0.693</td><td>0.046</td><td>0.012</td><td>0.269</td><td>0.000</td><td>0.160</td></tr><tr><td>WA-PLS</td><td>genus</td><td>sample</td><td>sample</td><td>0.665</td><td>0.060</td><td>0.029</td><td>0.241</td><td>0.017</td><td>0.148</td></tr><tr><td>W-AVG</td><td>species</td><td>station-year</td><td>station-year</td><td>0.599</td><td>0.049</td><td>0.032</td><td>0.193</td><td>0.009</td><td>0.108</td></tr><tr><td>W-AVG</td><td>species</td><td>station-year</td><td>sample</td><td>0.561</td><td>0.063</td><td>0.030</td><td>0.193</td><td>0.007</td><td>0.115</td></tr><tr><td>W-AVG</td><td>species</td><td>sample</td><td>sample</td><td>0.482</td><td>0.036</td><td>0.017</td><td>0.178</td><td>0.011</td><td>0.082</td></tr><tr><td>W-AVG</td><td>genus</td><td>station-year</td><td>station-year</td><td>0.646</td><td>0.057</td><td>0.034</td><td>0.165</td><td>0.006</td><td>0.122</td></tr><tr><td>W-AVG</td><td>genus</td><td>station-year</td><td>sample</td><td>0.626</td><td>0.089</td><td>0.043</td><td>0.151</td><td>0.006</td><td>0.145</td></tr><tr><td>W-AVG</td><td>genus</td><td>sample</td><td>sample</td><td>0.601</td><td>0.045</td><td>0.018</td><td>0.109</td><td>0.009</td><td>0.085</td></tr></tbody></table>

<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Linear regressions between the EQR values of the selected trophic metric based on nitrates (MS-N) and the values of the total phosphorus (TP), CSI, nitrates and Kjeldahl nitrogen, for the dataset used in the index development (in black; N = 963 station-years) and for the validation dataset (in blue; N = 168 station-years). Dotted lines correspond to the regression lines.</figcaption></figure>
method (Table 4). In contrast with the other two trophic metrics (Tables 2 and 3), the best results, here, were obtained at the species level. Adjusted R² values did not get higher than 0.400 for nitrates, as they ranged from 0.109 to 0.378 (Table 4). Adjusted R² values for the other parameters, namely total phosphorus, Kjeldahl nitrogen and chlorides, were really low, with values always lower than 0.100 (Table 4). Nevertheless, performances were somewhat higher for CSI, with adjusted R² values comprised between 0.085 and 0.229 (Table 4). The range of average DE values was a little bit lower than what was observed for both previous trophic metrics (Tables 2 and 3), with values comprised here between 0.482 and 0.844 (Table 4).

The best performing metric, i.e. with the highest adjusted R² value for nitrates (Table 4), was selected as a constituent metric for the

IPHYGE index. We named this metric MS-N, for specific composition metric for nitrates ("Métrique de composition à l'eSpèce - Nitrates"). The trophic scores and stenoecy coefficients of the 355 species contained in the metric MS-N are given in Table A.3, in the Supplementary data. The performances of the MS-N metric were confirmed on the validation dataset, with ranges of observed adjusted R² values similar to those observed with the development dataset (Fig. 7).

### 3.6. Performances of the IPHYGE candidates

The performances of the candidate indices were in accordance with the weights of the constituent metrics, albeit generally lower than what was observed for each metric separately (Table 5). Performances for

<caption>**Table 5**</caption>

Performances of the candidate indices (CI) for the IPHYGE, calculated using different weights for the four selected metrics. MBP = phytoplanktonic biomass metric, MG-P = generic composition metric for total phosphorus, MG-A = generic composition metric for Kjeldahl nitrogen, MS-N = species composition metric for nitrates. DE<sub>avg</sub> = mean discrimination efficiency for four pressure categories linked to eutrophication and the "Bloom" pressure category (cf. §2.1.). CSI = Combined Stressor Index (cf. §2.3.).

<table><thead><tr><th rowspan="2">Candidate indices</th><th colspan="4">Weights</th><th rowspan="2">DE<sub>avg</sub></th><th colspan="4">Adjusted R<sup>2</sup></th></tr><tr><th>MBP</th><th>MG-P</th><th>MG-A</th><th>MS-N</th><th>Total phosphorus</th><th>Kjeldahl nitrogen</th><th>Nitrates</th><th>Chlorides</th><th>CSI</th></tr></thead><tbody><tr><td>CI1</td><td>1</td><td>1</td><td>1</td><td>1</td><td>0.929</td><td>0.332</td><td>0.363</td><td>0.124</td><td>0.048</td><td>0.554</td></tr><tr><td>CI2</td><td>0.5</td><td>1</td><td>1</td><td>1</td><td>0.933</td><td>0.340</td><td>0.343</td><td>0.161</td><td>0.040</td><td>0.567</td></tr><tr><td>CI3</td><td>0.5</td><td>2</td><td>1</td><td>1</td><td>0.939</td><td>0.383</td><td>0.359</td><td>0.133</td><td>0.050</td><td>0.571</td></tr></tbody></table>

<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Linear regressions between the EQR values of the IPHYGE and the values of the total phosphorus (TP), CSI, nitrates and Kjeldahl nitrogen, for the dataset used in the index development (in black; N = 963 station-years) and for the validation dataset (in blue; N = 168 station-years). Dotted lines correspond to the regression lines.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Boxplots describing the distributions of the IPHYGE values in relation with the chemical quality classes observed for three pressure categories for the development dataset (N = 963 station-years). The lettering of the boxplots indicates the grouping of pressure levels based on post hoc multiple comparison tests following significant Kruskal-Wallis tests. Each boxplot represents the minimum/Q25/median/Q75/maximum values, respectively. Outliers (open circles) are outside the 1.5 interquartile range of the corresponding distribution. Mod. = Moderate.</figcaption></figure>

total phosphorus and Kjeldahl nitrogen were similar, with all adjusted R² values for both parameters comprised between 0.332 (CI1 vs total phosphorus) and 0.383 (CI3 vs total phosphorus). The candidate indices exhibited adjusted R² values for nitrates that were intermediate between the performance of the MS-N metric alone (Table 4) and those of the other trophic metrics (Tables 2 and 3): adjusted R² values ranged from 0.124 (CI1) to 0.161 (CI2). Performances were still limited for chlorides, with adjusted R² values comprised between 0.040 (CI2) and 0.050 (CI3). Of note, the candidate indices exhibited better performances for the CSI (Table 5) than the constituent metrics alone (Tables 2, 3 and 4): adjusted R² values varied from 0.554 (CI1) to 0.571 (CI3).

Based on these results, we selected the candidate index CI2 for the IPHYGE, as it exhibited good results for both total phosphorus and Kjeldahl nitrogen, with both adjusted R² higher than 0.30, while keeping some level of performance for nitrates. Its performance for CSI was also

quite good, with an adjusted R² higher than 0.50, and close to the best possible value, exhibited by CI3.

The performances of the IPHYGE were quite similar on the validation dataset, with ranges of observed adjusted R² values similar to those observed with the development dataset, albeit a little bit lower for nitrates, with the adjusted R² values going from 0.161, for the development dataset, to 0.101, for the validation dataset (Fig. 8). The IPHYGE values allowed for a significant discrimination between impaired (chemical quality classes = Moderate and Poor) and less impaired situations (High and Good) for the pressure categories “Phosphorous compounds”, “Nitrogen compounds (except nitrates)” and “Nitrates” (Fig. 9) on the development dataset. Discrimination between chemical quality classes Moderate and Poor only appeared significant for the pressure category “Nitrates”.
<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Boxplots describing the distributions of total phosphorus concentrations and of CSI values in relation with the ecological quality classes assigned by IPHYGE. The lettering of the boxplots indicates the grouping of quality classes based on post hoc multiple comparison tests following significant Kruskal-Wallis tests. Each boxplot represents the minimum/Q25/median/Q75/maximum values, respectively. Outliers (open circles) are outside the 1.5 interquartile range of the corresponding distribution. Colored boxplots indicate values from the development dataset, whereas grey colors indicate the validation dataset. No "Bad" ecological quality class was assigned to station-years belonging to the validation dataset.</figcaption></figure>

## 3.7. IPHYGE quality classes and anthropogenic pressure gradients

Finally, we explored how the ecological quality classes assigned by the IPHYGE would be linked to value gradients for two parameters indicating anthropogenic pressures, here total phosphorus and CSI (Fig. 10). The boxplots confirmed that the IPHYGE quality classes were well linked to the pressure gradients for the development dataset and the validation dataset as well. The distribution of the parameter values were quite similar for both dataset, confirming the good performance of the IPHYGE for the validation dataset: the distribution of the parameters did allow for a good discrimination, statistically significant (Kruskal-Wallis' tests, $p < 0.001$ for each parameter), between impaired situations (classes "Moderate" and "Poor") and less impaired ones ("High" and "Good"). The discrimination between "High" and "Good" was not really well defined, but the discrimination between the classes "Moderate" and "Poor" was significant (Fig. 10). We could not explore how the discrimination worked for the class "Bad" due to the fact that the IPHYGE only classified one station-year to this class (for the development dataset).

# 4. Discussion

## 4.1. The IPHYGE index

The newly developed IPHYGE index is a multimetric index consisting of one biomass-based metric and three trophic metrics, related to three different parameters: total phosphorus, Kjeldahl nitrogen and nitrates. Its value correctly highlights pressure gradients, especially eutrophication. Its performance towards total phosphorus are in line with what was observed for other phytoplankton-based indices used for the monitoring of European large rivers (Mischke et al., 2016). Although the index performance are lower than its constituents' ones for the main parameters, it exhibits better performances for the CSI gradient. As a reminder, the CSI is a synthetic pressure index based on three parameters that best model concentrations of chlorophyll-a in European large rivers (Mischke et al., 2016). Thus, the good performance of the IPHYGE index for the CSI shows its ability to highlight conditions which could promote algal blooms.

Ecological quality classes assigned with the IPHYGE are coherent with what was known for rivers and their associated monitoring stations. Overall, "High" and "Good" quality classes are mainly observed for stations located on rivers already identified as less impacted by anthropogenic activities, i.e. on the Saône and Doubs rivers, on the Dordogne river, upstream on the Loire river, and upstream on tributaries of the Seine river (pers. com. with the steering committee and developers of the other WFD indices for large rivers; Fig. A.2 in the Supplementary data). The majority of the station-years found in a "Poor" quality class are channelized rivers in Northern France, a region known for its historical pollution (Fig. A.2; Pyrygel et al., 2015; Superville et al., 2015; Net et al., 2015). The majority of the other station-years exhibited a "Moderate" ecological quality class. It highlights that we rarely observed highly eutrophic situations in our dataset, and it is thus also coherent with the distribution of the values of the IPHYGE in the impaired situations (IRR) found in our dataset (Fig. 3).

## 4.2. Biomass-based metrics

For the development of the IPHYGE we explored if either the concentrations of chlorophyll-a or total biovolumes would allow for a better biomass-based metric, i.e. which could exhibit a good relationship with eutrophication gradients, mainly total phosphorus. We observed better performances for the metrics based on chlorophyll-a concentrations, and we thus chose to include such a metric in the IPHYGE.

Nevertheless, the proportion of the variance of total phosphorus explained by the chosen biomass-based metric was not high, close to 15 %. However, such a value was in line with similar metrics retained in other indices (e.g., Mischke et al., 2016; Laplace-Treyture and Feret, 2016). The low performance raises the question on the necessity of including a biomass-based metric in the IPHYGE. Indeed, the inclusion of a biomass-based metric in the IPHYGE was driven by the criteria of the WFD for phytoplankton-based methods (European Council, 2000; Mischke et al., 2016). Ultimately we still decided to include such a metric in the IPHYGE, in order to be comparable with what has been done for other European methods and in order to respect the WFD criteria. Nevertheless, we chose to assign a lower weight to the MBP metric in the IPHYGE calculation, in order to limit the decrease of index
performances.

Total biovolumes did not correlate as well as chlorophyll-a concentrations with total phosphorus. This result was in accordance with results obtained in lakes by Canfield et al. (2019), who also observed that chlorophyll-a was a better proxy of phytoplanktonic biomass than biovolumes. Total biovolumes are estimated based on known and fixed values of biovolume for each phytoplanktonic taxon, usually based on the geometric shape of the cells (for example, Sun and Liu, 2003). Such individual and specific biovolumes may thus be somewhat imprecise. Combined with possible individual variations of biovolumes, it may explain why the performance of total biovolumes for total phosphorus is lower than chlorophyll-a, which is a less indirect measurement of phytoplanktonic biomass.

### 4.3. Weighted average and WA-PLS methods

The WA-PLS method allowed for far better performances, whatever the studied parameter, over the standard weighted average method (Pajunen et al., 2016). Nevertheless, the WA-PLS method presents some limits that should be stated here:

(i) this method may lead to an overfitting of the developed metric to the development dataset. Although not reported in the result section, we should highlight that for nearly all developed metrics using the WA-PLS method, we had to work with only two components (which are somewhat akin to components from a Principal Component Analysis; see ter Braak and Juggins, 1993), as identified during the cross-validation step of the method. Such a low number of components indicates that overfitting could occur within a few components. Although we only worked with two components (rarely three) for our trophic metrics, their performances were nearly always higher than those observed for the standard metrics. We can conclude that the WA-PLS method is a method of interest for the development of trophic metrics (Pan et al., 1996; Stevenson, 2014; Pajunen et al., 2016);

(ii) the trophic scores of all taxa are all interdependent, due to the peculiarities of the WA-PLS method. It means that it is not possible to add, modify and/or correct the trophic scores of only one taxon without recalculating the scores of the whole taxa list. It's not a real limitation *per se*, but it also means that adding new taxa to the contributive taxa list would necessitate a recalculation of all scores. Thus, updating older methods based on WA-PLS may lead to more index value changes than updating scores with the standard weighted average method, for example when adding new taxa.

### 4.4. Trophic score and taxon ecological profile

Our results have shown that when describing the ecological profile of a taxon for a given nutrient parameter (i.e. calculating both the trophic score and stenoecy coefficient), potential trophic metrics exhibited better performances when we worked at the station-year scale, i.e. when we worked with seasonal average over the growing season (from April to October). It may highlight that when describing the optimum of a taxon for a given parameter it may be more robust to work with seasonal averages, as they may allow to limit the influence of temporal variability of measurements on the definition of the optimum.

In contrast, we obtained the best results when we used these “seasonal” scores at the sample scale, i.e. when we use these scores to calculate one index value per phytoplanktonic sample, usually monthly. It suggests that calculating a metric value for each sample may better represent the temporal variations of the modeled parameter, e.g. total phosphorus, and thus better correlate with the yearly average. Or, simply, multiplying measures over the year just limits the uncertainty of the index value (e.g., Thackeray et al., 2013). Other methods exhibit differing ways for the calculations of their respective main metric,

trophic or not: for example, Laplace-Treyture and Feret (2016) and Borics et al. (2007) calculated the main metric value of their respective method for each phytoplanktonic sampling campaign, whereas other European methods (e.g., Mischke et al., 2011, 2016; Wolfram et al., 2014) calculated one metric value per year by using the average biovolumes of each taxon over the growing season. To the best of our knowledge, these studies did not explore whether their approach was the most appropriate one. Nevertheless, we may highlight that the new version of the German method (in its V5; Mischke and Riedmüller, 2020) does now calculate the value of its main trophic value separately for each phytoplanktonic sample, like us.

### 4.5. Contributive taxa

The composition of both contributive taxa lists (at the species or genus level) were similar to what was observed for other phytoplankton-based methods (Mischke et al., 2011; Laplace-Treyture and Feret, 2016), with the majority of the taxa belonging to algal groups such as chlorophytes, diatoms and cyanobacteria. Nevertheless, the number of contributive taxa for the IPHYGE could be considered as high, with more than 300 taxa, whatever the taxonomical level. Other methods used in Europe, be they for rivers or lakes, exhibit differing taxonomic richness for their contributive taxa lists: for example, 63 taxa for the German method (in its second version; Mischke et al., 2011), 80 taxa for the Polish method (Picińska-Faltynowicz and Blachuta, 2012), 162 taxa for the Brettum index for Alpine lakes (Wolfram et al., 2014), 165 taxa for the French method for lakes (Laplace-Treyture and Feret, 2016). Several complementary hypotheses may be advanced in order to explain why we considered more taxa in our method. First, we may have been less strict in our selection process. Although we excluded rare taxa from our list, we did not add a step of selection based on further validation tests of the possible robustness of the scores of the remaining taxa (e.g., Mischke et al., 2011). Second, the size of the dataset may constrain the observed taxonomic richness. For example, Laplace-Treyture and Feret (2016) “only” considered 165 taxa, whereas we considered more than 300 taxa. But they also developed their method with a smaller dataset, containing 254 station-years, whereas our development dataset was near 4 times bigger, with 963 station-years. Nevertheless, we should note that Mischke et al. (2011), working with “only” 470 station-years, started the development with 830 taxa before all filtration and selection steps. Last, but not least, the diversity of the large rivers located in France may drive a higher taxonomic richness and diversity, and thus a possible longer contributive taxa list. Stations along the French large rivers were actually located in 15 different hydro-ecoregions (sensu Wasson et al., 2002), among the 22 possible hydro-ecoregions, and stations exhibited a relatively homogeneous distribution in France (Fig. 1; but note the absence of stations in the Mediterranean part of France). Furthermore, before excluding rare taxa, we observed a high taxonomic richness, with 1776 different taxa (even if it included unidentified taxa and taxa identified at taxonomic levels higher than genus).

Last, the trophic scores we obtained for the trophic metric related to total phosphorus (MG-P) were comparable with trophic scores obtained by other European methods (namely, for the German and Polish methods for large rivers, and for the IPLAC method for French lakes; Mischke et al., 2011, 2016; Picińska-Faltynowicz and Blachuta, 2012, Laplace-Treyture and Feret, 2016, Fig. A.3 in the Supplementary data): regression slopes were in accordance with the respective trophic gradient returned by each method and their scores. Although these regressions were globally significant, the links between this and other methods' scores were not necessarily good (i.e. $R^2$ were low; Fig. A.3). Nevertheless, such low linkage between these scores could be explained by the fact that these scores were defined for different regions and river types (and for lakes, for the IPLAC) or maybe because we used the WA-PLS method, which iteratively adjusts all scores based on the performance of the model, whereas other methods used more traditional approaches. These iterative adjustments can thus lead to taxa scores which
are not representative of their real ecology, as the model try to maximize
its performances. For example, looking only at some of the most
"extreme" taxa scores (i.e. for genera either indicating eutrophic or
oligotrophic conditions) for total phosphorus, both our method and the
German one (in its V5) converged for several taxa, i.e. these taxa were
indicating similar trophic conditions: e.g. for eutrophic taxa, the diatom
*Actinocyclus*, the green algae *Pteromonas* and the euglen *Euglena*, or as an
oligotrophic example, the chrysophyte *Chrysolykos*. But we also
observed divergent genera: e.g. the cyanobacteria *Anathece* exhibited a
really high score for the MG-P, indicating oligotrophic conditions,
whereas it was generally associated with more meso- to eutrophic con-
ditions in other methods and studies (e.g. Reynolds et al., 2002; Borics
et al., 2007; Mischke and Riedmüller, 2020). We can also note that
among these "extreme" genera, the majority of them were not found in
other methods. It highlights once again the importance of developing a
method specific to French large rivers, as we could thereby take these
taxa into account in our method. We can also hypothesize that this
higher taxonomic richness allowed for the WA-PLS to better adjust the
trophic scores, and thus, to exhibit better performances compared to
other traditional methods.

5. Conclusions

The IPHYGE index is the new multimetric index for the evaluation of the ecological quality of French large rivers in the context of the WFD. It includes both a biomass-based metric and three trophic metrics. Such a metric composition allowed us to comply with all criteria from the WFD, while still reliably identify situations impaired by eutrophication and associated blooms. The overall diversity of French large rivers and their phytoplanktonic communities may have limited the performance of this newly-developed method, but the use of the WA-PLS method allowed to overcome such a potential problem.

The development of this new method detailed in this study could
prove to be pertinent for the future development of a method specific to
large rivers in French Guyana. Although these rivers are located in an
oversea territory, they are also covered by the WFD. It remains to be
checked whether the IPHYGE method could be directly used for the
biomonitoring of such rivers, albeit it is unlikely as this method was
developed for mainland France. Nevertheless, the WA-PLS approach
could be applied once again for the development of a future method for
French Guyana.

Last, we may also highlight that this method could be used for the
bioindication of artificial waterbodies, such as channelized rivers.
Compared to the dataset used for its development, a preliminary anal-
ysis (Dumortier, 2022) confirmed that the IPHYGE index would exhibit
similar performances for such watercourses. Phytoplankton could thus
also be a pertinent biological component to evaluate the ecological
potential.

Credit authorship contribution statement

**Albin Meyer:** Writing – review & editing, Writing – original draft, Visualization, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Emilie Prygiel:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Christophe Laplace-Treyture:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

Declaration of competing interest

The authors declare the following financial interests/personal re-
lationships which may be considered as potential competing interests:

Albin Meyer reports financial support was provided by the French Biodiversity Office. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.

Acknowledgment

The development of the IPHYGE was an objective of the DIPCEAU
project. This project was supported by a grant from the French Office for
Biodiversity (Office Français de la Biodiversité, grant OFB-20-1094).
The authors wish to thank Nicolas Hette-Tronquart (Office Français de
la Biodiversité), Laura Moreau (DREAL Lorraine) and Loïc Imbert
(Agence de l'Eau Rhône-Méditerranée-Corse) for their participation in
the project steering committee.

**Appendix A. Supplementary data**

Supplementary data to this article can be found online at https://doi.
org/10.1016/j.ecolind.2024.112303.

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