The Malaspina-2010 cruise crossed tropical, subtropical and temperate oceans around the globe between 35°N and 40°S in seven consecutive legs (Fig. 1). The cruise started and ended in Cartagena, Spain, and crossed the Atlantic, Indian and Pacific oceans (Tables S1 and S2). To summarize information for some analyses performed in this work, a loose latitudinal classification into coastal, and equatorial, subtropical and tropical open ocean geoclimatic zones was adopted (Table S1).

At each station, two or more vertical profiles of conductivity-temperature-depth (CTD) were obtained with a CTD SeaBird 9/11-plus equipped with additional sensors of dissolved oxygen concentration, turbidity, fluorescence, light transmission, underwater photosynthetically active radiation (PAR), surface irradiance and bottom proximity (measured using an altimeter). During the second CTD cast, which started around 10:00 local time, water samples for determination of total Chl a and nutrient concentrations were collected from the surface (3 m depth) by means of a 30-litre Niskin bottle and from 9 additional depths using 12-litre Niskin bottles mounted on a “rosette”. In general, these 9 depths included 10 m, the depths of 50% and 20% of surface PAR, an “intermediate depth 1”, the depth of 7% surface PAR, an “intermediate depth 2”, the DCM depth (as determined from the CTD profile), the DCM depth + 20 m and the DCM depth + 50 m.

The mixed layer depth (MLD) was calculated as the first depth (z) for which σ_θ(z)-σ_θ(10)≥0.125 kg m^-3, where σ_θ(z) and σ_θ(10) are, respectively, the potential density anomalies at depths z and 10 m (Levitus 1982). The stratification profile of the water column was characterized by means of the Brunt-Väisälä (B-V) frequency (N²), calculated at 2 m intervals. The strength of stratification in the upper 200 m was estimated as σ_θ(200)-σ_θ(6) (hereafter σ200-σ6), the difference between the potential density anomalies (with reference pressure of 0 dbar) at 200 and at 6 m depth (Behrenfeld et al, 2006). The euphotic zone depth was considered to be the depth of 1% of the surface irradiance, calculated from the PAR CTD records. The Ocean Data View software (Schlitzer 2023) was used to present the distribution of hydrographical variables and to calculate B-V frequencies and potential density anomalies.

Analysis of total Chl a (Chl a_tot) was performed for samples taken between the surface (3 m depth) and 50 m below the DCM depth. From 250 to 500 mL of seawater were filtered through 25 mm GF/F filters, which were frozen for about 6 hours at 20°C, introduced in acetone 90% and left for 24 hours at 4°C in the dark. The Chl a concentration in the acetonic extracts was determined fluorometrically with a Turner Designs fluorometer calibrated with pure Chl a (Sigma-Aldrich). Size-fractionated analyses of Chl a were carried out for samples from the surface, the 20% surface PAR and a deeper depth that in general coincided with the DCM depth [the main exceptions were stations 45 (Agulhas Current region), 16 (Atlantic equatorial upwelling) and 90-96 (Pacific equatorial upwelling), which did not show a DCM]. Stations at which the deeper fractionation depth differed by more than 10 m from the DCM depth were excluded from the DCM calculations in Table 2. The measurements were performed by sequential filtration through 47 mm Poretics polycarbonate membrane filters of 20, 2 and 0.2 µm pore sizes, which were subsequently treated as the GF/F ones (Estrada, 2012; Estrada et al., 2016). The fractional contribution of microphytoplankton (f_micro, >20 µm), nanophytoplankton (f_nano, >2 and <20 µm) and picophytoplankton (f_pico, >0.2 and <2 µm) was calculated with respect to the sum of Chl a in the three size fractions (Chl a_pol), which tended to be slightly lower than the total Chl a determined by filtration onto GF/F filters (Chl a_pol=0.91*Chl a_tot - 0.21, r²=0.87, p<0.0001). For comparison, the relative contribution of the three phytoplankton size fractions (f_micro, f_nano and f_pico) was also estimated by means of the Chl a-based approach of Hirata et al. (2008, 2011):

f_micro [0.9117+exp (-2.733x + 0.4003)]^-1

f_nano 1-f_micro-f_pico

f_pico - [0.1529+exp (1.0306x-1.5576)]⁻¹-1.8597x + 2.9954,

where x=log10(Chl a_tot)

The possibility of fitting the three-component model of Brewin et al. (2010, 2014), which derives the fractions of picophytoplankton (<2 µm) and combined pico- and nanophytoplankton (<20 µm) chlorophyll with total chlorophyll concentration, was examined, but our data could not be adjusted to the model equations because these include a parameter representing an asymptotic maximum chlorophyll concentration for the <2 µm and <20 µm size classes that was not reached in our data set.

Nutrient (silicate, nitrate, nitrite and phosphate) concentrations were determined by means of a Skalar autoanalyser, using standard spectrophotometric procedures (Grasshoff et al. 1999, Blasco et al. 2012); in leg 1, nitrite was not determined, and phosphate was measured using a manual method (Vidal et al. 2012). The nutricline depth was represented by that of the nitracline, which was defined as the depth at which nitrate (nitrate + nitrite in leg 1) concentrations first reached 1 mmol m^-3; in most cases, it was determined by linear interpolation based on the closest samples encompassing this threshold. Some stations (mostly from the Pacific equatorial upwelling) with nitrate concentrations at surface exceeding 1 mmol m^-3 did not have a nitracline depth. In a few others, the calculated nitracline depth was slightly shallower than the MLD but was considered to be equal to the MLD. This was done because the limited number of vertical nutrient samples precluded a fine depth resolution and it was assumed that, in stratified conditions, a nitracline would not occur within the mixed layer. Different nutricline depths could be obtained if calculated from phosphate, but we chose nitrate because nitrogen is considered to be the main limiting nutrient in stratified subtropical gyres (Browning and Moore 2023).

Chl a profiles matching the CTD records (available at 1 or 2 m intervals) were obtained as described in Estrada et al. (2014). First, CTD in situ fluorescence readings were converted to Chl a concentrations (hereafter Chl a_CTD) based on calibration equations obtained for each leg from the regression of Chl a_tot values measured in the ship laboratory vs. in situ fluorescence readings corresponding to the same depth. Chl a_tot concentration between 0 m and 10 m depth was assumed to be equal to Chl a_tot concentration at 3 m. Second, a linear interpolation (Chl a_tot-int) of Chl a_tot based on the closest available Chl a_tot above and below the interpolation depths was assigned to each depth of the high-resolution (1-2 m intervals) vertical CTD profiles between 10 m and the DCM + 50 depths. Third, a similar interpolation procedure was carried for Chl a_CTD to calculate Chl a_CTD-int based on the Chl a_CTD values of the same depths adopted to interpolate Chl a_tot. Fourth, we multiplied the interpolated Chl a_tot-int at each depth by a correction factor consisting of the ratio between the Chl a_CTD derived from the actual in vivo fluorescence reading and the linearly interpolated Chl a_CTD-int for this depth. This correction factor was introduced to compensate for non-linearity of the Chl a profiles and was based on the assumption that, at subsurface depths, in situ fluorescence would be proportional to Chl a concentration. Integrated Chl a between 0 and 200 m depth (Chl a_int) was then computed using the trapezoidal rule (for this calculation, Chl a between the DCM + 50 and 200 m was supposed to be equal to the corresponding Chl a_CTD).

Linear regressions and correlation coefficients were calculated using the Systat 13 software. A t test was used to estimate the significance of differences among regression slopes (Paternoster et al. 1998). The distribution of size class fractions among light levels and oceans or geoclimatic zones was evaluated with a two-way ANOVA followed by post-hoc Tuckey tests, using the Systat software. Chl a concentration values were log-transformed to approximate the distributions to normality. Since our interest was to quantify the pattern of covariation rather than to carry out an estimation of the dependent variables, the analysis of the bivariate linear relationships between the Chl a size fractions and Chl a_pol was carried out with the reduced major axis regression model (RMA), using the PAST4 software (https://www.nhm.uio.no/english/research/resources/past/). In this way, we also tried to minimize the influence of the different degrees of dispersion of the data around the regression lines. Chl a (http://hdl.handle.net/10261/345389) and nutrient (https://doi.org/10.20350/digitalCSIC/16127) data are available at Digital CSIC (www.digital.csic.es).

Chl a_tot concentrations encountered during the Malaspina expedition (Fig. 2) ranged from 0.03 to 0.69 mg m^-3 at surface (3 m depth), from 0.05 to 1.08 mg m^-3 at the 20% light level and from 0.11 to 1.92 mg m^-3 at the DCM. Among oceans, average Chl a_tot values ranged from 0.12 mg m^-3 in the Atlantic to 0.21 mg m^-3 in the Pacific at surface and from 0.42 mg m^-3 in the Indian to 0.5 mg m^-3 in the Pacific at the DCM (Table 1). By geoclimatic zones, average Chl a_tot went from 0.10 mg m^-3 in the subtropical zone to 0.30 mg m^-3 in the equatorial at surface and from 0.38 mg m^-3 in the subtropical zone to 0.68 mg m^-3 in the coastal zone for the DCM (Table 1). In general, there was a marked temperature stratification, with MLDs ranging between 40 and 100 m (Fig. 2A). The seasonal changes between the North Atlantic crossings of legs 1 and 7 were reflected in higher sea surface temperatures and shallower MLDs in the later leg. The thinnest MLDs and the highest surface Chl a (Chl a_srf) concentrations were found (Figs. 1 and 2) in regions such as the equatorial upwelling zone of the Atlantic, the Costa Rica or Mesoamerican Dome and the eastern coast of South Africa (Agulhas Current, station 45). Another zone with relatively high Chl a concentrations was the Eastern Great Australian Bight, which showed a cool, deep (MLD of 60-80 m) mixed layer on top of a dome of relatively cold water (Fig. 2). This situation was accompanied by a high contribution of Prochlorococcus and a homogeneous vertical distribution of phytoplankton, suggesting an early autumn mixing event (Latasa et al. 2023).

Most stations showed a DCM between 60 and 150 m depth, close to the level of 1% surface PAR (Figs 2 and 3A). In general, the DCM was deeper than the MLD (Fig. 3B) and was either absent or above 40-60 m in regions influenced by upwelling or divergences, such as the equatorial upwellings, the Costa Rica Dome and the Eastern Great Australian Bight. For simplicity, these areas will be subsequently designated as upwelling-divergence (U-D) regions, as in Estrada et al. (2016). The DCM appeared well below the depth of maximum B-V frequency (data not shown) in the open Indian Ocean and tropical and subtropical Pacific, and was found near the maximum B-V frequency depth in the U-D regions.

The linear regression equations of DCM depth on nitracline depth were positive and significant (p<0.001) and had similar slopes for all three oceans (Table S3). Above 100 m depth, the nitracline and the DCM depth were approximately aligned in a 1:1 relationship, but below 100 m the DCM tended to be shallower than the nitracline (Fig. 4A). When the data were categorized according to geoclimatic zones, the slopes of the relationship decreased from the equatorial to the tropical and the subtropical zones, with intermediate values for the coastal samples (Table S3); however, only the difference between the equatorial and the subtropical zones was significant at the p<0.05 level. The nitrite maximum depth was in general deeper or coincident with the DCM depth, and both parameters were significantly correlated with fairly similar regression slopes for all three oceans (Fig. 4B), although the low vertical resolution of the nutrient sampling originated a substantial dispersion of the points. There was a negative relationship between total Chl a at surface (Chl_a_srf) and DCM depth, with slopes that were more negative for the Pacific than for the Atlantic and Indian oceans, according to the t test (Fig. 5A, Table S4). Chl a_tot concentration at the DCM (Chl a_DCM) was negatively correlated with the DCM depth (Fig. 5B, Table S4), with similar slopes for all oceans.

The proportion of picophytoplankton Chl a (f_pico) (Table 2) was significantly higher at the DCM, with mean values (expressed in percentages) around 70%, than at surface and the 20% light levels, where it ranged between 49% and 60% (two-way ANOVA, p<0.0001). Among oceans, the Atlantic showed lower f_pico values than the Indian and Pacific, in particular at surface and 20% PAR (two-way ANOVA, p<0.001). The mean proportion of nanophytoplankton (f_nano, Table 2) ranged from 24% to 38%, was lower at the DCM than at surface and the 20% light levels (two-way ANOVA, p<0.0001) and showed no significant differences between oceans. The relative contribution of the microplankton (f_micro, Table 2) showed ranges (expressed in percentages) from 6% to 14% at the upper two light levels and from 4% to 6% at the DCM and was significantly different between light levels (lower values at the DCM) and oceans (two-way ANOVA, p<0.0001); the lowest overall values corresponded to the Indian Ocean.

The slopes of the RMA linear regressions of the log-transformed Chl a concentration of pico-, nano- and microphytoplankton versus the log-transformed Chl a_pol (the sum of the three fractions measured on polycarbonate filters) for the separate and combined light levels ranged between 0.98 and 1.49 (Table S5). Nanophytoplankton showed the lowest slope for surface, the 20% light level and the pooled data, while the slopes of micro- and picophytoplankton were not significantly different (Fig. 6, Table S5A). The same pattern was found when Chl a_tot (from GF/F filters) was used instead of Chl a_pol (data not shown). The correlation coefficients between the proportions of the three size classes (f_micro, f_nano and f_micro) and Chl a_pol (Table S5B) were in general significant but r² did not exceed 0.23. The RMA regression of f_pico on log(Chl a_pol) had a positive slope for all light levels, while the RMA regressions of f_nano on log(Chl a_pol) were all negative and those of f_micro were either non-significant (for the surface and the 20% light level) or negative (for the DCM and the whole data set) (Fig. S1, Table S5B). Neither f_pico nor f_nano were significantly correlated with temperature (whether for separate light levels or the whole data set, data not shown). Only f_micro showed a significant but low correlation with temperature for the surface and the 20% light levels (Spearman correlation coefficients of 0.45 and 0.48, respectively, for n=127 -136).

For all light levels, the correlation coefficients between the measured micro- and picophytoplankton proportions (f_micro and f_pico, respectively) and those derived from the Hirata (2011) equations (Fig. S2) were significant, although with low r² (0.03 and 0.22, respectively, p<0.001). When light levels were considered separately (data not shown), only the correlation between the picophytoplankton proportions remained significant, but also with low r² (r²=0.15, p<0.001, r²=0.14, p<0.001 and r²=0.06, p<0.005, for surface, 20% and the DCM, respectively).

Surface temperature (SST) and stratification (σ200-σ6) were positively correlated for all oceans and regions (Table 3). Integrated Chl a (Chl a_int) values between surface and 200 m depth (Fig. S3) ranged from 19 mg m^-2 at station 141, in the subtropical North Atlantic, to 101 mg m^-2 at station 45, near the East African coast (Agulhas Current region). The correlations between the logarithms of Chl a_int and Chl a_srf were significant (p<0.05) for the whole data set and for the different oceans and geographical zones except for the coast (Table 3). Linear regression slopes of Chl a_int on Chl a_srf were not significantly different among oceans and zones (Fig. 7A, Table S4). Log(Chl a_srf) showed a significant positive correlation with SST for the Atlantic and negative correlations for the Indian Ocean and the subtropical region; log(Chl a_srf) and σ200-σ6 were also negatively correlated for the Indian Ocean, but showed significant positive correlations for the other oceans and the equatorial zone. Log(Chl a_int) was negatively correlated with SST for the tropical region; the remaining relationships between log(Chl a_int) with SST and σ200-σ6 for other oceans and zones were either positive or non-significant (Fig. 7B, Table 3).

The Malaspina cruise visited tropical and subtropical regions of the northern and southern hemispheres in general during the corresponding spring-summer period, so most stations showed stratified water columns with wide MLDs and nitraclines below 50 m. These conditions are typically associated with low Chl a concentrations at surface (from 0.03 to 0.69 mg m^-3) and vertical profile features such as deep chlorophyll and nitrite maxima. Locations with shallow MLDs and nitraclines and with relatively high Chl a_srf concentrations, which deviated from this pattern, were those associated with upwellings or divergences in the U-D regions (Figs. 2, S4) and included stations 90-96 (Pacific equatorial upwelling), 13-16 (Atlantic equatorial upwelling), 45 (Agulhas Current), 123-126 (Costa Rica or Mesoamerican Dome) and 74-78 (Eastern Great Australian Bight). The presence of these U-D zones resulted in higher average Chl a_srf and shallower average DCMs (Table 1) in the Pacific Ocean and the equatorial zone than in the other areas, as found in previous works (Weingartner and Weisberg 1991, Wyrtki 1981, Fiedler and Talley 2006, van Ruth et al. 2018). However, even in U-D areas, only five samples from the 20% and DCM depths (from stations 13, 44-45 and 122) had Chl a concentrations exceeding 1 mg m^-3. As found in previous surveys (Zhang et al. 2012), both Chl a_srf and Chl a_int were higher at the eastern (stations 79-90) than at the central Pacific ones (stations 110-126) as a result of the shallower thermocline in the Costa Rica Dome region (Figs 2, S3).

Most of our data were obtained within low latitude regions (0°-40°), which Cornec et al. (2021), based on Argo float profiles, divided into two subzones, the subtropical gyres (20°-40°), with DCM mainly due to photoacclimation, and the subequatorial region (0°-10°), with DCM profiles contributed at least in part by deep biomass maxima. HPLC analyses of Chl a performed with samples from the same sampling depths as those used in this study (Latasa et al. 2023) showed that haptophytes and Prochlorococcus were the dominant contributors to total Chl a (36% and 35%, respectively), followed by green algae (11%), Synechococcus (6.5%), pelagophytes (6.7%), dinoflagellates (3.2%) and diatoms (1.6%). With the exception of diatoms and Synechococcus, which showed a fairly homogeneous vertical distribution in the water column, most of these groups increased their pigment contribution at or near the DCM. Enumerations of nano- and microphytoplankton by optical microscopy (Estrada et al. 2016) suggested that, globally, there were no significant differences between the mean abundances of diatoms, dinoflagellates, coccolithophores and nanoflagellates among the three light levels sampled (surface, 20% PAR and DCM). A rough estimate of the average (±SD) Chl a content per cell (obtained by dividing the sum of Chl a concentrations of the micro- and nanophytoplankton fractions by the corresponding abundance of nano- and microphytoplankton cells) gave, respectively, 2.6±1.6, 3.0±2.0 and 9.1±16.8.3 pg cell^-1 for the surface, 20% surface PAR and DCM samples. Regarding picophytoplankton, the proportion of <2 µm Chl a (Table 2) assessed by filtration was similar (or only slightly higher at the DCM) for all light levels (see below), but picophytoplankton cell counts by flow cytometry (Agustí et al. 2019), including Prochlorococcus, Synechococcus and picoeukaryotes, revealed that, in general, Prochlorococcus showed cell concentration maxima some tens of metres above the DCM, while Synechococcus were more abundant at shallower levels, and picoeukaryotes peaked at the DCM depth. A rough estimation of picoplankton carbon biomass obtained by using the conversion factors of Zamanillo et al. (2019) (51 fg C cell^-1 for Prochlorococcus, 175 fg C cell^-1 for Synechococcus and 1319 fg C cell^-1 for picoeukaryotes) showed that the picophytoplankton carbon biomass maximum occurred well above the DCM at most stations (data not shown). These observations suggest that the increased Chl a concentration at the DCM was due to photoacclimation of the phytoplankton cells (see also Latasa et al. 2023) rather than to increases in cell biomass. Another rough indication was obtained from the relationships between particulate organic carbon (POC) concentrations (Pérez et al. 2006) and Chl a. The problem with this approach is that POC includes an important and variable contribution of detritus and, while some studies have found that these represent a relatively stable fraction (21%-43% for 0-200 m integrated samples for the Sargasso Sea, DuRand et al. 2001), others have reported much wider ranges (12%-97% for surface samples of diverse marine ecosystems, Graff et al. 2015). In our study, POC/Chl a_tot ratios for the stations with DCM that had POC data for both surface and DCM (Table S6) averaged 270.1±184.9 (SD) w/w for surface waters and 48.8±24.1 w/w for the DCM. Assuming a similar contribution of phytoplankton carbon to total POC for the surface and DCM, this would represent a mean Chl a content per unit cell carbon 5.5 times higher at the DCM than at the surface. This difference would be sufficient to account for the average value (5) of the ratio between Chl a at the DCM and Chl a at the surface (Table S6). These estimations further support the conclusion that the Chl a increase at the DCM was mostly due to photoacclimation.

The DCM depth was located below the mixed layer and was associated with the irradiance level (as seen by the relationship with the depth of 1% surface PAR, Fig. 3A), and the nutricline, represented in our study by the nitracline (Fig. 4A). This finding agrees with previous studies (Agustí and Duarte 1998, Estrada et al. 1993, Cullen 1982, Mignot et al. 2014) and with the view that the DCM, including both enhanced biomass and photoacclimation components, is generated by the interaction between vertically opposite gradients of light and nutrients (Margalef 1978), with reduced vertical mixing below the MLD allowing for vertical heterogeneity. It can be noted that, as remarked by Cullen (2015), the relevant light parameter should be related to appropriately averaged absolute irradiance values rather than to relative light levels. In our case, when we considered samples taken between 9:00 and 15:00 solar time, the instantaneous irradiance range at the DCM depth was relatively narrow, with a mean (± standard deviation) of 11.4±11.4 µmol photons m^-2 s^-1 (median=8.8 µmol photons m^-2 s^-1).

The pattern shown in Figure 4A, where the DCM is deeper or shallower than the nitracline when it is, respectively, above or below 100 m depth, agrees with the findings of Cornec et al. (2021) and Richardson and Bengtsen (2019). According to the latter authors, a shallower DCM than nitracline at depths below 100 m results from the interaction between light availability and the likelihood of intermittent nutrient supply from a deeper nitracline. On the other hand, a DCM deeper than the nitracline, which occured at some stations, could be explained by limitation of another nutrient, such as phosphorus, below the nitracline depth. We explored the phosphate concentration profiles to test this possibility, but the conclusions were not straightforward because phosphate gradients were less marked than those of nitrate, probably due in part to more rapid remineralization of phosphorus relative to nitrogen (Monteiro and Follows 2012). We tried two definitions of the phosphocline: A) the shallowest depth where phosphate concentrations equalled or exceeded (without interpolation) 0.35 µM (this was based on a compilation of NW Mediterranean profiles by Segura-Noguera et al. 2016); and B), the shallowest depth where phosphate concentrations equalled or exceeded 0.10 µM. As can be seen in Figure S5A and B, the phosphate concentrations ≥0.35 µM were practically always much deeper than the nitracline (original data can be consulted at https://doi.org/10.20350/digitalCSIC/16127). On the other hand, apart from several stations that had phosphate concentrations ≥0.10 µM at the surface (Fig. S5C and D), the phosphate concentrations ≥0.10 µM tended to be deeper or shallower than the nitracline (we adopted an absolute minimum difference of 10 m to define these two situations) when the DCM was respectively 10 m deeper or shallower than the nitracline. This finding supports the idea that, in certain situations, phosphorus limitation below the nitracline may lower the depth of the DCM; it also indicates that comparing the depths of the DCM and the nitracline, along with those of the clines of other nutrients, could help identify the limiting element.

The occurrence of a primary nitrite maximum at subsurface levels (Fig. 4B) has been repeatedly documented (Kiefer et al. 1976, Estrada et al. 1993, Collos 1998). The maintenance of this nitrite maximum has been attributed to both microbial nitrification and nitrite release by phytoplankton, and the relative importance of both mechanisms is still discussed, with some authors favouring the preponderance of phytoplankton excretion (Blasco 1971, Lomas and Lipschultz 2006) and others favouring nitrification by chemoautotrophs (Meeder et al. 2012, Zakem et al. 2018). Our data showed in general a nitrite maximum either deeper or coincident with the DCM, but there were some exceptions. In principle, a nitrite maximum depth coinciding with that of the DCM would suggest phytoplankton excretion, while nitrification would result in a nitrite maximum deeper than the DCM, although both mechanisms might be operative at the same time. However, as described by Lomas and Lipschultz (2006), there are a number of physical disturbance and physiological scenarios that could decouple the depths of the nitrite maximum from those of the DCM and associated variables; for example, according to these authors, a shallower nitrite maximum than the DCM could arise from transient, light-induced uncoupling of nitrate and nitrite reduction by DCM phytoplankton exposed to periodic low-level nitrate inputs or short-lived light changes at sunrise or sunset.

Non-significant (Cox et al. 1982, Estrada et al. 1993) and negative (Herbland and Voituriez 1979, Cornec et al. 2021) relationships between Chl a_DCM and DCM depth (Fig. 5B) have been previously documented; the latter situation may be related to increasing light limitation with depth.

On average, picophytoplankton was the dominant contributor at all light levels, oceans and zones (Table 2); only at a few U-D locations, such as stations 90-94 (data not shown), was the picophytoplankton proportion lower than 50%. This is an expected result, given the general oligotrophic character of the sampled locations (Marañón 2009, IOCCG 2014). Picophytoplankton contribution increased with Chl a_pol without approaching an asymptotic value (Fig. 6A-D), as found by Agustí et al. (2019) for flow cytometry counts of Synechococcus, Prochlorococcus and picoeukaryotes. This result may be explained, at least in part, by the low values of the Chl a concentrations measured in the Malaspina expedition, which (except for station 45) did not reach the concentration of the inflexion point reported by other authors around 1 mg m^-3 (Marañón et al. 2009, Brewin et al. 2019). Regarding this particular value, it should be noted that many field Chl a data sets, including our own, are derived from fluorometric measurements, which tend to overestimate the concentration of Chl a as determined from HPLC, considered the technique of choice for pigment determination (Garrido and Roy, 2015); for Malaspina, the relationship was Chl a_tot=Chl a_HPLC*1.34+25, r²=0.77, where Chl a_HPLC is the total Chl a as determined by HPLC (Latasa et al. 2023). The linear correlation between our determinations of f_pico and f_micro and those derived from the Hirata equations (Fig. S3) was significant but explained only 3% of the variance for microphytoplankton and 22% for picophytoplankton, thus limiting the usefulness of this approximation, at least in data sets with relatively narrow variability.

For all light levels, the slope of f_pico with respect to log(Chl a_pol) was positive, while the relationships of f_nano and f_micro with log(Chl a_pol) were negative or non-significant (Table S5B), so f_pico increased (and f_nano and f_micro decreased or did not change significantly) with total Chl a (Fig. S1), in contrast with the findings of Brewin et al. (2019) when similar Chl a concentration ranges were considered. However, our findings must be interpreted with caution, given the strong dispersion of the regression lines related to micro- and nanophytoplankton data. Another caveat are the potential artefacts introduced by filtration, such as the effect of biomass accumulation on particle retention (Brewin et al. 2014); however, our sequential filtration methodology was similar to that employed by Brewin et al. (2019) and it is difficult to envision why higher biomass should favour pico- but not nanophytoplankton retention.

Picoplankton contribution (in particular that of cyanobacteria) has been often reported to increase with temperature (Flombaum et al. 2013). However, it must be noted that statistical relationships with temperature often result from its covariation with other variables, such as nutrient concentration (Otero-Ferrer et al. 2018, Agustí et al. 2019), rather than from any direct effects (see next section). Within the temperature range of our data set, the lack of correlation of f_pico and f_nano with temperature (data not shown) suggests that the relative contribution of these size classes was driven by factors such as resource availability, as found by Marañón (2015).

In temperate regions, high temperatures often cause increased stratification, diminishing nutrient availability in surface waters. This leads to negative correlations between both surface temperature and stratification indices, and Chl a_srf and integrated phytoplankton biomass estimates, which include integrated Chl a (Doney 2006, Behrenfeld et al. 2006, van de Poll et al. 2013). In our latitudinally-restricted data set, the best predictor of Chl a_int for the global data set and for the various oceans and regions was Chl a_srf (Table S4). Correlation coefficients of SST and σ200-σ6 with Chl a_srf or Chl a_int were mostly non-significant. Negative correlations were found only between SST and Chl a_srf for the Indian Ocean and between SST and Chl a_int for the tropical region (Table 3). These findings agree with those of Dave and Lozier (2013), who compared estimates of stratification (from hydrographic profiles) and Chl a (from satellite) for the global tropical and subtropical oceans. They found that a negative relationship was valid for globally averaged data at interannual time scales but broke down at the basin scale. As potential explanations for these results, they pointed out that stratification by itself does not predetermine the strength of vertical mixing and that lateral inputs of nutrients from other locations could also be important. Another example of different patterns depending on the scale of observation is reported by Barton et al. (2014), based on the Continuous Plankton Recorder and accompanying observations. They concluded that physical mechanisms, such as turbulent mixing, differentiated the fates of diatoms and dinoflagellates on seasonal timescales, but did not appear to drive their longer-term variability. In our analysis, we could add the relatively small range of temperatures in the visited regions and the confounding effect of pooling together data from various water masses with different SST, stratification and phytoplankton productivity backgrounds and temporal histories. In fact, for each of the three light levels, temperature (Table S7) was significantly lower in the Indian Ocean than in the Atlantic or the Pacific (ANOVA, p<0.0001, and Tuckey test, n=32-60), while σ200-σ6, Chl a_DCM and Chl a_int (Table 1) were higher for the Pacific than for the other oceans (ANOVA, p<0.0001, and Tuckey tests, n=32-61). The implication is that global relationships of phytoplankton variables with temperature or local stratification indices as indicators of nutrient fluxes and phytoplankton growth in the surface layer must be critically assessed taking into account the structure of each data set.