Zinc systematics quantify crustal thickness control on fractionating assemblages of arc magmas

Understanding the processes leading to the broad chemical variability of arc magmas is an essential, yet not fully elucidated, issue in Earth Sciences. Here, I show that Zn–MgO–SiO2 systematics of magmatic arc rocks correlate significantly with arc thickness. Because Zn–MgO–SiO2 systematics are mostly controlled by fractionation of different mineral phases, this suggests a systematic change in the proportions of fractionating mineral assemblages depending on arc thickness. Using a mass balance model with a Monte Carlo approach, I show that Zn–MgO–SiO2 systematics can be quantitatively explained by a continuous transition from plagioclase-dominated fractionating assemblages in thin arcs to amphibole-garnet-magnetite-dominated assemblages in increasingly thicker arcs. Most likely, such a systematic change results from the increase of average depth of magma differentiation that is ultimately controlled by arc thickness. Results presented have implications on the causes of different geochemical trends in arcs, the role of arcs as H2O filters, and their association with porphyry deposits.

). The light red symbols denote poor statistical significance for the Zn-MgO regressions (see Table 1). www.nature.com/scientificreports/ arcs do not show such a decrease because they do not evolve to rocks differentiated enough (Supplementary Figure S1). Average values of zinc median contents of magmas emplaced in thick arcs (> 30 km: Mexico, Aleutians, Cascades, NVZ), in contrast, display flat to slightly declining trends with decreasing MgO down to MgO values ~ 1.5 wt%, after which Zn decreases along a steeper trend in the most differentiated rocks to an average value of ~ 40 ppm ( Fig. 1a and Supplementary Figure S1) Figure S1). The most differentiated magmas of the Lesser Antilles arc display an increase in Zn contents rather than a decrease like all other arcs (Supplementary Figure S1).

. Zn trends in magmas of intermediate thickness arcs display an intermediate behavior (Supplementary
The trend of MOR magmatic rocks is characterized by a steeper negative slope than the average trend of the thin arcs in the Zn-MgO space (Fig. 1a). The most primitive MOR basalts have similar median Zn contents as the most primitive thin and thick arc basalts (~ 75 ppm) and grow to a median Zn content of ~ 170 ppm at ~ 2 wt% MgO, that is significantly higher than the average value of thin arcs (Fig. 1a), after which Zn contents drop to a median value of ~ 100 ppm with further differentiation.
In order to quantify the differences of the Zn-MgO trends in different arcs, slopes of the linear regressions between Zn and MgO were calculated for the early differentiation segments, i.e., excluding the median values corresponding to the strong Zn decreases (or increase for the Lesser Antilles) in the most differentiated rocks of all arcs (Table 1 and Supplementary Figure S1). Thicker arcs are characterized by positive Zn-MgO slopes, whereas thin arcs are characterized by negative Zn-MgO slopes and intermediate thickness arcs have intermediate slope values (Fig. 1b). Several arcs, which do not display statistically significant correlations between Zn and MgO (e.g., Bismark-New Britain, Ryukyu, Cascades, Luzon, Honshu, Central America: Table 1), are represented by shaded symbols in Fig. 1b. The slopes so calculated display a statistically significant correlation with the thickness of the corresponding arc crust (Fig. 1b).
Also MgO-SiO 2 trends of the early evolutionary paths of arc magmas (i.e., before a break in the slope of the trend to a significantly shallower slope for MgO contents below a variable arc-dependent threshold of 2-5 wt%; Supplementary Figure S2) display different slopes, steeper in thin arcs and shallower in thick arcs (Fig. 2a, Supplementary Figure S2, and Table 1). MOR magmatic rocks display an overall steeper slope than thin arcs during early evolution in the MgO-SiO 2 space (Fig. 2a). The values of the slopes defined by the early to intermediate differentiation trend of arc and MOR magmas in the MgO-SiO 2 space display again significant correlations with the crust thickness of the corresponding arc and of MOR (Fig. 2b). Although there might be some degree of arbitrariness in the choice of the point at which the slope breaks in the MgO-SiO 2 space (especially for some arcs: Supplementary Figure S2), changing the break point to higher MgO values does not significantly change the slope of arcs in such a way to affect the correlation of Fig. 2b. In fact, inter-arc changes of such slopes are much larger than the small changes that arise from a different choice of the break point within a specific arc.
Crustal thickness control on fractionating mineral assemblages. The data reduction of the large dataset used in this study leads to results (median values) that statistically represent the most common values within a population with a dominantly normal distribution like that for the elements here considered within the ~ 0.5 wt% MgO bins. This means that the interpretation of these results is forcedly a simplification of the processes occurring in arcs, as indicated by the large distribution clouds of single rock analyses compared to the median values calculated from them for the MgO bins within each arc (Supplementary Figures S1-S2). Therefore, the processes interpreted on such a basis are first-order processes and do not exclude, within each specific arc, the occurrence of additional second or lower order processes (e.g., ref. 23 ). Such processes might be important in some arcs, where correlations of median values of elements are not statistically significant (e.g., Fig. 1b and Table 1).
The different trends displayed by magmas of distinct arcs (and MOR) in the Zn-MgO and MgO-SiO 2 spaces (Figs. 1, 2 and Supplementary Figures S1-S2) must be, to their greatest extent, the result of differentiation processes occurring within the crust because of the large SiO 2 and MgO ranges that they encompass (Supplementary Figures S1-S2). A variety of studies agree in considering differentiation of arc magmas as the complex result of various processes, including fractional crystallization 24,25 , recharge/mixing 13,26,27 , partial melting 28 and assimilation of host rocks 29 . Arguably, fractional crystallization (and to some extent partial melting, which is the opposite process of fractional crystallization) can be considered as the main process responsible for the large SiO 2 and MgO variability observed in arc magmas 25 . Superimposed on this, assimilation, mixing and recharge are also universal processes occurring in arcs that tend to homogenize the signals of fractional crystallization 27 . Figure 1 shows that Zn displays different degrees of increase or decrease during magmatic differentiation that depend on the thickness of the arc crust. Because primitive basalts have very similar values (70-80 ppm) both in arcs of different thickness and in MOR (Fig. 1a) and because the continental (72 ppm: ref. 30 ) and oceanic crust (~ 75 ppm: Fig. 1a) Zn contents also fall within this same range, wholesale assimilation of crustal lithologies (either oceanic or continental) cannot explain alone the Zn systematics observed in arcs and MOR magmas. Partial melting of crustal lithologies producing SiO 2 -rich melts could be a significant process in arcs, especially at higher depths (and therefore in thicker arcs) because of thermal constraints 31 . Mixing of basalt with such SiO 2 -rich and either Zn-poor or Zn-rich partial melts would be needed to explain the decreasing and increasing trends of Zn with MgO in thick and thin arcs, respectively.
However, almost all arcs show a kink in both the Zn-MgO and MgO-SiO 2 trends suggesting that mixing with a SiO 2 -rich and Zn-poor or Zn-rich crustal melts is not a viable explanation either. Mixing and assimilation certainly occur in arcs (there is ample isotopic, petrographic and mineral chemistry evidence for that) and is probably also a cause of the scatter of single rock analyses around the kinked trends in the Zn-MgO and MgO-SiO 2 spaces (Supplementary Figures S1-S2). However, mixing and assimilation in the crust must involve end-member magmas whose Zn-MgO-SiO 2 systematics are controlled by fractionating or restitic minerals. www.nature.com/scientificreports/ Therefore, although treating the different trends observed in arcs in the Zn-MgO-SiO 2 space as the result of fractional crystallization is an approximation, these trends ultimately tell us what are the mineral phases that are involved in producing their different slopes through combined fractional crystallization, partial melting, assimilation and mixing processes. Thus, for simplicity I will model the distinct Zn-MgO-SiO 2 trends of arcs as the dominant result of fractional crystallization during which Zn behavior shifts from incompatible to compatible for magma differentiation occurring within an increasing crustal thickness (Fig. 1a). Such a behavior should be discussed considering the partition coefficients of Zn between melt and the main minerals fractionating in arc (and MOR) magmas (i.e., olivine, plagioclase, amphibole, clinopyroxene, garnet and magnetite). A compilation of K D values from the literature (Supplementary Table S1 and Fig. 3) suggests that, among the potential fractionating phases during the early and intermediate stages of arc magma differentiation, magnetite is the one for which Zn has the highest affinity, compared to pyroxenes and particularly to plagioclase, which has very low K D values for Zn. Zn is slightly incompatible in olivine in equilibrium with basalt but becomes compatible in this mineral when the latter crystallizes from basaltic andesite and andesite melt (Fig. 3). In contrast Zn is compatible in magnetite  Figure S1). (a) From 64 , except Tonga thickness, which is from 65 , Kermadec thickness, which is from 66 , Aleutians thickness which is from 67 , and Northern Andes thickness which is from 68 . The Tonga crustal thickness here taken corresponds to the maximum crustal thickness of 65 because arc magmatism occurs in coincidence with the thickest part of the Tonga arc ( Fig. 9 in 65 ). Crustal thicknesses have been calculated by 64 using the global crustal model at 2° × 2°, CRUST 2.0, administered by the US Geological Survey and the Institute for Geophysics and Planetary Physics at the University of California 69 , which is an updated version of CRUST 5.1, a global crustal model at 5° × 5°7 0 .The model is based on seismic refraction data published up to 1995 and a detailed compilation of sediment thickness. The crustal thicknesses of 64 are within the ranges of crustal thicknesses reported in previous studies 71,72 with which they show good linear correlations (r = 0.70 with respect to crustal thicknesses of 71 , and r = 0.74 with respect to crustal thicknesses of 72 ). Oceanic crust thickness is from. (b) Attribution to a crust thickness type takes into account the 1σ uncertainty and the geochemical systematics: for instance, Bismark/New Britain has average crust thickness slightly above 20 km, but taking into account the 1 uncertainty minimum values are largely < 20 km and geochemical trends are more typical of arcs < 20 km thick. This subdivision is purely semantic and does not change the mathematical correlations. (c) errors and correlation coefficients r 2 of the regressions were calculated using the "LINEST" function in Excel.  www.nature.com/scientificreports/ already crystallizing from basalt and its compatibility strongly increases with magmatic differentiation (Fig. 3). Zn has K D values slightly < 1 for garnet in equilibrium with basaltic to andesitic melts 32 ( Fig. 3 and Supplementary  Table S1). At intermediate stages of magmatic evolution (andesite, dacite) Zn becomes increasingly compatible in amphibole, clinopyroxene (Fig. 3) and biotite (K D ~ 18 in dacitic melts: Supplementary Table S1). The onset, in the most evolved stages of arc magmas, of crystallization of biotite and magnetite, plus other accessory mineral  Table 1).  www.nature.com/scientificreports/ phases (e.g., ilmenite) for which Zn has a strong affinity, is likely responsible for the strong Zn decreases in most arcs below 2-4 wt% MgO. Only some thin arcs do not display such a decrease (South Sandwich, Kermadec, New Hebrides, Kurile), perhaps because not enough differentiated rocks occur in the databases of these arcs. Zn contents display a strong increase in the most differentiated rocks of the Lesser Antilles arc. Although these trends in the most differentiated rocks may be of interest for those specific arcs, their discussion is beyond the scope of this work which considers the Zn-MgO trends of the early to intermediate differentiating magmas, excluding the most differentiated rocks.  Figures S1-S2).

Modelling trends in the
Overall, results of the Monte Carlo simulations of fractionation processes applied to Zn-MgO-SiO 2 systematics (Supplementary Table S4) show that the fractionating mineral assemblages gradually shift from plagioclasedominated in thin arcs to amphibole-, magnetite-, and garnet-dominated in increasingly thicker arcs (Fig. 4). Clinopyroxene and olivine do not significantly correlate with crustal thickness, suggesting that these minerals act as buffers in the fractionating assemblages. High proportions of both olivine and plagioclase in fractionating magmas of thin arcs are needed to explain on one hand the steep decrease of MgO at low SiO 2 values (olivine effect, because of SiO 2 /MgO < 1 in olivine: Supplementary Table S5) and on the other the broadly incompatible behavior of Zn (plagioclase effect, due to the very low K D values of Zn in plagioclase: Fig. 3). In contrast, the  Table S5) and with the slightly compatible behavior of Zn (due to the K D values of Zn in these minerals around or slightly > 1: Fig. 3). These results agree with petrographic observations that phenocrysts in relatively primitive thin arc rocks (e.g., Mariana, South Sandwich: refs. 23,34,35 ) consist of olivine, plagioclase and pyroxenes (with virtually no amphibole), whereas relatively primitive rocks and cumulates of thick arcs (e.g., Ecuador, Mexico, Cascades, Central Andes: refs. [36][37][38][39] ) contain variable amounts of amphibole. They also support and quantify the suggestion that extensive cryptic amphibole (and garnet) fractionation may occur in arcs 40 , especially in increasingly thicker ones.
Crust thickness control on fractionating assemblages. The systematic correlations of the changing proportions of fractionating amphibole, garnet, magnetite, olivine and plagioclase with changing crustal thickness are consistent with experimental petrology results carried out on hydrous basaltic to andesitic melts fractionating at different pressures [41][42][43][44][45][46][47][48] . These results show that plagioclase, clinopyroxene and olivine are the main minerals crystallizing at the liquidus of hydrous mafic melts at low pressures (e.g., < 0.1-0.3 GPa depending on H 2 O content) whereas amphibole, garnet, clinopyroxene, and magnetite crystallize at or near the liquidus of hydrous mafic melts at high pressures (> 0.8 GPa). The data presented and discussed here suggest that there is a gradual and continuous crustal thickness-controlled change in the proportions of fractionating minerals between the above two end-member assemblages that results in the systematic changes of SiO 2 -MgO-Zn trends of arc magmas.
The preferential fractionation of amphibole and garnet in thicker arcs is unlikely to result only from higher H 2 O contents in the primitive basalts of thicker arcs 10,11,14 . In fact, available data point to similarly variable H 2 O contents of primitive arc basalts, comprised between 0.5 and 7wt% 49,50 , independent of their thickness 49 . A similar average H 2 O content (3.9 ± 0.4 wt%, 1SD) for primitive arc basalts has been suggested based on H 2 O contents measured in melt inclusions in olivine and other mafic minerals 49 , although such contents may be questioned because of post-entrapment hydrogen loss or gain 51 . Regardless, the occurrence of variable amounts of garnet required for the thicker arcs by the modelling here presented indicates pressures of crystallization of at least 0.8 GPa, even in H 2 O-rich magmas 43 . A thicker crust will result, as suggested by the data above discussed, in an average magma evolution at deeper levels 8 which will increase H 2 O contents in the residual magma more significantly than magma evolution at shallower levels already in the early fractionation stages (Supplementary Note 2 in Supplementary Information), because of the strong pressure dependency of H 2 O solubility in silicate melts 52 . This will, in turn, further stabilize the fractionation of amphibole and garnet from relatively unevolved basaltic andesite and andesite magmas at mid-to lower crustal levels 42,43 . If a systematic H 2 O enrichment in primary basalts of thick arcs does occur 11,14 , this would further enhance amphibole and garnet fractionation in thick arcs.
The variable crustal thickness-controlled proportions of the fractionating mineral assemblages obtained by modelling Zn-MgO-SiO 2 arc systematics also correlate with the median Fe 2 O 3tot values at 4-6 wt% MgO of arcs (Fig. 5), which are a measure of the tholeiitic versus calc-alkaline character of arc magmas 7,53 . Overall, these data suggest that first order processes of differentiation observed in arc magmas and the generation of a continuous transition from tholeiitic to calc-alkaline character are the result of pressure-dependent stability of different fractionating mineral phases in hydrous magmas (see also ref. 25 ), which is ultimately controlled by crustal thickness. A thicker crust results in an average evolution of arc magmas at deeper crustal levels 8,54 and, therefore, is characterized by fractionation of higher-pressure assemblages (olivine, clinopyroxene, amphibole, garnet, magnetite) from the hydrous basalts typical of the arc environment. This leads to the development of a typical calc-alkaline trend in associated arc magmas (Fig. 5). In contrast, a thinner crust results in an average shallower crustal evolution of arc magmas characterized by the fractionation of the assemblage olivine, plagioclase, pyroxenes from such hydrous basalts. This leads to the development of dominantly tholeiitic trends in associated arc magmas (Fig. 5). It is important to highlight that the results presented here suggest that there is a www.nature.com/scientificreports/ continuum between these two extremes without a neat subdivision between calc-alkaline and tholeiitic trends, but rather a gradual transition, that is controlled by the role that crustal thickness of the arc has on the proportions of fractionating minerals. This is consistent with the development of calc-alkaline trends also at intermediate to relatively low pressures under H 2 O-saturated conditions 44 . H 2 O contents on the high side of the 0.5-7 wt% range of primitive arc basalts, as discussed above, may thus result in subordinate calc-alkaline trends even in thin arcs otherwise dominated by tholeiitic trends 35 .
On the other hand, it is significant that MOR magmas, which are almost anhydrous 55 , fall on the continuation of the trends of Figs. 1b and 2b suggesting that Zn-MgO and MgO-SiO 2 systematics seem to be rather insensitive to the largely different H 2 O contents of primitive basalts in MOR (~ 0.1-0.2 wt%: ref. 55 ) and thin arcs (~ 0.5-7 wt% 49,50 ) and that crustal thickness seems to be the main controlling factor on the different Zn-MgO-SiO 2 systematics of magmas in these distinct settings.

Discussion
The results above discussed have several implications for large-scale processes associated with arc magmatism, encompassing Zn contents in the mantle, the crust role in modulating the H 2 O flux from mantle to Earth surface, and the formation of porphyry Cu deposits.
The most primitive basalts from both thick and thin arcs and from MOR have similar Zn contents (~ 75-80 ppm: Fig. 1a). This suggests that, like Cu 56 , arc basalts and MORB derive from a similar mantle in terms of Zn contents and that Zn, like Cu 57 , is not significantly enriched in the mantle wedge by subductionrelated processes. A possibility allowing for a Zn flux from the subducted slab would be that the mantle wedge be depleted in Zn compared to MOR mantle (Fig. 6a). However, this seems to be inconsistent with available data suggesting similar Zn contents for both Primitive and Depleted Mantle (~ 55 ppm: https://earthorg/GERM) and even higher Zn contents in Enriched Mantle types (> 100 ppm 17 ). Alternatively, differential partial melting in subduction versus MOR settings ("Methods" section) could possibly be compensated by a Zn flux from the slab in the subduction setting if mantle wedge-derived basalts were Zn-depleted with respect to MORBs. However, also this seems to be unlikely. In fact, using available partition coefficients for olivine, clinopyroxene and orthopyroxene 17 , that allow calculating the bulk partition coefficient between basaltic melt and the above mentioned lherzolite minerals, it results that Zn is only slightly incompatible during mantle melting (see "Methods" section). It follows that the 75-80 ppm content in a primary mantle-derived basalt is quite insensitive to the melt fraction, using either batch melt or fractional melt models (Fig. 6b). In contrast to the similar Zn contents of primitive basaltic rocks in arcs and MOR, primitive Hawaii basalts display a significant Zn enrichment www.nature.com/scientificreports/ (> 100 ppm), which is consistent with their derivation from an enriched mantle source 22,58 compared to that sourcing basalts in arcs and MOR (Fig. 1a).
The results of this work also indicate that the suggested role of amphibole as a crustal filter of mantle-derived water is modulated by the crustal thickness of the arc: in other words, not all arcs act as a crustal sponge for H 2 O. In fact, results here presented suggest that intermediate magmas in the thinnest arcs carry towards the surface > 99% of the initial H 2 O content (e.g., average ~ 4 wt% 49 ) of their basaltic parent (because very little H 2 O is lost to the trivial amounts of amphibole crystallizing in thin crust: Fig. 7 (Fig. 8), which is thicker than that of the thinnest intraoceanic arcs (Table 1). Therefore, magmas in such thin arcs exsolve and loose water since the early stages of differentiation because they cannot evolve at depths high enough to allow them to retain in solution the H 2 O they carry from the mantle during differentiation ( Fig. 8; Supplementary Note 2 in Supplementary Information). Thus, the mantle-derived H 2 O is nearly completely fluxed towards the surface in thin arcs (Fig. 8).
In contrast, primitive basalts in thick continental arcs can lose up to ~ 10% of their initial H 2 O (e.g., ~ 4 wt% 49 ) to amphibole crystallized in the crust (Fig. 7 and Supplementary Table S5). This implies the formation of progressively more abundant amphibole-rich cumulates in the crust of increasingly thicker arcs. Therefore,  www.nature.com/scientificreports/ only in thick arcs a significant portion of mantle-derived H 2 O is, at least temporarily, locked in amphibole-rich cumulates. Such structurally-bound H 2 O may subsequently be released during ascent of magma incorporating cumulate amphibole 39 or during metamorphism to promote dehydration-assisted crustal melting or source fluids that may be at the origin of different types of ore deposits 60 .
The data here presented and discussed also provide quantitative explanations for the link between various geochemical systematics of arc magmas (e.g., Cu and Sr/Y 7-9 ) and arc thickness-controlled fractionation of different mineral assemblages. The systematic loss of Cu in intermediate magmas of increasingly thicker arcs could be the result of continuous iron depletion in this setting 61 due to fractionation not only of magnetite 7 and garnet 61 , as previously suggested, but also of abundant amphibole (Figs. 5 and 9a) as recently suggested by ref. 62 : fractionation of all these minerals drive the evolution of thick arc magmas into the calc-alkaline field. A dominant proportion of amphibole in the fractionating assemblage of thick arc magmas (Fig. 4a,b) is also consistent with the dominant spoon-shaped REE patterns of thick arc magmas 62 . Also the progressively higher Sr/Y values in intermediate magmas of increasingly thick arcs 8,9 can be quantitatively explained by the increasing amounts of fractionating amphibole plus garnet (Fig. 9b) and decreasing amounts of fractionating plagioclase in thicker arcs. All these inter-correlations suggest an overarching role played by crustal thickness-controlled differential fractionation of amphibole plus garnet, plagioclase and magnetite in the development of variable Sr/Y and calc-alkaline signatures in arc magmas. As already pointed out by ref. 8 , high Sr/Y magmas display the strongest calc-alkaline affinities (i.e., lowest Fe 2 O 3tot values at MgO contents between 4 and 6 wt%).
Despite the apparent negative effects of the thick arc setting on H 2 O and Cu contents of residual thick arc magmas discussed above, the latter are the most fertile for the formation of porphyry Cu deposits because they compensate such losses with a deeper crust evolution of the magmas 59 . This leads to significant magma volume accumulation through time in the lower to mid-crust, with such magma being characterized by high H 2 O concentrations 59 because of the pressure dependency of H 2 O solubility in silicate magmas 52 ( Fig. 8; Supplementary Note 2 in Supplementary Information). In fact, in the thickest arc settings, residual intermediate magmas, despite losing ~ 10% of the initial H 2 O to amphibole crystallizing in the crust (Fig. 7), still hold ~ 90% of the average initial mantle-derived (e.g., ~ 4 wt%) H 2 O content 49 59 . These data could finally explain the association of Au-rich porphyry Cu-Au deposits with thinner island arcs (e.g., Indonesia, Papua New Guinea, Philippines: ref. 4 ) which would be favored by the early H 2 O exsolution typical of thin arc magmas (Fig. 8). Such early fluid exsolution, during the magma differentiation process, allows Au partitioning into the fluid phase before magmatic sulfide saturation, which would strongly deplete Au in the residual magma and make Au-rich porphyry mineralization impossible 63 .

Methods
Arc crustal thickness. Average crustal thicknesses of arcs and associated uncertainties were taken from Zellmer (2008), except the thickness of Tonga 65 , Kermadec 66 , Aleutians 67 , and Northern Andes 68 . The Tonga crustal thickness here taken corresponds to the maximum crustal thickness of ref. 65 because arc magmatism occurs in coincidence with the thickest part of the Tonga arc (Figure 9 in ref. 65 ). Crustal thicknesses have been calculated by ref. 64   www.nature.com/scientificreports/ ranges of crustal thicknesses reported in previous studies 71,72 with which they show good linear correlations (r = 0.70 with respect to crustal thicknesses of ref. 71 , and r = 0.74 with respect to crustal thicknesses of ref. 72 ). Oceanic crust thickness is from ref. 73 .
Data collection and treatment. Geochemical data of bulk volcanic rocks (N = 42,600) from 21 recent arcs were collected from the Georoc database (http:// georoc. mpch-mainz. gwdg. de/ georoc/; Supplementary Data File 1). The Central Volcanic Zone of the Andes was excluded because of the very large thickness of the crust that biases the correlations between geochemical parameters and arc thickness (see also ref. 10 ). The Izu Bonin arc was excluded because of the extensive occurrence of boninitic rocks that are formed through different processes than typical arc basalts in the other arcs. As in ref. 7 , to reduce the bias induced by outliers and to extract information on general trends, median values of Zn, SiO 2 , and MgO for subpopulations corresponding to bins of 0.5 wt% MgO were calculated (Supplementary Data File 1). When less than 10 data were available for one of the investigated elements within the 0.5 wt% MgO bin, the MgO interval was extended to a higher value (e.g., 1 or 1.5 wt%) to incorporate more values of that element. For comparison with arc systematics, data were also collected for MORB (https:// www. earth chem. org/; N ~ 24,000) and for Hawaii (http:// georoc. mpch-mainz. gwdg. de/ georoc/; N ~ 5000), and treated in the same way as for arcs. Linear correlations for the median arc values in the Zn-MgO and MgO-SiO 2 spaces were detected for the arc products going from the most primitive rocks to variably evolved rocks, depending on the arc (Supplementary Figures S1-2). Statistically significant linear correlations in the Zn-MgO space were detected down to variably low MgO values ~ 0-4 wt% (Supplementary Figure S1 and Table 1), after which, in most arcs, Zn drops to low values. Statistically non-significant correlations are highlighted in Table 1.
The linear correlations considered in the MgO-SiO 2 space were those regarding the early to intermediate stages of magmatic evolution (e.g., for MgO > 2-5 wt%). Below MgO values in the 2-5 wt% range, depending on the arc, the more differentiated median values displayed a visible change in the slope with respect to the less evolved median values (Supplementary Figure S2).  Table S2) was changed by subtracting variable proportions of 6 typical fractionating minerals in arc and MOR magmas (olivine, clinopyroxene, amphibole, plagioclase, magnetite, garnet). The objective of the model was to constrain the statistically most probable fractionating mineral assemblage (in terms of mineral proportions) and the extent of fractionation (residual melt fraction).

Modelling the linear trends in the tridimensional
For each arc the composition of the most primitive median value was taken as that of the parental melt (Supplementary Table S2 and Supplementary Figures S1-S2). Sometimes, when the median values showed some scatter on the parent side, the parent compositions were allowed to vary within a tight range (< ± 0.2 wt% for SiO 2 and MgO, ≤ 4 ppm for Zn; Supplementary Table S2). The target values were the compositions of the most evolved median values (i.e., the points with the lowest MgO content) of the individual linear MgO-SiO 2 and Zn-MgO trends, i.e., the last points of these trends on the low MgO side before the change in the slopes (Supplementary Figure S2; target compositions in Supplementary Table S2). The target compositions were also allowed to vary within < ± 0.2 wt% for SiO 2 and MgO and ≤ 4 ppm for Zn (Supplementary Table S2). The model was run using a Monte Carlo approach, i.e., besides the small ranges of parent and target compositions discussed above, also the mineral compositions were allowed to vary randomly within given ranges (Supplementary Tables S3-S4). MgO and SiO 2 mineral composition ranges were derived from experimental petrology and were typical of those minerals fractionating in basaltic to andesitic magmas (Supplementary Table S3). The Zn contents in those same minerals were instead modelled using a range of Zn K D values for those minerals crystallizing from basaltic to andesitic magmas (Supplementary Tables S1 and S3).
The model was initially run (5 million simulations) leaving a large degree of freedom for the proportions of all potential fractionating minerals (i.e., 0-0.7 for plagioclase, amphibole, clinopyroxene, olivine, 0-0.3 for garnet and 0-0.15 for magnetite) and for the residual melt fraction (20-70%). The 5 million simulation runs were carried out for these broad ranges between 15 and 20 times for each arc to identify the most recurrent proportions of minerals and residual melt fractions. After this initial step, the ranges of fractionating minerals were narrowed down progressively to narrower ranges around the median values obtained in step 1 until a variably high number of successful solutions were obtained (depending on the arc), most of the times with a normal distribution (i.e., average ~ mean value: Supplementary Table S2) of all parameters involved (mineral proportions, residual melt fraction). Then, 5 million simulation runs, corresponding to the conditions (mineral proportions and residual melt fraction ranges) returning the highest number of solutions, were repeated five times for each arc and an average value with associated standard deviation was calculated from those 5 repeats (Supplementary Table S4; Supplementary Data File 2).
It is important to highlight that the model was run in order to obey simultaneously to the constraints imposed by both the Zn-MgO and MgO-SiO 2 trends (in a tridimensional MgO-SiO 2 -Zn space). This reduces significantly the number of successful solutions but at the same time provides more stringent constraints on mineral proportions and residual melt fractions.
Modelling of Zn contents in basaltic melts from partial mantle melting. The Zn content of melt from mantle melting was calculated for both batch and fractional melting (Fig. 6b)  www.nature.com/scientificreports/ where Zn melt is the Zn concentration in the melt (in ppm), Zn mantle is the Zn concentration of the mantle (55 ppm or 30 ppm in the calculations), K D−bulk is the bulk partition coefficient for Zn between mantle lherzolite and melt, and F is the melt fraction. More than 5000 simulations were run using the above equations and allowing random variations of F between 0.05 and 0.3 and of K D−bulk between 0.5 and 0.7. The range of F encompasses potential melt fractions in the sub-arc and sub-MOR mantle 74 whereas the range of K D−bulk is a common range of values based on olivine, clinopyroxene and orthopyroxene partition coefficients between melt and peridotite 17

Data availability
All data needed to evaluate the conclusions in the paper are present in the paper and/or in the Supplementary Information.