not analyzed. The origin of sulfur in these fluids is the source water, together with volcanic gas and rock leaching. The concentration of SO₄ is controlled by the source water composition and the degree of leaching from rocks and sediments, but can also be influenced by anhydrite saturation in some cases (Fig. 4.37a; Stefánsson and Arnórsson 2002) through the reaction

$$ \text{Anhydrite} = \text{Ca}^{2+} + \text{SO}_4^{2-} \qquad (4.97) $$

Regarding aqueous sulfide, it is commonly assumed to be controlled by equilibrium with sulfur containing mineral buffers (Fig. 4.37), for example reactions involving pyrite, pyrrhotite and magnetite (PPM buffer):

$$ \text{Pyrite} + 2 \text{Pyrrhotite} + 4 \text{H}_2\text{O} = \text{Magnetite} + 4 \text{H}_2\text{S} \qquad (4.98) $$

or more complex reactions among minerals like epidote and prehnite (PPPE) (Stefánsson and Arnórsson 2002):

$$ \text{Pyrite} + \text{Pyrrhotite} + 2 \text{Prehnite} + 2 \text{H}_2\text{O} = 2 \text{Epidote} + 3 \text{H}_2\text{S} \qquad (4.99) $$

The concentrations of sulfur species in surface hydrothermal fluids are very variable. Hot springs with alkaline pH values that are formed upon boiling of reservoir fluids have similar dissolved sulfate but lower dissolved sulfide concentrations relative to parent reservoir fluid. Other intermediate species, particularly thiosulfate, have been observed in such waters, with concentrations ranging on a scale of ppb to few ppm. These intermediate sulfur species are considered to be produced upon oxidation of dissolved sulfide at alkaline pH values. Thiosulfate may also form upon oxidation and hydrolysis of native sulfur and dissolved polysulfides, the latter being formed upon oxidation of dissolved sulfide at acid to mildly alkaline pH values (Xu et al. 1998; Kaasalainen and Stefánsson 2011b). Lastly, thiosulfate may also form upon hydrolysis of SO₂ of magmatic origin (Giggenbach 1987). These oxidation and disproportionation reactions may also involve other intermediate sulfur oxidation states, for example dissolved sulfite and polythionates (Xu et al. 2000; Kaasalainen and Stefánsson 2011b).

In steam-heated acid hot springs, the concentration of sulfate can be very high, up to a few thousand ppm. Dissolved sulfide in reservoir fluids partitions into the vapor formed upon depressurization boiling when fluids ascend to surface resulting in H₂S enriched vapor. At surface, condensation of such vapor and its mixing with shallow groundwater and surface water followed by oxidation result in enrichment in dissolved sulfate (Fig. 4.38). The low pH further enhances dissolution of many rock-forming elements resulting in high metal content of many of these acid waters (Giggenbach 1987, 1997; Hedenquist et al. 1993, 1994; Markússon and Stefánsson 2011; Kaasalainen and Stefánsson 2012).

The concentration of H₂S in the vapor phase at surface discharged from boreholes and fumaroles depends on the reservoir concentrations and the nature and degree of boiling, generally
being in the range of a few ppm to 100s ppm. Typically, H₂S quantitatively (>90%) partitions into the vapor phase upon initial boiling resulting in high concentrations. Prolonged boiling, however, results in a decrease in H₂S concentrations as the vapor fraction increases.

In deep-sea geothermal systems, circulating seawater results in hydrothermal vent fluids being emitted into cold seawater. Hydrothermal vent fluids contain elevated chloride concentration, similar to or higher than seawater. Dissolved sulfide is the dominant form of sulfur in such fluids with low to insignificant amounts of sulfate. Sulfur sources in hydrothermal vent fluids are similar as for terrestrial geothermal systems and include leaching of sulfide present in crustal host rocks and sediments, reduction of seawater-derived sulfate to hydrogen sulfide, and magmatic sulfur volatiles. Mixing of vent fluids with seawater usually results in metal sulfide precipitation and deposition. Moreover, the heating up of seawater sulfate in the recharge zone of the systems, together with retrograde solubility of anhydrite, may further result in deposition of calcium sulfate.

### 4.5.2 Magmatic-hydrothermal fluids

Magmatic-hydrothermal systems include deposits from the porphyry family (porphyry Cu-Mo-Au deposits and associated skarn, Cordilleran, high- and intermediate-sulfidation epithermal deposits), vein-type and Sn-W skarn deposits, as well as iron-oxide copper gold (IOCG) deposits. Various fluid types are involved in mineralization processes in these systems (Table 4.2; Kouzmanov and Pokrovski 2012 and references therein). They may be classified into four types according to their origin (Table 4.2): i) supercritical fluids that separate from hydrous magma, ii) and iii) high to low-density vapors and hypersaline liquids (brines), both generated by phase separation of the supercritical fluid upon its ascend, typical for proximal high-temperature parts of the systems, and, finally, iv) lower-temperature and lower-salinity aqueous fluids, typical for more distal parts of these systems.

A detailed interpretation of metal concentrations in fluid inclusions from magmatic-hydrothermal systems has been made by Kouzmanov and Pokrovski (2012), based on a large LA-ICPMS dataset, along with very limited data for sulfur. Over the last decade, the sulfur dataset has been largely extended owing to recent publications (Table 4.2, Supplementary Table 4.S1). Figure 39a,b compiles sulfur concentrations in the four major types of fluid inclusions from magmatic-hydrothermal systems as a function of temperature and salinity, as measured by LA-ICPMS. Sulfur concentrations vary within more than three orders of magnitude – from 100 ppm (its typical detection limit) to ~100,000 ppm. Sulfur concentrations from high-temperature fluid inclusions (supercritical, brine and vapor types) are independent of inclusion homogenization temperature and salinity. Low-temperature and low-salinity fluid inclusions (aqueous type) show an overall tendency
of decreasing sulfur concentrations with decreasing temperature (Fig. 4.39a). Thus, the temperature trend mostly reflects the cooling of the magmatic system. Such cooling results in a large decrease of metal sulfide solubility, which is the major phenomenon in the magmatic-hydrothermal environment. Thus, the 2–3 orders of magnitude decrease in sulfur concentration, parallel with up to a 4–5 orders of magnitude decrease of metal concentration in the fluids in individual systems, is due mainly to direct sulfide mineral precipitation from the fluid upon cooling (e.g., Fig. 4.25a; Kouzmanov and Pokrovski, 2012 and references therein). This sulfide formation mechanism is accompanied by that of sulfidation of Fe(II)-bearing mafic minerals (e.g., biotite; hornblende) in the host intrusions and wall rock. Cooling is generally accompanied by a salinity decrease due to fluid mixing with external waters, resulting in a further decrease of metal solubility. Sulfur often remains in excess of metals (see below and Fig. 4.40). The apparent sulfur decrease with increasing salinity observed in some aqueous-type inclusions (Fig. 4.39b) is likely to reflect the origin of this type of inclusions. Many of them are the product of condensation of S-rich supercritical fluid or vapor of relatively low salinity (<5–10 wt% NaCl) at the closer-to-surface parts of the magmatic-hydrothermal systems (e.g., Heinrich 2005; Pokrovski et al. 2013a). The total sulfur budget of a magmatic-derived fluid thus controls the degree of sulfide precipitation on cooling (Heinrich 2006; Seo et al. 2009). Comparing the amount of total sulfur and water, necessary to precipitate all major metal sulfides in a polymetallic vein within a porphyry-centered district, with the measured sulfur concentrations in fluid inclusion assemblages from the same vein, Catchpole et al. (2011) concluded that ore-forming fluids were enriched in sulfur compared to metals. Their findings thus demonstrate a largely sufficient amount of sulfur to precipitate all of the available metals from the fluid as sulfide minerals, despite possible loss of part of sulfur due to H₂S degassing and sulfidation of wall rock.

Figure 4.40 summarizes the relationships between sulfur and selected metal concentrations of the four fluid inclusion types in magmatic-hydrothermal systems. As mentioned above, most of the inclusions from the supercritical, vapor and aqueous types of fluids are significantly enriched in sulfur compared to most metals (plotting below the 1:1 mole ratio line). In contrast, brine inclusions systematically show an excess of iron over sulfur (Fig. 4.40a), in agreement with the increasing stability of Fe chloride complexes and therefore iron minerals solubility in highly saline fluids (see section 4.4.6 and Fig. 4.25b). Interestingly, a significant part of the data on the Cu vs. S plot for brine and vapor inclusions (Fig. 4.40b) cluster around the 2:1 line (when converted to mole ratio), corresponding to the chalcopyrite stoichiometry, CuFeS₂. This characteristic feature of the Cu-S relationships is due to a post-entrapment rapid inward diffusion of Cu⁺ through the quartz host structure from the external fluid. This diffusion is compensated by outward diffusion of H⁺ and/or Na⁺ from the inclusion and is mainly controlled by the initial sulfur concentration in the fluid
inclusion (e.g., Seo et al. 2011; Lerchbaumer and Audétat 2012; Pokrovski et al. 2013a; Seo and Heinrich 2013 for details of the mechanism). In contrast, due to lower diffusion coefficients, other base metals (Fe, Zn, Pb) and gold are much less affected by such a diffusion process. The post-entrapment enrichment of Cu is more pronounced in vapor-type inclusions resulting in apparent vapor-liquid partitioning coefficients of Cu up to 100, as was inferred from cogenetic vapor-brine inclusion assemblages (see Kouzmanov and Pokrovski 2012 for a compilation). Such vapor-brine inclusion data resulted in overestimation of the role of vapor on Cu transport in porphyry systems in some earlier studies (e.g., Heinrich et al. 1992, 1999; Audétat et al. 1998; Cauzid et al. 2007; Seo et al. 2009). However, extensive experimental measurements of vapor-liquid distribution of metals at magmatic-hydrothermal conditions in laboratory water-salt-sulfur systems (Pokrovski et al. 2013a; references therein) clearly demonstrated that Cu partitions always in favor of the brine phase (typical $D_{vap/liq}$ (Cu) values of 0.01–0.1), along with all other base metals (Fe, Zn, Pb, Ag) and metalloids (As, B, Sb, Si). The only exception is Au¹ and Pt¹¹ that are able to be enriched in the vapor phase compared to the coexisting brine, due to formation of volatile hydrosulfide complexes (see Pokrovski et al. 2013a for a detailed overview of the metal vapor-phase transport). In general, sulfur concentrations in fluids from magmatic-hydrothermal systems do not show clear correlations with other metals and metalloids. A lack of correlation does not mean, however, the absence of sulfur control on those metals. Given the multiplicity of parameters simultaneously affecting metal solubility in the magmatic-hydrothermal systems such as temperature, pressure, redox, salinity, acidity and sulfur speciation and concentration (see section 4.4.1 and Fig. 4.25) along with limited inclusion datasets, the effect of sulfur may be obscured in such systems.

The key feature of supercritical, vapor and aqueous types of fluids in magmatic-hydrothermal systems is significant sulfur excess over metals forming sulfide minerals, by a factor of 10 on average (Supplementary Table S1). This excess is mostly conditioned by the fluid source, originated from magma and carrying together metals and sulfur (mainly as H₂S and SO₂), along with its subsequent evolution upon its ascent through the crust, which is mainly controlled by cooling and decompression (e.g., Figs. 20, 25 and 30; Hedenquist and Lowenstern 1994; Hedenquist 1995; Sillitoe 2010; Kouzmanov and Pokrovski 2012; Fontboté et al. 2017, for an overview). As to the fate of sulfur, these combined processes result in a number of phenomena i) precipitation of part of sulfur with Fe, Cu, Ag, Au, Zn, Pb, As as sulfide ore minerals (pyrite, chalcopyrite, bornite, and, at lower temperature, sphalerite, galena, sulfosalts, e.g., reactions 4.56–4.60); ii) enrichment in volatile sulfur species (H₂S and SO₂) of the vapor phase upon vapor-brine unmixing (reactions 4.23 and 4.26), whereas base metals remain more enriched in the brine; iii) transfer or sulfur-rich vapor phase to epithermal parts of the system followed by condensation (resulting in aqueous-type
inclusions) and, sometimes, boiling closer to the surface, depending on the temperature-pressure gradient; iv) hydrolysis of magmatic SO₂ in aqueous solution upon cooling, according to the disproportionation reaction:

$$4 \text{SO}_2 + 4 \text{H}_2\text{O} = 3 \text{SO}_4^{2-} + 6 \text{H}^+ + \text{H}_2\text{S} \quad (4.100)$$

This important reaction provides additional SII⁻ necessary to form metal sulfides, the SVI necessary to form sulfates such as alunite and anhydrite common in these systems, and significant acidity (H⁺) that may greatly facilitate base metal transport in the form of chloride complexes (e.g., reactions 4.56–4.60), in particular through altered rocks of low pH buffering capacity (e.g., Hedenquist et al. 2000; Heinrich 2005; Kouzmanov and Pokrovski 2012; Reed et al. 2013).

In contrast to surface geothermal fluids whose sulfur concentrations may be reasonably approximated by the solubility of anhydrite (for sulfate sulfur) and of the pyrite-pyrrhotite(-magnetite/epidote/phengite) assemblages (Fig. 4.37), sulfur concentrations analyzed in fluid inclusions of magmatic-hydrothermal fluids as well as in metamorphic and sedimentary fluids (see below and Fig. 4.41 and 4.42), appear in significant excess of those in equilibrium with the most common sulfur and oxygen mineral buffers in the upper crust such as pyrite-pyrrhotite-magnetite (PPM) and pyrite-magnetite-hematite (PMH) (Fig. 4.43). It is only at the highest temperatures recorded by the fluid inclusions (>500 °C) or pressures below 500 bar that such buffers may approximate the sulfur concentrations recorded in natural fluid inclusions. Note that sulfur concentrations in equilibrium with PPM and PMH are almost insensitive to variations in salinity and acidity, in contrast to most metal concentrations (Fig. 4.25). The significantly higher sulfur concentrations from magmatic-hydrothermal systems than those of the PPM and PMH buffers are thus mainly a result of the excess of sulfur over iron in the original fluids, and the lack of significant fluid-rock interactions that may occur in some settings where the porphyry system is overprinted by an epithermal system on already altered rocks due to significant acidity generated by reaction (4.100) on cooling (e.g., Heinrich 2005; Kouzmanov and Pokrovski 2012; Simon and Wilke 2025).

### 4.5.3 Metamorphic fluids

Metamorphic fluids, formed by extraction of small amounts of volatiles from large crustal terrains, have rock-buffered major element and isotopic compositions because they are controlled by equilibria with the minerals of their source rocks (Yardley 1983; Cox et al. 1987; Ridley and Diamond 2000). Orogenic gold deposits which occur in metamorphic terrains are thought to involve ore fluids produced by metamorphic devolatilization (e.g., Goldfarb et al. 2005). The behavior of sulfur in metamorphic processes is discussed in more detail in this Book by Schwarzenbach and Evans (2025) and Harlov (2025). Here we focus on direct evidence of metamorphic fluid
compositions from fluid inclusions. These data are provided by recently published LA-ICPMS analyses of total sulfur concentration in fluid inclusions from gold mineralization associated with late metamorphic quartz veins and Alpine fissure veins (Marsala et al., 2013; Miron et al., 2013; Rauchenstein-Martinek et al., 2014, 2016) and will be compared here with thermodynamic predictions of sulfur solubility and speciation.

Fluid inclusions from metamorphic systems vary in composition from dominantly aqueous – in sub-greenschist and greenschist facies host rocks, to aqueous-carbonic inclusions – in amphibolite facies rocks. Volatile contents (CO2, H2S) in the fluid inclusions systematically increase as a function of increasing metamorphic grade, indicating that the fluids have been produced by prograde devolatilization reactions. Reported temperatures of homogenization range from 80 to 300 °C, and salinity varies between 0.4 and 10.3 wt% NaCl eq. (Table 4.2; Fig. 4.39c,d). However, the true fluid entrapment temperatures may be several 100 °C higher. Sulfur concentrations vary within two orders of magnitude, from 10s to 1000s ppm, and do not show correlations with temperature, but tend to have generally higher values in lower-salinity fluid inclusions (Fig. 4.39c,d). Metals are strongly depleted in the fluids compared to sulfur (in general, one to two orders of magnitude; two to four orders of magnitude for Au). Metal concentrations in metamorphic fluids are several orders of magnitude lower than those in fluids from magmatic-hydrothermal systems (Fig. 4.40, 4.41, Table 4.2). Positive correlations between S and As concentrations are often recorded, arsenic representing the largest data set among metals and metalloids (Fig. 4.41c). The As-S trends imply a common solubility control on both elements by dissolution-precipitation of As-bearing pyrite and arsenopyrite, which are the most common sulfide minerals in such systems. Gold concentrations do not clearly correlate with S in the fluids, and show a large scatter, between 0.001 and 1 ppm Au for sulfur concentrations ranging from <10 to 1000s ppm (Fig. 4.41d). Gold concentrations are correlated neither with As nor Ag concentrations (e.g., Rauchenstein-Martinek et al. 2014). Although gold hydrosulfide complexes such as AuHS⁰ and Au(HS)₂⁻ (and eventually Au(HS)S₃⁻ at high temperatures and S concentrations) are the gold transporting species in low salinity and near-neutral pH typical of metamorphic fluids (see sections 4.4.1 and 4.4.4), the increase in sulfur concentrations with metamorphic grade does not result in respectively higher Au concentrations as would have been expected. This observation, together with thermodynamic calculations showing fluids to be under-saturated with respect to the native gold phase, indicates that Au concentrations in the generated fluid should be limited by the availability of gold in the source rocks from which the fluids were produced (Rauchenstein-Martinek et al. 2014) rather than gold solubility-controlling reactions (such as 4.64–4.66).
The main processes affecting sulfur during the ore-bearing fluid evolution in orogenic deposits are fluid-rock interactions, dominated by so called sulfidation reactions between aqueous H₂S and an FeII-rich rock acting as a sink for sulfur via precipitation of pyrite (and pyrrhotite). Efficient H₂S consumption from the fluid shifts reactions (4.64) and (4.65) to the left, leading to gold precipitation. Mafic rocks rich in ferrous iron are, thus, an excellent sink for sulfur. Wall-rock sulfidation is the primary control on metal deposition in deep and high-temperature orogenic gold systems; in addition, with decreasing depth of formation, phase separation favored by significant CO₂ content may also contribute to Au precipitation (e.g., Mikucki 1998; references therein). During progressive metamorphism at depth, a large amount of sulfur released into the fluid was expected at the breakdown of sedimentary pyrite to pyrrhotite occurring at temperatures >500 °C (e.g., Tomkins 2010; Large et al. 2011; Pokrovski et al. 2015). However, because FeII rock content in metamorphic terrains is usually superior to that of SII⁻, sulfur release may be over-competed by backward sulfide sulfur scavenging from the fluid by the excess of Fe oxide and silicate in the host rock (e.g., Zhong et al. 2015). Therefore, the solubility of the PPM buffer assemblage may be regarded as a reasonable proxy for sulfur concentrations observed in metamorphic fluid inclusions. These inclusions must, however, be corrected for the entrapment temperature typical of greenstone-amphibolite facies, which should typically be 200-300 °C higher than the homogenization temperature (section 4.2.3). It can be seen in Fig. 4.43 that such corrected fluid-inclusion data would match well the calculated PPM buffer solubility.

### 4.5.4 Sedimentary brine fluids

Basinal brine fluids (also called basement brines; Walter et al. 2020b) are involved in mineralization processes in a number of hydrothermal environments such as sediment-hosted metal deposits (e.g., sedimentary exhalative - SEDEX, Mississippi Valley type - MVT, Kupferschiefer, Irish-type Pb-Zn, unconformity-related U deposits), various rift-related or basement-hosted polymetallic, fluorite-barite or uranium deposits, as well as IOCG deposits (e.g., Leach et al. 2005; Williams et al. 2005; Wilkinson 2010; Richard et al. 2016). Hot, oxidized, chloride-rich basinal brines are able to transport high concentrations of base metals as chloride complexes (up to 10,000s of ppm of Cu, Pb, Zn - Table 4.2; Wilkinson et al. 2009), via substantial fluid flow focusing, from the crystalline basement reservoirs to shallow crustal levels. However, mixing with other types of oxidized fluids, such as shallower sediment-derived fluids or meteoric waters alone commonly produces carbonate-barite-fluorite veins poor in sulfide. Precipitation of metal sulfide ore mineralization requires a mechanism that efficiently supplies reduced sulfur or reducing agents (e.g.,
CH₄ or organic matter) capable of reducing sulfate-bearing brines (Goldhaber et al. 1995; Fusswinkel et al. 2013; Burisch et al. 2017; Walter et al. 2020a).

LA-ICPMS data on metal concentrations in basinal brine fluid inclusions are abundant in the literature; however, sulfur data were reported only in a few studies. Recently, total sulfur concentrations in fluid inclusions of basinal brine fluids from a number of barren and Pb-Zn veins from Schwartzwald, Germany, have been published (Fusswinkel et al. 2013; Burisch et al. 2016; Walter et al. 2018, 2019). Temperatures of homogenization are relatively low (100–180 °C), and salinity varies between ~2 and ~30 wt% (NaCl + CaCl₂), with most values being restricted in the 20–26 wt% range (Fig. 4.39e,f; Table 4.2). Sulfur concentrations vary over four orders of magnitude, from ~10 to almost 100,000 ppm. Such concentrations are comparable to the ones recorded by supercritical, hypersaline liquid and vapor inclusions from magmatic-hydrothermal systems (see section 4.5.2; Table 4.2). Metals (Fe, Cu, Zb, Pb) and metalloids (As, Sb) are generally depleted compared to sulfur in this fluid type, with some exceptions for Fe and, more rarely, for other base metals, as this is also the case for brine inclusions in magmatic-hydrothermal systems (Fig. 40). In some case examples (not identified in the figure), negative correlations are observed between sulfur and metal (Fe, Cu, Zn, As) concentrations that vary within comparable magnitudes, ~1 to 10,000 ppm (Fig. 4.42). Such correlations are likely due to the negative effect of the fluid H₂S content on base metal sulfide solubility (Fig. 4.25d). These natural cases indicate fluid mixing as the likely cause of precipitation, as inferred from halogen systematics in these systems (Fusswinkel et al. 2013; Walter et al. 2020a). However, H₂S was not directly detected in those fluid inclusions (e.g., by using Raman spectroscopy, section 4.2.4), but sulfate minerals (e.g., gypsum) were observed, for example in fluid inclusions from Schwartzwald. Their crush-leach analyses show that sulfur is dominantly present as SO₄²⁻ in the mineralizing fluid, at least at ambient conditions of those analyses (Walter et al. 2018, 2019), attaining high sulfate concentrations approaching those of chloride (SO₄²⁻/Cl⁻ mole ratios of 0.2–0.6; Walter et al. 2017). The abundance of sulfide mineralization in the district is conditioned by the availability of H₂S as controlled by reactions (4.56–4.66) or similar. Generation of H₂S in such environments is often driven by reducing agents (like CH₄, hydrocarbons, or graphite) that may react with the abundant sulfate present in the metal-transporting saline fluid. This reaction commonly occurs in sedimentary environments in which dissolved sulfate (in basinal brines and other formation waters) encounters hydrocarbons between 100 and ~160°C or, at higher temperatures, in the presence of bitumen or graphite. Upon this encounter, sulfate is reduced in a reaction called thermochemical sulfate reduction (TSR) represented in a simplified form as

$$2 \mathrm{H}^{+} + \mathrm{SO}_{4}^{2-} + \mathrm{CH}_{4} = \mathrm{CO}_{2} + \mathrm{H}_{2}\mathrm{S} + 2 \mathrm{H}_{2}\mathrm{O} \qquad (4.101)$$
The extent and kinetics of TSR reactions and the associated S, C and O isotope fractionation have been extensively studied in numerous natural settings as well as laboratory experiments since >50 years (e.g., Orr 1974; Cai et al. 2022; Meshoulam et al. 2023; references therein). The observation of native sulfur in fluid inclusions from sedimentary-basin settings (e.g., Barré et al. 2017) is direct evidence of the existence of hydrothermal fluids containing both sulfate and sulfide from which Sº precipitates on cooling. Reaction (1.101) not only leads to more reducing conditions, but also generates more H₂S and consumes H⁺. The concomitant increase in both H₂S concentration and pH strongly reduces base metal solubility in the form of chloride complexes (reactions 4.56–4.60, Fig. 4.25c,d) but, at the same time, greatly favors gold solubility as hydrosulfide and trisulfur ion complexes (reactions 4.64 and 4.65). This sulfur control may be key for gold transport from magmatic bodies emplaced into a sedimentary basin and its economic accumulation in structural traps as, for example, occurred in the Shahuindo and Algamarca epithermal gold deposits in northern Peru and similar deposits worldwide (Galdos et al. 2024; Vallance et al. 2024). Hydrogen sulfide generation due to TSR, as well as lower-temperature biogenic sulfate reduction (BSR) and simultaneous or subsequent fluid mixing, are also the main processes leading to sulfide ore mineralization in MVT and five-element vein deposits (Burisch et al. 2017; Walter et al. 2019; Sośniska et al. 2023; references therein). Sulfur excess over metals with a large portion of sulfate sulfur in basinal fluids from such systems is also demonstrated by much lower sulfur (dominantly H₂S) concentrations predicted in equilibrium with the PPM buffer than those analyzed in fluid inclusions even if the latter are corrected to true entrapment temperature of 150–250 °C (Fig. 4.43).

This overview shows the large variability of sulfur transformation reactions and solubility controls and the complex effect of sulfur on metal fate in different types of hydrothermal fluids. This complexity will be better comprehended when a number of challenges have been addressed in our understanding of sulfur in geological fluids. Some of these future challenges are summarized in the following section.
## 4.6 Perspectives and challenges

This overview highlighted the fascinating complexity of sulfur aqueous speciation in hydrothermal fluids, its transformation reactions and its relationships with metals. Despite unprecedented advances gained over the last 20 years on these topics, many aspects of the role played by sulfur in hydrothermal fluids remain to be understood and quantified.

Our state of knowledge of the speciation of sulfur and metals in hydrothermal fluids is strongly temperature- and pressure-dependent. This knowledge weakens significantly with increasing *T* and *P* even for the most common and abundant sulfur forms such as sulfate and sulfide. For example, their degree of protonation, which is the fundamental parameter affecting sulfur mineral solubility, degassing and complexation with metals, is subject to large uncertainties at *T*-*P* close to and above the water critical point. The thermodynamic stability of the molecular H₂SO₄⁰ and of the sulfide ion S²⁻ at magmatic-hydrothermal conditions is poorly known. Protonation and alkali ion pairing of most sulfur anions become increasingly important with temperature rise, but very meagre direct data are available above 300 °C. The last 10-year advances of in situ approaches applied to hydrothermal fluids have revealed that many intermediate-valence sulfur species, such as S₃⁺, S₂⁻, SO₂⁰, Sₙ⁰, and protonated polysulfide dianions are virtually unquenchable in aqueous solution. As a result, they cannot be properly detected by traditional ex situ techniques involving fluid sampling and cooling in laboratory or from studies of natural samples which are final products of the high *T*-*P* processes. The quantification of these important sulfur players thus requires in situ spectroscopic approaches coupled with molecular modeling.

In-depth understanding of sulfur relationships with metals in hydrothermal fluids is another outstanding issue. If the relative affinities of metals to the S-, Cl- and O-type ligands are qualitatively known, we are far from a quantitative picture of the metal interactions with the key sulfur ligands (sulfide, sulfate and polysulfides) in front of their major rivals, Cl⁻ and OH⁻. There is yet great disparity in our knowledge for different metals. For example, if complexes of precious (Au, Ag) and some base (Cu) metals with the hydrosulfide and chloride ligands are relatively well quantified at present, those of Mo, Re, and many PGE are virtually unknown in hydrothermal fluids. There is growing experimental and theoretical evidence that mixed ligand (H)S-Cl-O(H)-Na species may play an increasing role for many metals (e.g., Cu, Ag, Au, Mo, PGE) in magmatic-hydrothermal fluids; however, the robust evidence of those species and their quantification across the geologically pertinent *T*-*P* range are lacking. Likewise, polysulfide dianions (Sₙ²⁻) and their protonated counterparts may play a significant role in chalcophile metal transport at least at moderate
temperatures (<300 °C). The di- and trisulfur radical ions have recently emerged as other potentially important sulfur ligands for chalcophile metals making complexes of high stability (e.g., with Au, Pt, Pd, Mo). These findings open perspectives for in-depth investigations of their impact on the transport and fractionation of different metals across the lithosphere.

Metal complexes with intermediate-valence sulfur ligands may also play a crucial role in the kinetics of sulfide mineral (e.g., pyrite) precipitation processes in hydrothermal systems. The mechanisms behind these processes drive trace metal incorporation into major sulfide minerals that are economic hosts for many critical and precious metals in hydrothermal ore. Their quantification requires elaborate micro- and nano-scale spectroscopic and imaging techniques coupled with novel physical-chemical models of metal and sulfur speciation at the fluid-mineral interface. Quantifying the partitioning of different sulfur species between minerals/melts and the fluid phase is another major challenge. If the distribution of major volatile sulfur forms (H₂S, SO₂) between fluids and magmas at relatively shallow depths is thoroughly constrained to date, much remains to be done for deeper subduction-zone and metamorphic environments where ionic and intermediate-valence sulfur species become increasingly abundant. Some of those environments may preserve silicate and phosphate minerals (zeolites, apatite, scapolite, cancrinite, serpentinite, and zircon) capable of accommodating in their structure a large range of sulfur redox states, which may reflect those that existed in the parental fluid. Data on fluid-mineral partition coefficients of the different sulfur species are required for using such minerals as novel tracers of the redox state and composition of deep fluids.

The challenges above can only be met through a judicious combination of analytical, spectroscopic, experimental, and modeling approaches. Among the analytical issues, improvement of sulfur preservation and separation procedures for sampled geothermal fluids (e.g., by coupled chromatography and mass spectrometry techniques) would provide a far better knowledge of sulfur intermediates in sulfur redox reactions and of metal complexes with different sulfur ligands. Lowering the detection limits for sulfur in LA-ICPMS techniques (e.g., by using a new generation of triple quadrupole, usually abreviated as TQ, QQQ or QqQ, mass spectrometers and cleaner ablation procedures) would significantly extend the fluid-inclusion database for sulfur, which is currently limited by a few studies and relatively high analytical detection limits. Extending in situ spectroscopy on sulfur in aqueous fluids at elevated temperatures and pressures to methods, such as XANES, NRIXS, EPR and UV-Vis, will be a near-future perspective for both geoscience and chemistry communities. These methods are particularly sensitive to sulfur redox and electronic states thereby providing an excellent complement to Raman spectroscopy, which is currently the only technique routinely used for sulfur in hydrothermal fluids both in nature (fluid inclusions) and
experiment (spectroscopic cells). More generally, development of in situ spectroscopy for geologically pertinent fluid-mineral-melt systems should be a major advance for experimental geochemistry and petrology.

A formidable challenge of the modeling of sulfur and metals in geological fluids across the range of terrestrial *T-P* conditions is developing a common framework of physical-chemical equations of state enabling predictions of thermodynamic properties of aqueous species from “classical” aqueous solution to hypersaline brines and to low-density vapor phases. Popular thermodynamic models for aqueous fluids discussed in this chapter (e.g., HKF, density, AD, RB models) cover restricted *T-P*-density ranges and/or a limited choice of species, and are subject to increasing uncertainties in predictions beyond those ranges. Another important type of sulfur-bearing geological and planetary fluids, the mixed H₂O-CO₂(-CH₄) ones typical of deep metamorphic and magmatic contexts, has received only a scarce coverage by thermodynamic modeling. Therefore, experimental data on the speciation of both sulfur and economic metals at such conditions are needed to validate the model predictions and assess their uncertainties. Finally, linking thermodynamic equilibrium models of silicate melts with those of aqueous fluids in a single framework is another great perspective.

As emphasized in this overview, in the 2000s, molecular modeling approaches, in particular FPMD, have started providing new insights into the molecular structure and energetics of sulfur species and ore metal complexes thereby helping to interpret spectroscopic and solubility data. An important outcome of these approaches is the possibility to calculate, at virtually any temperature and pressure, the values of the Gibbs energies of complexation reactions for relatively simple metal complexes and sulfur species. Realistic uncertainties associated with such calculations are yet much greater than those from more direct experimental measurements, but the situation is improving with rapid advances in computer codes. In the meantime, acquiring new experimental data for sulfur and metals in hydrothermal fluids remains the primary necessity for parameterizing models of fluid-rock interactions.

Another advance of the 21st century is the growing application of physical hydrology approaches based on heat distribution, fluid flow models and permeability changes. Such computational methods have allowed integrated reactive transport modeling of fluid paths and three-dimensional ore distribution and shape. However, the chemistry of fluid-rock interactions, mineral solubility, and chemical element speciation are not yet quantitatively accounted for in such models, in particular for sulfur and economic metals. Integration of both chemistry and physics in the same conceptual model would thus be another major computational challenge and would contribute to
our fundamental understanding of deep geochemical cycles, assessing the role of sulfur in metal deposit formation, as well as improving mineral resources management.

## Acknowledgments

This chapter was motivated by the results of >25 years of research of our teams on sulfur and related metals in hydrothermal fluids supported by funding from Agence Nationale de la Recherche (grants SOUMET ANR-2011-Blanc-SIMI-5-6/009-01, RadicalS ANR-16-CE31-0017), Institut des Sciences de l'Université of the CNRS (INSU-CNRS), Mission pour les initiatives transverses et interdisciplinaires (MITI) interdisciplinary programs of the CNRS "MetalloMix 2021" (grant PtS3) and "ConditionsExtremes 2024" (grant ExtremeS), Institut Carnot ISIFOR (grants OrPet and AsCOCrit), Swiss National Science Foundation (grants 200020_134872, 200021_127123, and 200021_165752), Université de Toulouse, and French Embassy. We thank Dan Harlov for organizing and pushing forward this book, and reviewers Chris Gammons and Tris Chivers for their thoughtful and insightful comments that greatly improved the paper. For the purpose of open access the authors have applied a CC-BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission.
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Figures

<figure><img src="image_2.png" /><figcaption>**Fig. 4.1** Sampling methods for hot springs (liquid water) (a), fumaroles (vapor) (b) and two-phase (liquid and vapor) well discharges (c). The hot springs are sampled using pump and a filter holder containing filter with <0.45 µm pore size. The fumarole samples are collected by placing a funnel over or inserting a titanium tube into the vapor stream, connecting the outflow by silicone tube to a gas bottle. For the two-phase well discharges the liquid and vapor phases are separated using a Webre separator and the two phases sampled as for hot springs and fumaroles. For further details see Arnórsson et al. (2006).</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>**Fig. 4.2** (a) Schematic representation of a quartz-hosted aqueous saline fluid inclusion, the ablation pit, and the resulting analytical signal for selected elements. The parts of the spectrum corresponding to the background signal, the signal from the host quartz, and the fluid inclusion signal are indicated. The analysis is stopped after the ablation of the entire inclusion. Note a shift of the signal for some elements, due to ablation of solids such as halite (NaCl) or chalcopyrite (Cp, CuFeS₂) inside the inclusion cavity. Judging from the overlap in time between the maxima of the S, Cu and Fe intensities, the sulfur signal is mainly associated with the ablation of chalcopyrite present in the inclusion as daughter crystals. (b) Representative LA-ICPMS elemental signals of single brine (upper left), vapor (upper right), aqueous-carbonic (lower left) and aqueous (lower right) fluid inclusions. Brine and vapor are magmatic-hydrothermal fluids from the Morococha polymetallic district, central Peru (data from Catchpole et al. 2015); aqueous-carbonic and aqueous – metamorphic fluids from the Alpine orogenic belt (from Rauchenstein-Martinek et al. 2016).</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Fig. 4.3** Example of Raman spectra of an aqueous S-bearing fluid initially containing sulfide ($H_2S$) and sulfate ($SO_4^{2-}$) as a function of temperature from $P_{sat}$ to 1 kbar bar, measured using the capillary cell technique shown on the right (see Pokrovski and Dubessy 2015 for details). Raman peaks of the major sulfur aqueous species are indicated. The photos of the capillary cell at each corresponding temperature show color changes in the fluid with changing temperature, reflecting the growing formation of the blue chromophore $S_3^{3-}$ ion at the expense of sulfate and sulfide that are the only species detected at $T< 200°C$. Chain-like $S_n^0$ polymers also form at moderate temperatures (250–350°C), but disappear at the expense of the radical ions at higher temperatures. At the highest $T$, the $S_2^{3-}$ disulfur radical ion is also clearly detected. Quenching results in immediate disappearance of the blue color and the radical ion spectral signature, demonstrating that the radical ions can only be studied using in situ methods. The spectral pattern and colors are fully reversible in cooling-heating cycles, and are stable at a given temperature within at least the experiment duration (few days).</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 4.4** Normalized S K-edge XANES spectra of three representative ultramarine minerals recorded at ID12 beamline (ESRF) at ambient conditions. BRO and VZL = synthetic blue and green ultramarines, respectively (courtesy of B. Ledé); Baikal = natural blue sodalite from the lake Baikal metamorphic complex, Siberia (courtesy of A. Bychkov). The typical energy positions and shapes of the sulfur major formal oxidation states are indicated, together with the radical ions $S_3^{·−}$ and $S_2^{·−}$ that can be distinguished using their respective pre-edge peak positions (spectral data from Pokrovski et al. 2025).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 4.5** Chemical forms of sulfur known in aqueous solution, solid or gas phases at near-ambient conditions (modified and extended from Pokrovski and Dubessy 2015). Formal redox state of sulfur is indicated (where appropriate).</figcaption></figure>
<figure><img src="image_7.png" /></figure>

**Fig. 4.6** Typical range of experimental and predicted rate constants ($k_r$) of the reaction between sulfide and sulfate as a function of fluid pH at 300°C and saturated vapor pressure, highlighting three major trends in the constant depending on the pH range. Intermediate-valence sulfur species that might act as a rate-controlling species are indicated for each pH range (as per Ohmoto and Lasaga 1982; Chu et al. 2004; Pokrovski and Dubessy 2015).
<figure><img src="image_8.png" /><figcaption>**Fig. 4.7** Time (in years) necessary to reach 90% of equilibrium for the sulfate-sulfide pair in aqueous solution at a total sulfur concentration of 0.01 mol/kg, as a function of temperature at the indicated pH values, according to the thiosulfate kinetic model of Ohmoto and Lasaga (1982).</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Fig. 4.8** Dissociation constant of hydrogen sulfate in aqueous solution as a function of the reciprocal of absolute temperature according to the available experimental data and thermodynamic predictions by HKF model (Shock and Helgeson, 1988). Ha34 = Hamer (1934), Da52 = Davis et al. (1952), Li61 = Lietzke et al. (1961), Ry64 = Ryzhenko (1964), MJ66 = Marshall and Jones (1966), Wa66 = Wallace (1966), RC69 = Readnour and Cobble (1969), MO88 = Matsushima and Okuwaki (1988), Os88 = Oscarson et al. (1988), Di90 = Dickson et al. (1990), Ru96 = Rudolph (1996), Hnedkovsky et al. (2005). Note that the linear van't Hoff equation (4.9) would fail to account for the curvature of log K vs. 1/T; more extended polynomial equations (e.g., 4.11 and 4.12) were used in some studies to describe the data to 300–350°C (not shown), but cannot account for the effect of pressure. In contrast, the HKF model, based on pre-1970 measurements, accurately reproduces the whole set of data including more recent ones and accounts for the pressure effect.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Fig. 4.9** Dissociation constant of sulfuric acid in aqueous solution as a function of the reciprocal of absolute temperature (a) and water density (b), according to available experimental data. Qu65 = Quist et al. (1965), Os88 = Oscarson et al. (1988), Xi96 = Xiang et al. (1996), Su04 = Sue et al. (2004), Hn05 = Hnedkovsky et al. (2005), LN21 = LLNL database (thermo.dat, Johnson et al. 2000), BS24 = Baudry and Sverjensky (2024), which is an HKF fit of Qu65; -pHw = log a(H+) of pure water. The dissociation constants are strongly P-dependent in the supercritical region. While the density model allows for significant linearization of Kdiss trends, the values from different sources yet remain rather discrepant, spanning over 2 to 4 log units at high (>300 °C) and low (<100 °C) temperatures, respectively.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Fig. 4.10** Henry's constant of H₂S solubility in pure water as a function of the reciprocal of absolute temperature, according to major available experimental data sets and thermodynamic model predictions at saturated vapor pressure (P₃sat) and at 1 kbar. Ko64 = Kozintseva (1964), CG71 = Clarke and Glew (1971), LM77 = Lee and Mather (1977) including Selleck et al. (1952) data, Dr81 = Drummond (1981), Ki89 = Kishima (1989), SK94 = Suleimenov and Krupp (1994), HKF = HKF model updated by Schulte et al. (2001); AD = Akinfiev and Diamond (2003) model. Note that the AD model provides a slightly better match of the available experimental data than the HKF model, in particular at elevated temperatures and pressures. Note that the differences between the models grow with increasing T and P and may be significant outside the T-P range covered so far by experiments.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Fig. 4.11** First dissociation constant of hydrogen sulfide in aqueous solution as a function of the reciprocal of absolute temperature, according to the available experimental data and thermodynamic predictions by the HKF model for $HS^-$ (Shock and Helgeson 1988) and $H_2S$ (updated by Schulte et al. 2001) and the AD model for $H_2S$ (Akinfiev and Diamond 2003). WM32 = Wright and Maass (1932), EM67 = Ellis and Millestone (1967), EG71 = Ellis and Giggenbach (1971), Ts76 = Tsonopoulos et al. (1976), Sr77 = Sretenskaya (1977), KS78 = Kryukov and Starostina (1978), Barbero et al. (1982), SS97 = Suleimenov and Seward (1997). Note that both models give almost undistinguishable results (curves overlap at all pressures), by accurately reproducing most of experimental data acquired from 0 to 350 °C at $P_{sat}$, and yielding very similar predictions of the pressure effect, in good agreement with rare $P$-dependent experimental data (to at least 90 °C and 3 kbar, Sretenskaya 1977). For comparison are also plotted the negative pH values of the neutrality point of pure water ($pH_w$) at $P_{sat}$ and 5 kbar (blue curves), see text.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Fig. 4.12** Second dissociation constant of hydrogen sulfide in aqueous solution as a function of the reciprocal of absolute temperature, according to the major available experimental data and compilations (all at saturated vapor pressure, *P*<sub>sat</sub>): KH05 = Küster and Heberlein (1905), Kn06 = Knox (1906), Ma59 = Maronny (1959), Di66 = Dickson (1966), He69 = Helgeson (1969), EM67 = Ellis and Milestone (1967), SC71 = Stephens and Cobble (1971), Gi71 = Giggenbach (1971a), EG71 = Ellis and Giggenbach (1971), Kr74 = Kryukov et al. (1974), Me83 = Meyer et al. (1983), LM87 = Licht and Manassen (1987), SB88 = Schoonen and Barnes (1988), Li90 = Licht et al. (1990), Ec98 = Eckert (1998), LN00 = LLNL database (Johnson et al. 2000), PP00 = Phillips and Phillips (2000), Mi02 = Migdisov et al. (2002), Ma18 = May et al. (2018) and references therein. The arrow symbol of Ma18 indicates the most plausible range of maximum values of *K*<sub>diss</sub>(HS<sup>-</sup>) at ambient conditions according to those authors. For comparison, water dissociation constant (*K*<sub>diss</sub> (H<sub>2</sub>O), H<sub>2</sub>O = H<sup>+</sup> + OH<sup>-</sup>) is also plotted at *P*<sub>sat</sub> and 5 kbar pressure (blue curves).</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Fig. 4.13** Henry's constant of SO₂ solubility in pure water as a function of the reciprocal of absolute temperature, according to selected available high-T experimental data sets at saturated vapor pressure (Pₘsat) and thermodynamic model predictions at Pₘsat and 2 kbar. CM30 = Campbell and Maass (1930), BS40 = Beuschlein and Simenson (1940), RM92 = Rumpf and Maurer (1992), GP85 = Goldberg and Parker (1985) based on critical evaluation of extensive previous data (validity 0–150 °C), HKF = HKF model updated by Schulte et al. (2001); AD = Akinfiev and Diamond (2003) model.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Fig. 4.14** First (1) and second (2) dissociation constants of sulfur dioxide in aqueous solution as a function of the reciprocal of absolute temperature, according to the major available experimental or compilation datasets and thermodynamic models (at saturated vapor pressure, *P*<sub>sat</sub>, unless indicated): MC85 = Murray and Cubicciotti (1983), Ba83 = Barbero et al. (1983), ER61 = Ellis and Anderson (1961), GP85 = Goldberg and Parker (1985), RD85 = Rhee and Dasgupta (1985), HKF model = Schulte et al. (2001), AD model = Akinfiev and Diamond (2003). The bisulfite ion, HSO₃⁻, includes both isomers, (HS)O₃⁻ and (HO)SO₂⁻.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>**Fig. 4.15** First ($K_{0-1}$) and second ($K_{1-2}$) protonation constants of polysulfide dianions at ambient conditions as a function of the reciprocal of the number of sulfur atoms in the polysulfide chain (1/n) according to available data: SF60 = Schwarzenbach and Fischer (1960), both experiment and estimation, SB88 = Schoonen and Barnes (1988), Ch99 = Chadwell et al. (1999), Ka04 = Kamyshny et al. (2004), Li13 = Liu et al. (2013a). exp = experiment, estim = estimation, FPMD = first principles molecular dynamics calculations.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>**Fig. 4.16** Distribution of the indicated individual sulfur forms as a function of pH at ionic strength of 0.1 and 25 °C, 1 bar (solid curves) and 300 °C, $P_{\text{sat}}$ (dashed curves), calculated using the thermodynamic data adopted in this study as overviewed in the text. Data for the species with question marks yet remain uncertain.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Fig. 4.17** Dissolved molecular sulfur concentrations in water in equilibrium with solid α-allotrope of sulfur (<120 °C) and molten sulfur at higher temperatures, according to available experimental data and thermodynamic models. Ka09 = Kamishny (2009), Bo78 = Boulëgue (1978b), WT09 = Wand and Tessier (2009); DS93 = Dadze and Sorokin (1993); PD15 = Pokrovski and Dubessy (2015). The discrepancy between the two HKF model predictions at elevated temperatures (see **Table 4.5** for parameters) indicates the formation of molecular sulfur species other than S<sub>8</sub><sup>0</sup> in hydrothermal fluids (indicated by the vertical orange arrow).</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>**Fig. 4.18** Decimal logarithm of the equilibrium constant of reaction (4.44) versus the reciprocal of absolute temperature (in Kelvin). Symbols show the data derived in the indicated studies: PD11 = Pokrovski and Dubrovinsky (2011), PD15 = Pokrovski and Dubessy (2015), Gi71 = Giggenbach (1971b), To12 = Tossell (2012). Solid curve is the 3-term equation from PD15: $logK_{44} = -123.3(±20.5) - 10585(±1380)/T + 45.57(±6.50)×logT$. The corresponding set of HKF-model parameters is available in PD15 consistent with those of $H_2S_{(aq)}$ and $SO_4^{2-}$ from the SUPCRCT database. Note that this set is attached to the thermodynamic properties of $H_2S_{(aq)}$ (Schulte et al. 2001) that were used in its deviation (see Pokrovski and Dubessy 2015 for in-depth discussion of errors related to the use of other models and datasources).</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Fig. 4.19** Concentrations of S<sub>3</sub><sup>-</sup> and other major sulfur forms (expressed as ppm of S) calculated in model hydrothermal fluids of 10 wt% salinity (NaCl+KCl) equilibrated with the quartz-muscovite-potassic feldspar assemblage, at 450°C and indicated conditions as a function of (a) total S content, (b) oxygen fugacity, (c) pH, and (d) pressure. Curves show concentrations of each indicated species (ΣSO<sub>4</sub> stands for the sum of SO<sub>4</sub><sup>2-</sup>, HSO<sub>4</sub><sup>-</sup>, and their K<sup>+</sup> and Na<sup>+</sup> ion pairs). QFM = quartz-fayalite-magnetite, NNO = nickel-nickel oxide, PPM = pyrite-pyrrhotite-magnetite, and HM = hematite-magnetite (modified after Pokrovski and Dubessy 2015).</figcaption></figure>