Modelling Isotopic Responses to Disequilibrium Melting in Granitic Systems

Modelling Isotopic Responses to Disequilibrium Melting in Granitic Systems Abstract Granite petrogenesis is an important component of crustal growth and evolution; however, the isotope systems commonly applied to investigations of such processes (Sr, Nd, Pb and Hf) may behave in a more complex manner during partial melting and crystallization than is often assumed in petrogenetic models. Using a range of experimentally determined melting reactions and accessory mineral dissolution equations, the Sr-, Nd- and Hf-isotopic compositions of melt, source (protolith), and restite (residual source material including peritectic phases) have been calculated for a variety of hypothetical melting scenarios, in which the protoliths have acquired an isotopically heterogeneous mineral assemblage by aging in the crust prior to melting. It is shown that the disequilibrium amphibole dehydration melting of meta-igneous protoliths that have resided in the crust for 1·0 Gyr can generate differences between protolith and melt compositions of –4·2 to +7·2 εHf units. This implies that bulk-rock (particularly mafic, restite-rich) samples may have Hf isotope compositions significantly different from the melt-precipitated zircons within them. The modelling also predicts differences between protolith and melt Sr and Nd isotope compositions and decoupling between these systems. Furthermore, we demonstrate that simple restite separation from a single protolith can produce magmas exhibiting a range of Sr–Nd–Hf isotope compositions; that is, producing within-suite isotopic heterogeneity independent of source variation. The results imply that great care should be taken in the interpretation of the isotopic compositions of zircons in granites, and that bulk-rock compositions of mafic samples from granitic suites, not zircons, may provide the most reliable constraint on the protolith isotopic composition. INTRODUCTION The extensive literature surrounding models for granite (sensu lato) formation and differentiation relies heavily upon the interpretation of petrographic, geochemical, and isotopic data (Chappell & White, 1974, 1992; O’Neil & Chappell, 1977; White & Chappell, 1977; DePaolo, 1981; McCulloch & Chappell, 1982; Gray, 1984; Chappell et al., 1987, 2004; Langmuir, 1989; Bea, 1996a; Chappell, 1996b, 2004; Collins, 1996; O’Hara & Fry, 1996; Sawyer, 1996; Keay et al., 1997; Clemens, 2003; Kemp et al., 2007; Stevens et al., 2007; McLeod et al., 2012; Dorais & Spencer, 2014). Often the origins of granite suites have remained contested owing to the challenges of reconciling isotope data with major and trace element data and petrographic observations in competing petrogenetic models. In perhaps the most notable example, detailed studies of the granite batholiths of the Lachlan and New England Fold Belts (LFB and NEFB) in eastern Australia have led to (1) the identification of two distinct granite types (I- and S-types; Chappell & White, 1974), and (2) development of the ‘restite’ model as an explanation for the petrographic and geochemical features observed, particularly systematic variations such as linear within-suite trends in bivariate element plots (White & Chappell, 1977). The restite model proposes that partial melting of a crustal source results in a crystal-rich magma that undergoes liquid–crystal separation, or ‘unmixing’, to produce a range of compositions (from relatively mafic to felsic granites between the protolith and melt compositions) defined by varying proportions of an initially largely anhydrous restitic mineral assemblage and a hydrous melt (Chappell et al., 1987). In this way the granite is thought to ‘image’ the source, and the mineralogical and chemical characteristics of granites that give rise to the I- and S-type classification are features of two end-member protolith affinities (igneous/infracrustal and sedimentary/supracrustal, respectively), preserved most distinctly in the most mafic granites (Chappell et al., 1987; Chappell & Stephens, 1988; White & Chappell, 1988; Chappell & White, 1992; Chappell, 1996a). It should be noted that in the restite model, the primary restitic mineral assemblage in the partially melted source is viewed as the combination of unmelted protolith grains and the solid products (peritectic phases) of incongruent melting reactions; however, the restite in solidified granites is probably largely secondary restite produced by the back-reaction of primary restite (which may survive as relict cores of grains) with the melt as temperature and pressure change during ascent, emplacement and crystallization (Chappell et al., 1987). Being a combination of components from the melt and from primary restite, secondary restite phases may be regarded as hybrid phases. Alternative hypotheses for the genesis of these rocks include various forms of magma mixing models, which propose that I- and S-type granitoids form part of a continuum (as shown by their bulk Nd and Sr isotopic compositions) generated through the mixing of varying proportions of mafic, mantle-derived melts, liquids fractionated therefrom, partial melts of mafic lower-crustal lithologies, and sediment-derived material (Gray, 1984; Collins, 1996; Keay et al., 1997; Kemp et al., 2006, 2007). Such models typically invoke a hybridization process to account for isotopic variability within or between granite suites, and fractional crystallization to account for petrographic variability and the common linear geochemical trends (Collins, 1996, 1998; Keay et al., 1997; Healy et al., 2004; Kemp et al., 2007). Support for mixing models has been derived from isotopic analyses of the mineral zircon. Intra-sample O–Hf isotope arrays in magmatic zircon rims record progressive changes in the isotopic composition of the melt of some Lachlan Fold Belt granites. Such arrays are interpreted to indicate the mixing of isotopically distinct magmas of different origins during zircon crystallization (Kemp et al., 2005, 2006, 2007). In contrast, zircon populations from some S-type granite samples display uncorrelated scatter in δ18O–εHfi plots as might be expected for the restite model, rather than from mixing (Ickert, 2010). In the study of Ickert (2010), O–Hf isotope trends suggestive of mixing or assimilation were found in zircon populations for some I-type granites, but not others. It is clear that, although assimilation or mixing of some form is involved in the genesis of some granite suites in the Lachlan Fold Belt, the restite model is still supported for many suites on the basis of the O–Hf isotope evidence from zircon as well as the petrographic and geochemical arguments that originally gave rise to the model. If, however, the restite model is to be retained as an important mechanism through which granite petrogenesis occurs, the isotopic variability between samples of the same suite, and within zircon populations, requires a more thorough explanation than originally, and currently, envisaged. Under the restite model, although the isotopic composition (and variability) of the granite is considered to reflect that of the source, no detail is provided as to what the relative contributions of the melt and restite to the bulk-rock isotopic composition could be, or the relationship between the isotopic composition of the source and the melt. In addressing implications of the restite model for isotopic variability, it must be recognized that restite-bearing granite magmas are complex mixtures of crystals and melt, so that homogeneity and perfect equilibration cannot be assumed, as might be the case for igneous rocks crystallized from essentially pure liquids (e.g. basalts). Indeed, recent studies have emphasized the incomplete segregation of melt from its residuum (i.e. the entrainment of restite by melt in early stages of magma extraction) and suggested incomplete equilibration between melt and solids (Acosta-Vigil et al., 2006; Sawyer, 2014; Carvalho et al., 2016). There is an emergence of interest in the potential for disequilibrium effects during melting and granite production (Hogan & Sinha, 1991; Watt & Harley, 1993; Ayres & Harris, 1997; Davies & Tommasini, 2000; Zeng et al., 2005; Beard, 2008; Farina & Stevens, 2011; McLeod et al., 2012; Villaros et al., 2012), but the implications for the petrogenesis of the iconic Lachlan Fold Belt granites have not been considered. In addition, only recently has disequilibrium melting during crustal anatexis been considered with respect to the Lu–Hf isotope system (Villaros et al., 2012; Farina et al., 2014; Tang et al., 2014). In this study we address these issues by developing a model for investigating the role of pre-existing protolith heterogeneity and melting conditions in contributing to the isotopic heterogeneity in granite magmas. This model is then used to explore the Sr–Nd–Hf isotope systematics of restite-bearing granite magmas, establishing a framework for future studies focusing on the application of this model to key I- and S-type granites of the Lachlan Fold Belt. MODELLING DISEQUILIBRIUM MELTING Disequilibrium melting—previous studies Various studies have examined the effect of an isotopically heterogeneous protolith on melt isotope compositions and the different influences that specific minerals can exert on the Pb, Sr, Nd, and Hf isotope systems (Hogan & Sinha, 1991; Ayres & Harris, 1997; Davies & Tommasini, 2000; Knesel & Davidson, 2002; Zeng et al., 2005; Perini et al., 2009; Farina & Stevens, 2011; McLeod et al., 2012; Tang et al., 2014). For example, to account for initial lead isotope heterogeneity in otherwise compositionally and mineralogically homogeneous granite plutons, Hogan & Sinha (1991) proposed a melting model incorporating melting reactions, zircon and monazite solubility, the temperature dependence of these processes, the trace element and Pb isotope composition of the source-rocks and the relevant phases, and modal abundances of minerals. This model indicated that the increased solubility of zircon and monazite at higher temperatures would result in greater Pb isotope variability in high-temperature (>850°C) weakly peraluminous to metaluminous melt batches (leading to heterogeneous plutons) compared with low-temperature peraluminous melt batches. Thus granites derived from the same source under isotopically closed-system conditions need not inherit the same initial Pb isotope composition. Additionally, Hogan & Sinha (1991) suggested that scatter in compositional trends may reflect source rock heterogeneity transferred to a pluton that was assembled in batches, and that isotope systems may be decoupled from each other and from other mineralogical and chemical parameters owing to their different behaviour in each mineral. Neodymium isotope systematics during melting were examined by Ayres & Harris (1997) in a study of two types of leucogranite in the Himalayas, emphasizing the importance of monazite and apatite as hosts of Nd in metapelitic source rocks. They demonstrated that prograde heating and melt extraction can be sufficiently rapid to prevent Nd isotope equilibration between the dissolving accessory phases, such that the Nd isotope composition of the melt is determined by the relative contributions of isotopically distinct monazite and apatite. Comparison of their model with that of Hogan & Sinha (1991) supports the idea that the Nd and Pb isotope systems might be decoupled, with greater Nd isotopic variability produced in low-temperature (650–800°C) peraluminous melts compared with the restricted range of Pb isotopic compositions produced in similar melts, because the two isotope systems are controlled by different assemblages, despite the similar mechanisms involved. Zeng et al. (2005) built upon previous work (e.g. Vielzeuf & Holloway, 1988; Hogan & Sinha, 1991; Watt & Harley, 1993; Bea, 1996a; Ayres & Harris, 1997; Davies & Tommasini, 2000) to model the disequilibrium melting of metapelites. They considered a range of parameters, including the coupling of apatite and monazite dissolution and the roles that they play in the isotopic evolution of granitic melts, the differing effects of a fluid-absent muscovite dehydration melting reaction and a fluid-fluxed melting reaction on the melt composition, and the interplay between melt extraction and accessory phase dissolution rates. The results suggest two distinct paths in εNd–87Sr/86Sr space that describe the isotopic composition that the melt acquires from the source, corresponding uniquely to the two possible melting reaction schemes. Greater apatite, but limited monazite dissolution is favoured by the higher temperature, dry conditions of mica dehydration melting, which together result in higher εNd and 87Sr/86Sr values in the melt compared with the source. Lower εNd and 87Sr/86Sr values in the melt relative to the source would arise from lower temperature, fluid-fluxed melting in which monazite dissolution is favoured over that of apatite (Zeng et al., 2005). Examining the role of major phases in the melting process, Davies & Tommasini (2000) considered two styles of disequilibrium melting that could occur. In the first, the melt is in equilibrium (i.e. Henry’s law partition coefficients operate) with the slowly dissolving rim of a grain, but slower diffusion prevents equilibrium between the rim and melt and the core. In the second case, dissolution is too fast to achieve rim–melt equilibrium partitioning (and much faster than diffusion), such that the melt obtains the same chemical and isotopic composition as the portion of the grain that is melting (this is assumed in many studies that examine the impact of reaction stoichiometry in controlling melt composition). Davies & Tommasini (2000) illustrated how the Nd- and Sr-isotopic compositions of a melt could evolve as melting of a metasediment that has been aged for 1 Gyr (disequilibrium between phases owing to different Rb/Sr and Sm/Nd ratios) progresses through three successive melt reactions (Patiño Douce & Johnston, 1991). Taking a similar approach, Farina & Stevens (2011) considered hypothetical source rocks, containing muscovite, biotite and plagioclase as Rb–Sr-bearing major phases, which have evolved (for 200 and 300 Myr) since an isotopic homogenization event. That is, their hypothetical source rocks contain minerals of different Rb and Sr concentrations and Rb/Sr ratios, and therefore ultimately develop a heterogeneous isotopic composition with the passage of time. During partial melting, the melt phase acquires its isotopic composition from the metasedimentary source according to mica dehydration reactions and the temperature dependence of the reaction stoichiometry (Vielzeuf & Montel, 1994; Montel & Vielzeuf, 1997; Patiño Douce & Harris, 1998). Furthermore, the melt segregates in discrete batches, so that variations in reaction stoichiometry will be translated into isotopic heterogeneity in a pluton. Farina & Stevens (2011) also examined the effect of compositional variability on the Sr-isotopic composition of the melt, given the likelihood that the entire source region consists of multiple compositional domains. Using the variations in melt reaction stoichiometry caused by changes in the Mg content of biotite, they extended their model to demonstrate that melt 87Sr/86Sr and temperature-dependent Sr-isotopic variability are positively correlated with source Mg#. They also argued that, owing to its relatively low Rb/Sr, apatite dissolution would lower the 87Sr/86Sr of the melt, but its contribution to Sr isotopic variation would be secondary to those of the dehydration reactions. In their study of volcanic rocks in the Central Andes, McLeod et al. (2012) demonstrated microscale Sr isotopic disequilibrium between the melt and bulk of a partially melted gneissic xenolith, as well as intra-melt disequilibrium (87Sr/86Sri range of 0·7164–0·7276 within 200 μm). This disequilibrium was interpreted as resulting from non-modal (stoichiometry-controlled) melting of biotite and feldspar that produced a range of melt compositions from high to low 87Sr/86Sri as the contribution from biotite is diluted by increasing contribution from feldspar, as has been discussed by Davies & Tommasini (2000) and Farina & Stevens (2011). Given the widespread use of Hf isotopes in zircon as an isotopic tracer and the significant literature on disequilibrium in the Rb–Sr and Sm–Nd systems, it is somewhat surprising that it has only been recently that similar studies have been undertaken on the Lu–Hf systems. Tang et al. (2014) emphasized the significance of zircon and garnet as hosts for unradiogenic and radiogenic Hf, respectively, in a protolith. They modelled the changing Zr and Hf concentrations and Hf isotope compositions of melts produced from different protoliths. The protoliths differ in bulk-rock Zr contents and zircon size distributions, but have the same bulk-rock Hf isotope compositions and crustal residence times (1 Gyr since last isotopic homogenization). Melt fraction was assumed to increase continuously with increasing temperature (750–950°C) until 40% of the protolith has been melted, but melt is extracted (and chemically isolated) continuously from the source once a critical porosity (10% melt) is reached. Time-integrated compositions were calculated for a range of anatexis time-scales by assuming that spherical zircons dissolve into the melt produced from major phases according to temperature- and composition-dependent equations for zircon dissolution rates and Zr solubility. These constraints were applied to two (dis)equilibrium conditions: (1) complete disequilibrium between all solids and melt and modal melting of phases other than zircon; (2) zircons are neither in equilibrium with the melt nor the other phases, but equilibrium partitioning occurs between major minerals and melt. Both cases produce ranges in melt εHf values of ∼10 ε units for protoliths with 10 μm zircons, 50 ppm bulk-rock Zr and 105 years anatexis time, and ∼100 ε units for protoliths with 50 μm zircons, 200 ppm bulk-rock Zr and 102 years anatexis time. The modelling produced melts that are initially more radiogenic than the protolith, except for a few scenarios, but reach parity and become less radiogenic than the protolith with increasing melt fraction. Tang et al. argued that a single source can produce melts that vary in Hf isotope composition, thus allowing zircons to crystallize variable compositions, and suggested disequilibrium melting as an alternative explanation to mixing of magmas from distinct sources for the origin of heterogeneous zircon populations in southern China. Although the modelling of Tang et al. (2014) demonstrated the potential for anatexis of a single source to generate significant melt Hf isotope variability, which could be reflected in magmatic zircon and granite bulk-rock compositions, some questions remain, as follows. What are the effects of changing reaction stoichiometry (which may alter the importance of the major phases relative to zircon) or of protoliths undergoing melting through successive melt-producing reactions (involving a stepwise change in the melt composition and temperature)? The studies discussed above emphasize the involvement of accessory phases other than zircon for the Pb, Nd and Sr isotope systems. Although apatite and monazite contain little Hf, their high Lu/Hf means they could contain extremely radiogenic Hf, which may be significant. What leverage might these phases have on granite magmas? Could changing the mineral assemblage (necessitating different melt-producing reactions at different temperatures) affect the variability of melt composition and the relationship between melt and protolith Hf isotope composition? Would this translate to different disequilibrium effects for I- and S-type granites? What within-suite bulk-rock heterogeneity and within-sample zircon versus bulk-rock differences would Hf isotope disequilibrium produce for samples inferred to contain restite? The model detailed below aims to address aspects of these questions, and provides insights that can be used to explain granite bulk-rock and zircon isotope data. Modelling approach To address the questions raised above, our approach needs to be able to account for the contributions of different minerals to the melt and to the restite assemblage. The work of Davies & Tommasini (2000), Zeng et al. (2005) and Farina & Stevens (2011) provides examples of how to model the way in which melt-producing reaction stoichiometry affects the compositions generated under disequilibrium. The formulation of our new model is as follows: protoliths are defined by mineral assemblages based on samples from melting studies; mineral trace element compositions are based on a dataset of actual analyses; the isotope compositions of minerals are calculated based on evolution over time from a common composition; published melt-producing reactions and accessory dissolution equations account for the contributions to melt and restite; the trace element composition of the melt and peritectic phases is calculated; the isotope composition of melt, source and restite is then calculated. Numerous studies within theoretical, experimental and natural systems have investigated partial melting in the crust (Clemens & Vielzeuf, 1987; Le Breton & Thompson, 1988; Vielzeuf & Holloway, 1988; Beard & Lofgren, 1991; Patiño Douce & Johnston, 1991; Sen & Dunn, 1994; Vielzeuf & Montel, 1994; Patiño Douce & Beard, 1995; Rapp & Watson, 1995; Singh & Johannes, 1996; Pickering & Johnston, 1998; Cesare, 2000; Vielzeuf & Schmidt, 2001; Petcovic & Grunder, 2003; White et al., 2003; Acosta-Vigil et al., 2010; Rajesh et al., 2013). Ideally the results of such studies need to report the proportions of the reactant and product phases involved in melting in order to be used in a quantitative model, which narrows the set of studies that can be used. The set of reactions to model is further reduced by restricting the scope of modelling to the production of I-type magmas from (meta)igneous protoliths—a choice made as a result of complexities inherent in modelling S-type magma generation, given the likely initial heterogeneity of metasedimentary rocks. A detailed investigation of S-type magmatism is the subject of a separate contribution. Melt-producing reactions from three studies have been used in this model. The reactions are expressed using the following abbreviations: amph (amphibole), bt (biotite), cpx (clinopyroxene), grt (garnet), ilm (ilmenite), Kspar (K-feldspar), mt (magnetite), opx (orthopyroxene), plag (plagioclase) and qtz (quartz). Sen & Dunn (1994) proposed the following reactions at 1·5 GPa to investigate the melting of metabasalt at the high pressures involved in melting a subducted slab. The first reaction occurs at c. 925°C: 0·24 qtz+0·6 plag+2·16 amph →1·22 cpx+0·86 grt+1·0 melt. When quartz is exhausted, the next reaction, at ∼950°C, is 1·0 plag+3·6 amph →2·2 cpx+1·5 grt+1·0 melt. For dehydration melting of amphibole-bearing lower crustal rocks, Beard & Lofgren (1991) determined that the following reaction will occur at 0·3 GPa and between 850 and 900°C: 9 qtz+5 plag+33 amph →20 cpx+6 opx+2 mt+19 melt. In the rocks they studied (used as example protoliths for this model) quartz and amphibole are expended simultaneously, thus further melting requires a higher temperature (900–1000°C) to break down anhydrous minerals according to the reaction 13 plag+2 mt+1 cpx+1 opx+1 ilm → 18 melt. To investigate the melting of source rocks containing both biotite and amphibole, two successive reactions have been modelled according to the phase relations determined by Petcovic & Grunder (2003). As that study inferred reactions from the petrography and geochemistry of a natural system, the temperature and pressure conditions are not as well constrained as for reactions from experimental studies. The reactions are estimated to have taken place at less than 0·5 GPa, and probably less than 0·3 GPa. The first reaction, completed by ∼925°C is 11·1qtz+6·6plag1+6·3Kspar+14·7amph+14·0bt→ 13·2plag2+10·1cpx+9·0opx+2·1mt+18·2melt. The second reaction, which occurs at close to 950°C, is 5·2qtz+7·1plag1+5·2plag2+1·2Kspar+7·3cpx+1·5mt→ 28·1melt. For the first two studies, the reactions have been quoted above as they were originally reported, but it is necessary to adjust the stoichiometry for modelling so that reactants and products are balanced. For the last study, the reaction stoichiometries provided are rounded from the proportions calculated from the data provided by Petcovic (2000) and Petcovic & Grunder (2003) for the two reactions. Unless specified otherwise by the reaction, the modelling assumes that the second reaction of a pair of successive reactions consumes peritectic phases of the first reaction before consuming any pre-melting equivalent. That is, peritectic clinopyroxene produced from the breakdown of amphibole, for example, is assumed to crystallize around any pre-existing clinopyroxene, so that when melting proceeds to a higher temperature and must consume clinopyroxene, the peritectic rim is consumed prior to the core. The contribution of accessory phases to the melt is determined by the degree to which they are expected to dissolve in melts of given compositions and temperatures. Apatite, zircon and monazite dissolution has been well studied (Watson & Harrison, 1983; Harrison & Watson, 1984; Rapp et al., 1987; Bea et al., 1992; Pichavant et al., 1992; Montel, 1993; Wolf & London, 1994; Boehnke et al., 2013), thus the contributions of these minerals can readily be modelled; however, the behaviour of neither titanite (present in most modelled protoliths) nor allanite (included in some protoliths) during anatexis is well constrained. The stability of titanite is affected by phase relations controlled by oxygen fugacity, water content and temperature (Wones, 1989; Xirouchakis & Lindsley, 1998; Frost et al., 2000) that are too complex to be integrated into this model in the way that apatite, monazite and zircon dissolution is. Nevertheless, whether titanite should break down or remain unmelted needs to be considered. Some research indicates that titanite becomes saturated early in some granitoid magmas (Watson & Harrison, 1984; Green & Pearson, 1986), which could occur if it were an undissolved or only partially dissolved residual phase, or if titanite were to break down completely during anatexis but become stable upon emplacement and cooling. Indeed, Noyes et al. (1983) suggested that titanite was early crystallizing and could have been a restitic phase in the Red Lake pluton, but that it was neither restitic nor early crystallizing in the Eagle Peak pluton (both I-type granites in the Sierra Nevada, California). In studies of amphibolite- to granulite-facies metamorphism and partial melting, Gregory et al. (2009) reported the presence of titanite throughout metamorphism and partial melting, and Bingen et al. (1996) reported partial breakdown of titanite with some preserved as relict grains in other phases. In consideration of these studies, it cannot be confidently assumed either that titanite would remain completely unmelted, or that it would completely dissolve in all scenarios considered by the modelling that follows. Nevertheless, for consistency it has been assumed that titanite remains unmelted for most scenarios, except a few that assume partial or complete breakdown, facilitating an assessment of the effect of titanite breakdown upon the modelling through comparison of the different scenarios. Hermann (2002) conducted experiments to investigate the phase relations of allanite and reported that although the mineral is stable at 700–1050°C and 2·0–4·5 GPa it will dissolve in the presence of granitic melt; however, Gregory et al. (2012) identified inherited allanite cores in migmatite samples, indicating incomplete dissolution. Thus, in the absence of constraints on its solubility, cases in which all allanite dissolves and others in which none dissolves have been modelled. Small amounts of xenotime have been included in some of the protoliths modelled, consistent with research suggesting a decreasing abundance of xenotime with metamorphic grade approaching melting conditions (Villaseca et al., 2003). Considering the absence of restitic xenotime in leucosomes studied by Villaseca et al. (2003) and the high solubility of other phosphate minerals (apatite and monazite) at the conditions modelled here, xenotime is assumed to completely dissolve. The solubility of apatite is controlled by the saturation of an essential structural constituent (ESC; phosphorus in this case) in the melt, and can be calculated using the equations of Pichavant et al. (1992) for the phosphorus oxide saturation concentration: P2O5PMR= P2O5HW+ P2O5PerP2O5Per=[Al(2Ca+K+Na)−1]×exp⁡(−5900T−3·22SiO2+9·31). The P2 O5HW term is the phosphorus oxide content derived from the Harrison & Watson (1984) apatite solubility expression for metaluminous melts: ln⁡DPapatite/melt=8400+[104×2·64(SiO2−0·05)]T−[3·1+12·4(SiO2−0·5)]. If the melt is metaluminous the P2 O5Per term is omitted (A/CKN is set to unity). The dissolution of monazite, controlled by light rare earth element (LREE) saturation, is modelled using the solubility equation of Rapp et al. (1987): lnC∑LREE=4·68 – (14160/T) where CΣLREE is the sum of the concentrations of La, Ce, Pr, Nd, Sm and Gd in ppm. This expression for monazite solubility has been chosen in favour of the refined solubility model of Montel (1993) so as to avoid incorporating Li and H2O contents, which would be poorly constrained. Zircon solubility is also related to the saturation concentration of its ESC (Zr). The Zr saturation can be calculated according to the equations of Watson & Harrison (1983), as updated by Boehnke et al. (2013): ln⁡DZrzircon/melt=−1·48−1·16(M−1)+(10108/T)M=(Na+K+2Ca)/(Al×Si). The terms used to calculate the parameter M are the mole fractions of the cations normalized to the total mole fraction. In all of the above equations temperature is in Kelvin. As the equations used to model the dissolution of zircon, apatite and monazite are in terms of the concentrations at which the melt becomes saturated in particular elements, the masses of the accessory phases that dissolve must be calculated from these, taking into account that multiple phases contribute the elements of interest to the melt (i.e. apatite is not the only source of phosphorus, zircon is not the only source of zirconium, and so on). Thus, the amount of apatite, monazite and zircon that dissolves is calculated as the amount of each mineral required to provide the P2O5, LREE and Zr, respectively, that could not be provided by other phases to bring the melt to saturation. To do this, contribution of monazite to the melt P2O5 budget is subtracted from the P2 O5PMR, and the mass of apatite (map) that dissolves is calculated as map= [(Pmelt×fmelt) – (Pmonz×fmonz)] × [Map/(3×MP)]Pmelt=(2×MP×P2O5PMR)/MP2O5 where Pmelt and Pmonz are the phosphorus contents in weight per cent of the melt and monazite (Pmonz = 10·43 wt %), respectively; fmelt and fmonz are the weight fractions of melt and dissolved monazite, respectively; and Map, MP and MP2O5 are the molecular masses of apatite (fluorapatite, 504·2977 g mol–1), phosphorus and P2O5, respectively. For monazite and zircon the masses (mmonz and mzrc) that dissolve are related to the concentrations of their ESC (∑LREE and Zr, respectively) by mmonz or zrc=mmelt×CESC*/CESCmonz or zrcCESC*=CESCmelt−[∑(mi×CESCi)−∑(mp×CESCp)/mmelt] where mi and mp are the masses of the phases that contribute to the melt and the peritectic minerals, respectively, and CESCi and CESCp are the corresponding ESC concentrations. CESCmelt is the saturation concentration of the ESC as determined by the solubility equations above, whereas CESC* is the portion of that concentration that must be provided by the relevant accessory mineral. As these equations are self-referential, the system is solved iteratively. The calculations are simplified if there is not enough of one of the accessory phases to meet the saturation concentration of its ESC, as it can be simply assumed that all of that phase dissolves, and the undersaturated concentration is calculated. The growth of one or more peritectic phases is a feature of many of the melt-producing reactions. Peritectic phases incorporate trace elements from the melt as they grow, thus removing them from the melt. This counteracts the contribution to the trace element concentration of the melt from phases undergoing melting or dissolution. This effect has been accounted for in the equations for the amount of monazite and zircon that dissolves, but a method for assigning the trace element compositions of peritectic phases is required. Following the approach of Davies & Tommasini (2000), it is assumed that equilibrium partition coefficients (K) only apply to the growth of peritectic minerals, allowing the concentration of an element X in a peritectic phase (CXp) to be calculated: CXp=CXmelt×KXp. The partition coefficients used are based on various previous studies (Luhr & Carmichael, 1980; Sisson & Bacon, 1992; van Westrenen et al., 1999; Kleine et al., 2000; Klemme et al., 2002; Ren et al., 2003; Rubatto & Hermann, 2007; Severs et al., 2009; van Kan Parker et al., 2010; Brophy et al., 2011), where possible utilizing a lattice strain model parameterization (Blundy & Wood, 1994), and are provided in the Supplementary Data (supplementary data are available for downloading at http://www.petrology.oxfordjournals.org). If there is enough zircon to achieve Zr saturation, then CZrmelt will be the saturation concentration, but for other elements or Zr undersaturation CXmelt is derived as follows: ∑(mi×CXi)=(mmelt×CXmelt)+∑(mp×CXp) which states the mass balance. Substituting the equation for CXp into this equation and rearranging gives CXmelt=∑(mi×CXi)/[mmelt+∑(mp×KXp)]. These are incorporated into the iterative calculation. With iteration, the sum of CXmelt for La, Ce, Pr, Nd, Sm and Gd should converge on the C∑LREE value from the Rapp et al. (1987) equation if enough monazite is present to saturate the melt. In terms of mineral assemblages, the different protoliths used for modelling are four greenschists, a hornblende hornfels and the average of these from Beard & Lofgren (1991), a basaltic amphibolite from Sen & Dunn (1994), a tonalite from Petcovic & Grunder (2003), an orthogneiss from Rajesh et al. (2013) and a pyroxene quartz-monzodiorite from Årebäck et al. (2008). As most of these studies did not report accessory mineral abundances, small amounts of accessory minerals have been included (chosen with reference to a variety of published accessory mineral abundances; Bingen et al., 1996; Ayres & Harris, 1997; Petcovic & Grunder, 2003; Villaseca et al., 2003; Zeng et al., 2005; Årebäck et al., 2008; Nehring et al., 2010; Rajesh et al., 2013), and the other mineral modes adjusted to keep the sum of modes at 100%. The modal abundances for these protoliths are listed in Table 1. Table 1: Modal abundances of minerals in the protoliths used for modelling Protolith: S&D B&L 557 B&L 555 B&L 478 B&L 466 B&L 571 B&L average B&L average + aln B&L average (low zrc) Quartz 2·29 11·05 6·70 9·53 8·96 7·07 8·66 8·6635 8·6644 Plagioclase 20·45 44·93 55·69 44·58 48·16 49·49 48·57 48·5683 48·5734 K-feldspar — — — — — — — — — Amphibole 76·12 40·52 24·55 34·96 32·86 25·94 31·77 31·7652 31·7686 Clinopyroxene 0·00 0·77 0·75 — — 6·40 1·58 1·5829 1·5831 Titanite 0·90 0·15 0·30 — — 0·90 0·27 0·2690 0·2690 Orthopyroxene — 0·21 4·10 3·85 1·53 0·00 1·94 1·9389 1·9391 Biotite — — — — — — — — — Apatite 0·20 0·20 0·20 0·20 0·20 0·20 0·20 0·2000 0·2000 Monazite 0·01 0·01 0·01 0·01 0·01 0·01 0·01 0·0078 0·0050 Zircon 0·03 0·03 0·03 0·03 0·03 0·03 0·03 0·0300 0·0150 Allanite — — — — — — — 0·0078 0·0150 Xenotime — — — — — — — — — Ilmenite — — 2·40 5·35 0·59 1·23 1·91 1·9099 1·9101 Magnetite — 2·10 5·30 1·48 7·66 8·73 5·06 5·0567 5·0573 Protolith: S&D B&L 557 B&L 555 B&L 478 B&L 466 B&L 571 B&L average B&L average + aln B&L average (low zrc) Quartz 2·29 11·05 6·70 9·53 8·96 7·07 8·66 8·6635 8·6644 Plagioclase 20·45 44·93 55·69 44·58 48·16 49·49 48·57 48·5683 48·5734 K-feldspar — — — — — — — — — Amphibole 76·12 40·52 24·55 34·96 32·86 25·94 31·77 31·7652 31·7686 Clinopyroxene 0·00 0·77 0·75 — — 6·40 1·58 1·5829 1·5831 Titanite 0·90 0·15 0·30 — — 0·90 0·27 0·2690 0·2690 Orthopyroxene — 0·21 4·10 3·85 1·53 0·00 1·94 1·9389 1·9391 Biotite — — — — — — — — — Apatite 0·20 0·20 0·20 0·20 0·20 0·20 0·20 0·2000 0·2000 Monazite 0·01 0·01 0·01 0·01 0·01 0·01 0·01 0·0078 0·0050 Zircon 0·03 0·03 0·03 0·03 0·03 0·03 0·03 0·0300 0·0150 Allanite — — — — — — — 0·0078 0·0150 Xenotime — — — — — — — — — Ilmenite — — 2·40 5·35 0·59 1·23 1·91 1·9099 1·9101 Magnetite — 2·10 5·30 1·48 7·66 8·73 5·06 5·0567 5·0573 Protolith: B&L average + aln + xen B&L average (no zrc) B&L average (no zrc or mon) P&G P&G (low zrc) R2013 R2013* A2008 Quartz 8·6627 8·66661 8·67 19·240 19·243 14·836 14·870 10·613 Plagioclase 48·5637 48·58561 48·59 42·767 42·773 40·551 40·645 45·657 K-feldspar — 31·77655 31·78 7·975 7·976 8·901 8·922 17·121 Amphibole 31·7622 1·58348 1·58 14·654 14·657 9·891 11·054 5·782 Clinopyroxene 1·5828 0·26908 0·27 — — 6·923 6·939 2·303 Titanite 0·2690 1·93958 1·94 0·150 0·150 0·180 Orthopyroxene 1·9387 — — — — 3·956 3·965 6·909 Biotite — 0·20000 0·20 13·957 13·959 11·869 10·527 5·507 Apatite 0·2000 0·01000 — 0·200 0·200 1·978 1·983 1·602 Monazite 0·0050 — — — — 0·005 0·005 0·005 Zircon 0·0300 1·91057 1·91 0·030 0·015 0·060 0·060 0·080 Allanite 0·0150 5·05852 5·06 0·030 0·030 0·030 0·030 0·035 Xenotime 0·0050 8·66661 8·67 — — — — — Ilmenite 1·9097 48·58561 48·59 0·000 0·000 0·500 0·500 4·205 Magnetite 5·0562 31·77655 31·78 0·997 0·997 0·500 0·500 — Protolith: B&L average + aln + xen B&L average (no zrc) B&L average (no zrc or mon) P&G P&G (low zrc) R2013 R2013* A2008 Quartz 8·6627 8·66661 8·67 19·240 19·243 14·836 14·870 10·613 Plagioclase 48·5637 48·58561 48·59 42·767 42·773 40·551 40·645 45·657 K-feldspar — 31·77655 31·78 7·975 7·976 8·901 8·922 17·121 Amphibole 31·7622 1·58348 1·58 14·654 14·657 9·891 11·054 5·782 Clinopyroxene 1·5828 0·26908 0·27 — — 6·923 6·939 2·303 Titanite 0·2690 1·93958 1·94 0·150 0·150 0·180 Orthopyroxene 1·9387 — — — — 3·956 3·965 6·909 Biotite — 0·20000 0·20 13·957 13·959 11·869 10·527 5·507 Apatite 0·2000 0·01000 — 0·200 0·200 1·978 1·983 1·602 Monazite 0·0050 — — — — 0·005 0·005 0·005 Zircon 0·0300 1·91057 1·91 0·030 0·015 0·060 0·060 0·080 Allanite 0·0150 5·05852 5·06 0·030 0·030 0·030 0·030 0·035 Xenotime 0·0050 8·66661 8·67 — — — — — Ilmenite 1·9097 48·58561 48·59 0·000 0·000 0·500 0·500 4·205 Magnetite 5·0562 31·77655 31·78 0·997 0·997 0·500 0·500 — Protoliths and reactions from the literature are listed as S&D for Sen & Dunn (1994); B&L for Beard & Lofgren (1991); P&G for Petcovic & Grunder (2003); R2013 for Rajesh et al. (2013); A2008 for Årebäck et al. (2008). The B&L protoliths use the sample numbers as in the original study. aln, allanite; zrc, zircon; xen, xenotime; mon, monazite. All modes sum to 100% and are quoted to the number of decimal places that retains that sum regardless of rounding. * Mineral modes were modified to ensure biotite and amphibole are exhausted at the same time. Table 1: Modal abundances of minerals in the protoliths used for modelling Protolith: S&D B&L 557 B&L 555 B&L 478 B&L 466 B&L 571 B&L average B&L average + aln B&L average (low zrc) Quartz 2·29 11·05 6·70 9·53 8·96 7·07 8·66 8·6635 8·6644 Plagioclase 20·45 44·93 55·69 44·58 48·16 49·49 48·57 48·5683 48·5734 K-feldspar — — — — — — — — — Amphibole 76·12 40·52 24·55 34·96 32·86 25·94 31·77 31·7652 31·7686 Clinopyroxene 0·00 0·77 0·75 — — 6·40 1·58 1·5829 1·5831 Titanite 0·90 0·15 0·30 — — 0·90 0·27 0·2690 0·2690 Orthopyroxene — 0·21 4·10 3·85 1·53 0·00 1·94 1·9389 1·9391 Biotite — — — — — — — — — Apatite 0·20 0·20 0·20 0·20 0·20 0·20 0·20 0·2000 0·2000 Monazite 0·01 0·01 0·01 0·01 0·01 0·01 0·01 0·0078 0·0050 Zircon 0·03 0·03 0·03 0·03 0·03 0·03 0·03 0·0300 0·0150 Allanite — — — — — — — 0·0078 0·0150 Xenotime — — — — — — — — — Ilmenite — — 2·40 5·35 0·59 1·23 1·91 1·9099 1·9101 Magnetite — 2·10 5·30 1·48 7·66 8·73 5·06 5·0567 5·0573 Protolith: S&D B&L 557 B&L 555 B&L 478 B&L 466 B&L 571 B&L average B&L average + aln B&L average (low zrc) Quartz 2·29 11·05 6·70 9·53 8·96 7·07 8·66 8·6635 8·6644 Plagioclase 20·45 44·93 55·69 44·58 48·16 49·49 48·57 48·5683 48·5734 K-feldspar — — — — — — — — — Amphibole 76·12 40·52 24·55 34·96 32·86 25·94 31·77 31·7652 31·7686 Clinopyroxene 0·00 0·77 0·75 — — 6·40 1·58 1·5829 1·5831 Titanite 0·90 0·15 0·30 — — 0·90 0·27 0·2690 0·2690 Orthopyroxene — 0·21 4·10 3·85 1·53 0·00 1·94 1·9389 1·9391 Biotite — — — — — — — — — Apatite 0·20 0·20 0·20 0·20 0·20 0·20 0·20 0·2000 0·2000 Monazite 0·01 0·01 0·01 0·01 0·01 0·01 0·01 0·0078 0·0050 Zircon 0·03 0·03 0·03 0·03 0·03 0·03 0·03 0·0300 0·0150 Allanite — — — — — — — 0·0078 0·0150 Xenotime — — — — — — — — — Ilmenite — — 2·40 5·35 0·59 1·23 1·91 1·9099 1·9101 Magnetite — 2·10 5·30 1·48 7·66 8·73 5·06 5·0567 5·0573 Protolith: B&L average + aln + xen B&L average (no zrc) B&L average (no zrc or mon) P&G P&G (low zrc) R2013 R2013* A2008 Quartz 8·6627 8·66661 8·67 19·240 19·243 14·836 14·870 10·613 Plagioclase 48·5637 48·58561 48·59 42·767 42·773 40·551 40·645 45·657 K-feldspar — 31·77655 31·78 7·975 7·976 8·901 8·922 17·121 Amphibole 31·7622 1·58348 1·58 14·654 14·657 9·891 11·054 5·782 Clinopyroxene 1·5828 0·26908 0·27 — — 6·923 6·939 2·303 Titanite 0·2690 1·93958 1·94 0·150 0·150 0·180 Orthopyroxene 1·9387 — — — — 3·956 3·965 6·909 Biotite — 0·20000 0·20 13·957 13·959 11·869 10·527 5·507 Apatite 0·2000 0·01000 — 0·200 0·200 1·978 1·983 1·602 Monazite 0·0050 — — — — 0·005 0·005 0·005 Zircon 0·0300 1·91057 1·91 0·030 0·015 0·060 0·060 0·080 Allanite 0·0150 5·05852 5·06 0·030 0·030 0·030 0·030 0·035 Xenotime 0·0050 8·66661 8·67 — — — — — Ilmenite 1·9097 48·58561 48·59 0·000 0·000 0·500 0·500 4·205 Magnetite 5·0562 31·77655 31·78 0·997 0·997 0·500 0·500 — Protolith: B&L average + aln + xen B&L average (no zrc) B&L average (no zrc or mon) P&G P&G (low zrc) R2013 R2013* A2008 Quartz 8·6627 8·66661 8·67 19·240 19·243 14·836 14·870 10·613 Plagioclase 48·5637 48·58561 48·59 42·767 42·773 40·551 40·645 45·657 K-feldspar — 31·77655 31·78 7·975 7·976 8·901 8·922 17·121 Amphibole 31·7622 1·58348 1·58 14·654 14·657 9·891 11·054 5·782 Clinopyroxene 1·5828 0·26908 0·27 — — 6·923 6·939 2·303 Titanite 0·2690 1·93958 1·94 0·150 0·150 0·180 Orthopyroxene 1·9387 — — — — 3·956 3·965 6·909 Biotite — 0·20000 0·20 13·957 13·959 11·869 10·527 5·507 Apatite 0·2000 0·01000 — 0·200 0·200 1·978 1·983 1·602 Monazite 0·0050 — — — — 0·005 0·005 0·005 Zircon 0·0300 1·91057 1·91 0·030 0·015 0·060 0·060 0·080 Allanite 0·0150 5·05852 5·06 0·030 0·030 0·030 0·030 0·035 Xenotime 0·0050 8·66661 8·67 — — — — — Ilmenite 1·9097 48·58561 48·59 0·000 0·000 0·500 0·500 4·205 Magnetite 5·0562 31·77655 31·78 0·997 0·997 0·500 0·500 — Protoliths and reactions from the literature are listed as S&D for Sen & Dunn (1994); B&L for Beard & Lofgren (1991); P&G for Petcovic & Grunder (2003); R2013 for Rajesh et al. (2013); A2008 for Årebäck et al. (2008). The B&L protoliths use the sample numbers as in the original study. aln, allanite; zrc, zircon; xen, xenotime; mon, monazite. All modes sum to 100% and are quoted to the number of decimal places that retains that sum regardless of rounding. * Mineral modes were modified to ensure biotite and amphibole are exhausted at the same time. The trace element compositions of each mineral in the protolith have in the first instance been set as the average of compositions reported for that mineral across a range of previous studies (Luhr & Carmichael, 1980; Bea et al., 1994, 2006; Bea, 1996b; Bingen et al., 1996; Pan & Fleet, 1996; Ayres & Harris, 1997; Belousova et al., 2002; Hermann, 2002; Villaseca et al., 2003; Storkey et al., 2005; Tiepolo & Tribuzio, 2005; Gregory et al., 2009, 2012; Acosta-Vigil et al., 2010; Driouch et al., 2010; Nehring et al., 2010; Starijaš Mayer et al., 2014; Xing et al., 2014). These compositions are listed in Table 2. Alternative trace element compositions have also been used for some of the modelling to test the sensitivity of the model in this respect. In choosing the alternative trace element compositions, an important consideration was to ensure that the adjusted trace element compositions remained consistent with the concentrations and Rb/Sr, Sm/Nd and Lu/Hf ratios recorded in the literature (cited above). Further details are provided in the context of the model results and two alternative sets of mineral trace element compositions are listed as ‘Modified 1’ and ‘Modified 2’ along with the ‘Mean values’ in Table 2. Table 2: Trace element compositions of minerals used in the modelling Phase Rb Sr La Ce Pr Nd Sm Gd ΣLREE* Lu Hf Zr Mean values Plagioclase 7·17 523·9 5·65 6·88 0·528 1·52 0·230 0·130 14·9 0·022 0·544 15·4 K-feldspar 370·4 731·6 0·618 1·05 0·120 0·276 0·040 0·071 2·17 0·010 0·376 13·0 Amphibole 14·7 46·8 8·54 27·8 4·59 23·8 7·11 7·81 79·7 0·514 2·97 62·0 Clinopyroxene 1·89 16·8 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·301 1·79 38·9 Titanite 0·529 33·6 660·4 1892 302·0 1339 323·6 257·5 4775 14·6 46·3 847·4 Orthopyroxene 0·114 0·487 0·136 0·250 0·037 0·173 0·096 0·156 0·846 0·160 0·103 1·84 Biotite 606·5 28·7 1·67 5·37 0·428 1·42 0·332 0·293 9·52 0·020 0·090 1·65 Apatite 0·235 446·7 481·7 1244 176·6 837·5 289·1 369·4 3398 16·9 0·031 1·01 Monazite 1·70 87·6 95789 234852 27923 113646 21084 13797 507091 39·7 0·165 2·23 Zircon 13·0 1·80 0·963 17·1 0·437 3·50 3·50 16·6 42·0 80·1 10870 498000 Allanite 0·347 3674 36540 73818 8098 23253 2946 1674 146329 11·5 0·384 9·72 Xenotime 21·5 8·50 127·9 1380 384·5 3224 3748 15619·6 24484 5584 132·3 274·0 Ilmenite — — 1·11 0·738 0·100 0·317 0·123 0·087 2·47 0·047 7·00 271·8 Magnetite — — 3·08 5·94 0·899 4·36 0·357 0·340 15·0 0·081 1·02 15·7 Modified 1 Plagioclase 7·17 523·9 2·53 3·12 0·243 0·721 0·025 0·130 6·77 0·047 0·065 0·454 Amphibole 27·6 28·9 8·54 27·8 4·59 23·8 7·11 7·81 79·7 0·514 2·97 62·0 Clinopyroxene 10·5 13·2 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·301 1·79 38·9 Titanite 1·04 29·1 386·5 1108 176·7 783·7 137·0 257·5 2849 24·6 19·5 66·5 Orthopyroxene 0·192 0·455 0·239 0·433 0·061 0·271 0·076 0·156 1·23 0·048 0·010 0·178 Apatite 0·370 251·5 481·7 1244 176·6 837·5 289·1 369·4 3398 16·9 0·031 1·01 Monazite 1·70 87·6 122620 251499 32518 129204 10978 6958 553777 39·7 0·165 2·23 Zircon 13·0 1·80 1·40 24·8 0·636 5·10 1·40 6·63 40·0 198·5 8800 498000 Allanite 0·720 905·2 35386 71487 7843 22519 1280 727·4 139242 4·13 0·086 2·18 Xenotime 21·9 7·30 145·6 1571 437·7 3669 1242 5175 12240 2418 107·6 274·0 Ilmenite — — 0·233 0·155 0·021 0·026 0·010 0·016 0·461 0·047 0·706 26·7 Magnetite — — 5·14 9·91 1·50 7·27 0·330 0·314 24·5 0·032 0·036 0·555 Modified 2 Plagioclase 7·17 523·9 2·53 3·12 0·243 0·721 0·025 0·018 6·66 0·012 0·016 0·454 K-feldspar 186·0 427·4 12·0 22·8 0·972 1·56 0·229 0·326 37·9 0·017 0·439 12·6 Amphibole 2·68 85·6 8·54 27·8 4·59 23·8 7·11 7·81 79·7 0·514 2·97 62·0 Clinopyroxene 0·025 24·4 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·301 1·79 38·9 Titanite 0·252 48·3 386·5 1108 176·7 783·7 137·0 257·5 2849 24·6 19·5 66·5 Orthopyroxene 0·048 0·707 0·239 0·433 0·061 0·271 0·076 0·156 1·23 0·048 0·010 0·178 Biotite 397·0 53·3 0·154 0·494 0·039 0·060 0·010 0·019 0·775 0·010 0·010 0·121 Apatite 0·054 877·1 481·7 1244 176·6 837·5 289·1 369·4 3398 16·9 0·031 1·01 Monazite 1·70 87·6 95789 234852 27923 113646 21084 13797 507091 39·7 0·165 2·23 Zircon 13·0 1·80 0·96 17·1 0·437 3·50 3·50 16·6 42·0 198·5 8800 498000 Allanite 0·267 5712 36689 77531 8775 27258 2383 1628 154262 15·8 0·329 8·34 Ilmenite — — 1·11 0·738 0·100 0·317 0·123 0·087 2·47 0·047 7·00 271·8 Magnetite — — 3·08 5·94 0·899 4·36 0·357 0·340 15·0 0·125 0·140 2·16 High Lu, Hf and Zr† Plagioclase 7·17 523·9 5·65 6·88 0·528 1·52 0·230 0·130 14·9 0·050 2·80 118·0 Amphibole 14·7 46·8 8·54 27·8 4·59 23·8 7·11 7·81 79·7 1·61 10·6 187·0 Clinopyroxene 1·89 16·8 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·589 6·90 137·0 Titanite 0·529 33·6 660·4 1892 302·0 1339 323·6 257·5 4775 31·2 135·0 2100 Orthopyroxene 0·114 0·487 0·136 0·250 0·037 0·173 0·096 0·156 0·846 0·170 0·113 4·00 Ilmenite — — 1·11 0·738 0·100 0·317 0·123 0·087 2·47 0·050 17·1 677·0 Magnetite — — 3·08 5·94 0·899 4·36 0·357 0·340 15·0 0·130 1·83 47·0 Phase Rb Sr La Ce Pr Nd Sm Gd ΣLREE* Lu Hf Zr Mean values Plagioclase 7·17 523·9 5·65 6·88 0·528 1·52 0·230 0·130 14·9 0·022 0·544 15·4 K-feldspar 370·4 731·6 0·618 1·05 0·120 0·276 0·040 0·071 2·17 0·010 0·376 13·0 Amphibole 14·7 46·8 8·54 27·8 4·59 23·8 7·11 7·81 79·7 0·514 2·97 62·0 Clinopyroxene 1·89 16·8 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·301 1·79 38·9 Titanite 0·529 33·6 660·4 1892 302·0 1339 323·6 257·5 4775 14·6 46·3 847·4 Orthopyroxene 0·114 0·487 0·136 0·250 0·037 0·173 0·096 0·156 0·846 0·160 0·103 1·84 Biotite 606·5 28·7 1·67 5·37 0·428 1·42 0·332 0·293 9·52 0·020 0·090 1·65 Apatite 0·235 446·7 481·7 1244 176·6 837·5 289·1 369·4 3398 16·9 0·031 1·01 Monazite 1·70 87·6 95789 234852 27923 113646 21084 13797 507091 39·7 0·165 2·23 Zircon 13·0 1·80 0·963 17·1 0·437 3·50 3·50 16·6 42·0 80·1 10870 498000 Allanite 0·347 3674 36540 73818 8098 23253 2946 1674 146329 11·5 0·384 9·72 Xenotime 21·5 8·50 127·9 1380 384·5 3224 3748 15619·6 24484 5584 132·3 274·0 Ilmenite — — 1·11 0·738 0·100 0·317 0·123 0·087 2·47 0·047 7·00 271·8 Magnetite — — 3·08 5·94 0·899 4·36 0·357 0·340 15·0 0·081 1·02 15·7 Modified 1 Plagioclase 7·17 523·9 2·53 3·12 0·243 0·721 0·025 0·130 6·77 0·047 0·065 0·454 Amphibole 27·6 28·9 8·54 27·8 4·59 23·8 7·11 7·81 79·7 0·514 2·97 62·0 Clinopyroxene 10·5 13·2 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·301 1·79 38·9 Titanite 1·04 29·1 386·5 1108 176·7 783·7 137·0 257·5 2849 24·6 19·5 66·5 Orthopyroxene 0·192 0·455 0·239 0·433 0·061 0·271 0·076 0·156 1·23 0·048 0·010 0·178 Apatite 0·370 251·5 481·7 1244 176·6 837·5 289·1 369·4 3398 16·9 0·031 1·01 Monazite 1·70 87·6 122620 251499 32518 129204 10978 6958 553777 39·7 0·165 2·23 Zircon 13·0 1·80 1·40 24·8 0·636 5·10 1·40 6·63 40·0 198·5 8800 498000 Allanite 0·720 905·2 35386 71487 7843 22519 1280 727·4 139242 4·13 0·086 2·18 Xenotime 21·9 7·30 145·6 1571 437·7 3669 1242 5175 12240 2418 107·6 274·0 Ilmenite — — 0·233 0·155 0·021 0·026 0·010 0·016 0·461 0·047 0·706 26·7 Magnetite — — 5·14 9·91 1·50 7·27 0·330 0·314 24·5 0·032 0·036 0·555 Modified 2 Plagioclase 7·17 523·9 2·53 3·12 0·243 0·721 0·025 0·018 6·66 0·012 0·016 0·454 K-feldspar 186·0 427·4 12·0 22·8 0·972 1·56 0·229 0·326 37·9 0·017 0·439 12·6 Amphibole 2·68 85·6 8·54 27·8 4·59 23·8 7·11 7·81 79·7 0·514 2·97 62·0 Clinopyroxene 0·025 24·4 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·301 1·79 38·9 Titanite 0·252 48·3 386·5 1108 176·7 783·7 137·0 257·5 2849 24·6 19·5 66·5 Orthopyroxene 0·048 0·707 0·239 0·433 0·061 0·271 0·076 0·156 1·23 0·048 0·010 0·178 Biotite 397·0 53·3 0·154 0·494 0·039 0·060 0·010 0·019 0·775 0·010 0·010 0·121 Apatite 0·054 877·1 481·7 1244 176·6 837·5 289·1 369·4 3398 16·9 0·031 1·01 Monazite 1·70 87·6 95789 234852 27923 113646 21084 13797 507091 39·7 0·165 2·23 Zircon 13·0 1·80 0·96 17·1 0·437 3·50 3·50 16·6 42·0 198·5 8800 498000 Allanite 0·267 5712 36689 77531 8775 27258 2383 1628 154262 15·8 0·329 8·34 Ilmenite — — 1·11 0·738 0·100 0·317 0·123 0·087 2·47 0·047 7·00 271·8 Magnetite — — 3·08 5·94 0·899 4·36 0·357 0·340 15·0 0·125 0·140 2·16 High Lu, Hf and Zr† Plagioclase 7·17 523·9 5·65 6·88 0·528 1·52 0·230 0·130 14·9 0·050 2·80 118·0 Amphibole 14·7 46·8 8·54 27·8 4·59 23·8 7·11 7·81 79·7 1·61 10·6 187·0 Clinopyroxene 1·89 16·8 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·589 6·90 137·0 Titanite 0·529 33·6 660·4 1892 302·0 1339 323·6 257·5 4775 31·2 135·0 2100 Orthopyroxene 0·114 0·487 0·136 0·250 0·037 0·173 0·096 0·156 0·846 0·170 0·113 4·00 Ilmenite — — 1·11 0·738 0·100 0·317 0·123 0·087 2·47 0·050 17·1 677·0 Magnetite — — 3·08 5·94 0·899 4·36 0·357 0·340 15·0 0·130 1·83 47·0 * The sum of the light rare earth elements (ΣLREE) excludes Eu, in accordance with the way monazite saturation is described in the main text. †Other minerals present use the ‘mean values’. All concentrations are given in parts per million. Table 2: Trace element compositions of minerals used in the modelling Phase Rb Sr La Ce Pr Nd Sm Gd ΣLREE* Lu Hf Zr Mean values Plagioclase 7·17 523·9 5·65 6·88 0·528 1·52 0·230 0·130 14·9 0·022 0·544 15·4 K-feldspar 370·4 731·6 0·618 1·05 0·120 0·276 0·040 0·071 2·17 0·010 0·376 13·0 Amphibole 14·7 46·8 8·54 27·8 4·59 23·8 7·11 7·81 79·7 0·514 2·97 62·0 Clinopyroxene 1·89 16·8 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·301 1·79 38·9 Titanite 0·529 33·6 660·4 1892 302·0 1339 323·6 257·5 4775 14·6 46·3 847·4 Orthopyroxene 0·114 0·487 0·136 0·250 0·037 0·173 0·096 0·156 0·846 0·160 0·103 1·84 Biotite 606·5 28·7 1·67 5·37 0·428 1·42 0·332 0·293 9·52 0·020 0·090 1·65 Apatite 0·235 446·7 481·7 1244 176·6 837·5 289·1 369·4 3398 16·9 0·031 1·01 Monazite 1·70 87·6 95789 234852 27923 113646 21084 13797 507091 39·7 0·165 2·23 Zircon 13·0 1·80 0·963 17·1 0·437 3·50 3·50 16·6 42·0 80·1 10870 498000 Allanite 0·347 3674 36540 73818 8098 23253 2946 1674 146329 11·5 0·384 9·72 Xenotime 21·5 8·50 127·9 1380 384·5 3224 3748 15619·6 24484 5584 132·3 274·0 Ilmenite — — 1·11 0·738 0·100 0·317 0·123 0·087 2·47 0·047 7·00 271·8 Magnetite — — 3·08 5·94 0·899 4·36 0·357 0·340 15·0 0·081 1·02 15·7 Modified 1 Plagioclase 7·17 523·9 2·53 3·12 0·243 0·721 0·025 0·130 6·77 0·047 0·065 0·454 Amphibole 27·6 28·9 8·54 27·8 4·59 23·8 7·11 7·81 79·7 0·514 2·97 62·0 Clinopyroxene 10·5 13·2 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·301 1·79 38·9 Titanite 1·04 29·1 386·5 1108 176·7 783·7 137·0 257·5 2849 24·6 19·5 66·5 Orthopyroxene 0·192 0·455 0·239 0·433 0·061 0·271 0·076 0·156 1·23 0·048 0·010 0·178 Apatite 0·370 251·5 481·7 1244 176·6 837·5 289·1 369·4 3398 16·9 0·031 1·01 Monazite 1·70 87·6 122620 251499 32518 129204 10978 6958 553777 39·7 0·165 2·23 Zircon 13·0 1·80 1·40 24·8 0·636 5·10 1·40 6·63 40·0 198·5 8800 498000 Allanite 0·720 905·2 35386 71487 7843 22519 1280 727·4 139242 4·13 0·086 2·18 Xenotime 21·9 7·30 145·6 1571 437·7 3669 1242 5175 12240 2418 107·6 274·0 Ilmenite — — 0·233 0·155 0·021 0·026 0·010 0·016 0·461 0·047 0·706 26·7 Magnetite — — 5·14 9·91 1·50 7·27 0·330 0·314 24·5 0·032 0·036 0·555 Modified 2 Plagioclase 7·17 523·9 2·53 3·12 0·243 0·721 0·025 0·018 6·66 0·012 0·016 0·454 K-feldspar 186·0 427·4 12·0 22·8 0·972 1·56 0·229 0·326 37·9 0·017 0·439 12·6 Amphibole 2·68 85·6 8·54 27·8 4·59 23·8 7·11 7·81 79·7 0·514 2·97 62·0 Clinopyroxene 0·025 24·4 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·301 1·79 38·9 Titanite 0·252 48·3 386·5 1108 176·7 783·7 137·0 257·5 2849 24·6 19·5 66·5 Orthopyroxene 0·048 0·707 0·239 0·433 0·061 0·271 0·076 0·156 1·23 0·048 0·010 0·178 Biotite 397·0 53·3 0·154 0·494 0·039 0·060 0·010 0·019 0·775 0·010 0·010 0·121 Apatite 0·054 877·1 481·7 1244 176·6 837·5 289·1 369·4 3398 16·9 0·031 1·01 Monazite 1·70 87·6 95789 234852 27923 113646 21084 13797 507091 39·7 0·165 2·23 Zircon 13·0 1·80 0·96 17·1 0·437 3·50 3·50 16·6 42·0 198·5 8800 498000 Allanite 0·267 5712 36689 77531 8775 27258 2383 1628 154262 15·8 0·329 8·34 Ilmenite — — 1·11 0·738 0·100 0·317 0·123 0·087 2·47 0·047 7·00 271·8 Magnetite — — 3·08 5·94 0·899 4·36 0·357 0·340 15·0 0·125 0·140 2·16 High Lu, Hf and Zr† Plagioclase 7·17 523·9 5·65 6·88 0·528 1·52 0·230 0·130 14·9 0·050 2·80 118·0 Amphibole 14·7 46·8 8·54 27·8 4·59 23·8 7·11 7·81 79·7 1·61 10·6 187·0 Clinopyroxene 1·89 16·8 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·589 6·90 137·0 Titanite 0·529 33·6 660·4 1892 302·0 1339 323·6 257·5 4775 31·2 135·0 2100 Orthopyroxene 0·114 0·487 0·136 0·250 0·037 0·173 0·096 0·156 0·846 0·170 0·113 4·00 Ilmenite — — 1·11 0·738 0·100 0·317 0·123 0·087 2·47 0·050 17·1 677·0 Magnetite — — 3·08 5·94 0·899 4·36 0·357 0·340 15·0 0·130 1·83 47·0 Phase Rb Sr La Ce Pr Nd Sm Gd ΣLREE* Lu Hf Zr Mean values Plagioclase 7·17 523·9 5·65 6·88 0·528 1·52 0·230 0·130 14·9 0·022 0·544 15·4 K-feldspar 370·4 731·6 0·618 1·05 0·120 0·276 0·040 0·071 2·17 0·010 0·376 13·0 Amphibole 14·7 46·8 8·54 27·8 4·59 23·8 7·11 7·81 79·7 0·514 2·97 62·0 Clinopyroxene 1·89 16·8 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·301 1·79 38·9 Titanite 0·529 33·6 660·4 1892 302·0 1339 323·6 257·5 4775 14·6 46·3 847·4 Orthopyroxene 0·114 0·487 0·136 0·250 0·037 0·173 0·096 0·156 0·846 0·160 0·103 1·84 Biotite 606·5 28·7 1·67 5·37 0·428 1·42 0·332 0·293 9·52 0·020 0·090 1·65 Apatite 0·235 446·7 481·7 1244 176·6 837·5 289·1 369·4 3398 16·9 0·031 1·01 Monazite 1·70 87·6 95789 234852 27923 113646 21084 13797 507091 39·7 0·165 2·23 Zircon 13·0 1·80 0·963 17·1 0·437 3·50 3·50 16·6 42·0 80·1 10870 498000 Allanite 0·347 3674 36540 73818 8098 23253 2946 1674 146329 11·5 0·384 9·72 Xenotime 21·5 8·50 127·9 1380 384·5 3224 3748 15619·6 24484 5584 132·3 274·0 Ilmenite — — 1·11 0·738 0·100 0·317 0·123 0·087 2·47 0·047 7·00 271·8 Magnetite — — 3·08 5·94 0·899 4·36 0·357 0·340 15·0 0·081 1·02 15·7 Modified 1 Plagioclase 7·17 523·9 2·53 3·12 0·243 0·721 0·025 0·130 6·77 0·047 0·065 0·454 Amphibole 27·6 28·9 8·54 27·8 4·59 23·8 7·11 7·81 79·7 0·514 2·97 62·0 Clinopyroxene 10·5 13·2 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·301 1·79 38·9 Titanite 1·04 29·1 386·5 1108 176·7 783·7 137·0 257·5 2849 24·6 19·5 66·5 Orthopyroxene 0·192 0·455 0·239 0·433 0·061 0·271 0·076 0·156 1·23 0·048 0·010 0·178 Apatite 0·370 251·5 481·7 1244 176·6 837·5 289·1 369·4 3398 16·9 0·031 1·01 Monazite 1·70 87·6 122620 251499 32518 129204 10978 6958 553777 39·7 0·165 2·23 Zircon 13·0 1·80 1·40 24·8 0·636 5·10 1·40 6·63 40·0 198·5 8800 498000 Allanite 0·720 905·2 35386 71487 7843 22519 1280 727·4 139242 4·13 0·086 2·18 Xenotime 21·9 7·30 145·6 1571 437·7 3669 1242 5175 12240 2418 107·6 274·0 Ilmenite — — 0·233 0·155 0·021 0·026 0·010 0·016 0·461 0·047 0·706 26·7 Magnetite — — 5·14 9·91 1·50 7·27 0·330 0·314 24·5 0·032 0·036 0·555 Modified 2 Plagioclase 7·17 523·9 2·53 3·12 0·243 0·721 0·025 0·018 6·66 0·012 0·016 0·454 K-feldspar 186·0 427·4 12·0 22·8 0·972 1·56 0·229 0·326 37·9 0·017 0·439 12·6 Amphibole 2·68 85·6 8·54 27·8 4·59 23·8 7·11 7·81 79·7 0·514 2·97 62·0 Clinopyroxene 0·025 24·4 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·301 1·79 38·9 Titanite 0·252 48·3 386·5 1108 176·7 783·7 137·0 257·5 2849 24·6 19·5 66·5 Orthopyroxene 0·048 0·707 0·239 0·433 0·061 0·271 0·076 0·156 1·23 0·048 0·010 0·178 Biotite 397·0 53·3 0·154 0·494 0·039 0·060 0·010 0·019 0·775 0·010 0·010 0·121 Apatite 0·054 877·1 481·7 1244 176·6 837·5 289·1 369·4 3398 16·9 0·031 1·01 Monazite 1·70 87·6 95789 234852 27923 113646 21084 13797 507091 39·7 0·165 2·23 Zircon 13·0 1·80 0·96 17·1 0·437 3·50 3·50 16·6 42·0 198·5 8800 498000 Allanite 0·267 5712 36689 77531 8775 27258 2383 1628 154262 15·8 0·329 8·34 Ilmenite — — 1·11 0·738 0·100 0·317 0·123 0·087 2·47 0·047 7·00 271·8 Magnetite — — 3·08 5·94 0·899 4·36 0·357 0·340 15·0 0·125 0·140 2·16 High Lu, Hf and Zr† Plagioclase 7·17 523·9 5·65 6·88 0·528 1·52 0·230 0·130 14·9 0·050 2·80 118·0 Amphibole 14·7 46·8 8·54 27·8 4·59 23·8 7·11 7·81 79·7 1·61 10·6 187·0 Clinopyroxene 1·89 16·8 2·34 8·40 1·46 8·19 2·70 2·97 26·1 0·589 6·90 137·0 Titanite 0·529 33·6 660·4 1892 302·0 1339 323·6 257·5 4775 31·2 135·0 2100 Orthopyroxene 0·114 0·487 0·136 0·250 0·037 0·173 0·096 0·156 0·846 0·170 0·113 4·00 Ilmenite — — 1·11 0·738 0·100 0·317 0·123 0·087 2·47 0·050 17·1 677·0 Magnetite — — 3·08 5·94 0·899 4·36 0·357 0·340 15·0 0·130 1·83 47·0 * The sum of the light rare earth elements (ΣLREE) excludes Eu, in accordance with the way monazite saturation is described in the main text. †Other minerals present use the ‘mean values’. All concentrations are given in parts per million. Heterogeneity in the protolith is the foundation of this and similar models; however, the exact character of the isotope heterogeneity and how it would actually arise in nature is not constrained. To define the Hf isotope composition of the protolith, the individual phases, and ultimately the melt, this model makes the assumption that, prior to melting, the protolith acquired time-integrated isotopic heterogeneity through the production of varying amounts of radiogenic Hf according to the various Lu/Hf ratios of the minerals (Table 3). This method for generating Sr–Nd–Hf isotope heterogeneity in the protolith was chosen for two reasons. First, it is used in many other studies examining disequilibrium melting. Second, it is a relatively simple and systematic approach to establishing different isotope compositions for different minerals, without allocating compositions to phases randomly and without reason. This approach follows a natural process, dictated by trace element compositions (based on real data), rather than potentially biased human input controls on the protolith’s isotopic variability. The range of crustal residence times (time since last isotopic homogenization) in previous studies is highly variable (100–1000 Myr; refer to studies discussed above), thus a few different residence times were tested and 1·0 Gyr was chosen as it provides the best comparison with bulk-rock and zircon data (Iles et al., unpublished data). The amount of time since last isotopic homogenization affects the size of the isotopic variability (between minerals in protolith, between melt and restite, between different protoliths) but not the underlying structure of variability and the isotopic relationships. Ultimately, the magnitude of the difference between protolith and melt scales proportionally with changes in the residence time, but the sign of the difference is not affected. The choice of initial Hf isotope composition (i.e. the composition when the protolith was homogeneous) is arbitrary with respect to the development of protolith heterogeneity and the difference between restite, protolith and melt compositions; however, the common initial Hf isotope composition used here was set so that the protolith and melt compositions will be comparable with granite samples, by calculating the composition that a rock with the crustal average 176Lu/177Hf (0·015) would have acquired by time 1·42 Ga (1·0 Gyr prior to I-type magmatism in the Kosciusko–Berridale region) if it evolved from a mantle composition at 1·52 Ga (within the range of the two-stage depleted mantle model ages of the I-types). Analogous approaches are taken for the Rb–Sr and Sm–Nd isotope systems. Table 3: Isotope compositions of minerals, corresponding to the trace element compositions of Table 2 Phase 87Rb/86Sr 87Sr/86Sr 147Sm/144Nd 143Nd/144Nd 176Lu/177Hf 176Hf/177Hf Mean values Plagioclase 0·0396 0·703140 0·0919 0·511689 0·00572 0·282258 K-feldspar 1·463 0·722891 0·0875 0·511660 0·00378 0·282222 Amphibole 0·908 0·715182 0·1804 0·512266 0·02460 0·282607 Clinopyroxene 0·324 0·707086 0·1991 0·512388 0·02388 0·282594 Titanite 0·0455 0·703221 0·1462 0·512043 0·04465 0·282978 Orthopyroxene 0·677 0·711986 0·3347 0·513271 0·2192 0·286202 Biotite 61·14 1·550829 0·1416 0·512013 0·03156 0·282736 Apatite 0·00152 0·702612 0·2088 0·512450 77·01 1·705015 Monazite 0·0561 0·703369 0·1122 0·511821 34·14 0·913047 Zircon 20·87 0·992148 0·6049 0·515033 0·00105 0·282172 Allanite 0·00027 0·702594 0·0766 0·511589 4·244 0·360567 Xenotime 7·310 0·804001 0·7034 0·515675 5·995 0·392919 Ilmenite — — 0·2351 0·512622 0·00095 0·282170 Magnetite — — 0·0496 0·511413 0·01127 0·282361 Modified 1 Plagioclase 0·0396 0·703140 0·0212 0·511228 0·1033 0·284061 Amphibole 2·766 0·740965 0·1804 0·512266 0·02460 0·282607 Clinopyroxene 2·304 0·734548 0·1991 0·512388 0·02388 0·282594 Titanite 0·103 0·704023 0·1057 0·511779 0·1791 0·285462 Orthopyroxene 1·224 0·719568 0·1696 0·512195 0·6859 0·294827 Apatite 0·00425 0·702650 0·2088 0·512450 77·01 1·705015 Monazite 0·0561 0·703369 0·0514 0·511425 34·14 0·913047 Zircon 20·87 0·992148 0·1661 0·512172 0·00320 0·282212 Allanite 0·00230 0·702623 0·0344 0·511314 6·816 0·408093 Xenotime 8·670 0·822868 0·2047 0·512424 3·191 0·341106 Ilmenite — — 0·2351 0·512622 0·00945 0·282327 Magnetite — — 0·0274 0·511268 0·1262 0·284485 Modified 2 Plagioclase 0·0396 0·703140 0·0212 0·511228 0·1033 0·284061 K-feldspar 1·258 0·720039 0·0889 0·511669 0·00546 0·282253 Amphibole 0·0905 0·703846 0·1804 0·512266 0·02460 0·282607 Clinopyroxene 0·00301 0·702632 0·1991 0·512388 0·02388 0·282594 Titanite 0·0151 0·702800 0·1057 0·511779 0·1791 0·285462 Orthopyroxene 0·194 0·705287 0·1696 0·512195 0·6859 0·294827 Biotite 21·51 1·001030 0·1008 0·511747 0·1420 0·284776 Apatite 0·00018 0·702593 0·2088 0·512450 77·01 1·705015 Monazite 0·0561 0·703369 0·1122 0·511821 34·14 0·913047 Zircon 20·87 0·992148 0·6049 0·515033 0·00320 0·282212 Allanite 0·00013 0·702593 0·0529 0·511434 6·816 0·408093 Ilmenite — — 0·2351 0·512622 0·00095 0·282170 Magnetite — — 0·0496 0·511413 0·1262 0·284485 High Lu, Hf and Zr Plagioclase 0·0396 0·703140 0·0919 0·511689 0·00254 0·282199 Amphibole 0·908 0·715182 0·1804 0·512266 0·02163 0·282552 Clinopyroxene 0·324 0·707086 0·1991 0·512388 0·01212 0·282376 Titanite 0·0455 0·703221 0·1462 0·512043 0·03282 0·282759 Orthopyroxene 0·677 0·711986 0·3347 0·513271 0·2124 0·286077 Ilmenite — — 0·2351 0·512622 0·00042 0·282160 Magnetite — — 0·0496 0·511413 0·01012 0·282339 Phase 87Rb/86Sr 87Sr/86Sr 147Sm/144Nd 143Nd/144Nd 176Lu/177Hf 176Hf/177Hf Mean values Plagioclase 0·0396 0·703140 0·0919 0·511689 0·00572 0·282258 K-feldspar 1·463 0·722891 0·0875 0·511660 0·00378 0·282222 Amphibole 0·908 0·715182 0·1804 0·512266 0·02460 0·282607 Clinopyroxene 0·324 0·707086 0·1991 0·512388 0·02388 0·282594 Titanite 0·0455 0·703221 0·1462 0·512043 0·04465 0·282978 Orthopyroxene 0·677 0·711986 0·3347 0·513271 0·2192 0·286202 Biotite 61·14 1·550829 0·1416 0·512013 0·03156 0·282736 Apatite 0·00152 0·702612 0·2088 0·512450 77·01 1·705015 Monazite 0·0561 0·703369 0·1122 0·511821 34·14 0·913047 Zircon 20·87 0·992148 0·6049 0·515033 0·00105 0·282172 Allanite 0·00027 0·702594 0·0766 0·511589 4·244 0·360567 Xenotime 7·310 0·804001 0·7034 0·515675 5·995 0·392919 Ilmenite — — 0·2351 0·512622 0·00095 0·282170 Magnetite — — 0·0496 0·511413 0·01127 0·282361 Modified 1 Plagioclase 0·0396 0·703140 0·0212 0·511228 0·1033 0·284061 Amphibole 2·766 0·740965 0·1804 0·512266 0·02460 0·282607 Clinopyroxene 2·304 0·734548 0·1991 0·512388 0·02388 0·282594 Titanite 0·103 0·704023 0·1057 0·511779 0·1791 0·285462 Orthopyroxene 1·224 0·719568 0·1696 0·512195 0·6859 0·294827 Apatite 0·00425 0·702650 0·2088 0·512450 77·01 1·705015 Monazite 0·0561 0·703369 0·0514 0·511425 34·14 0·913047 Zircon 20·87 0·992148 0·1661 0·512172 0·00320 0·282212 Allanite 0·00230 0·702623 0·0344 0·511314 6·816 0·408093 Xenotime 8·670 0·822868 0·2047 0·512424 3·191 0·341106 Ilmenite — — 0·2351 0·512622 0·00945 0·282327 Magnetite — — 0·0274 0·511268 0·1262 0·284485 Modified 2 Plagioclase 0·0396 0·703140 0·0212 0·511228 0·1033 0·284061 K-feldspar 1·258 0·720039 0·0889 0·511669 0·00546 0·282253 Amphibole 0·0905 0·703846 0·1804 0·512266 0·02460 0·282607 Clinopyroxene 0·00301 0·702632 0·1991 0·512388 0·02388 0·282594 Titanite 0·0151 0·702800 0·1057 0·511779 0·1791 0·285462 Orthopyroxene 0·194 0·705287 0·1696 0·512195 0·6859 0·294827 Biotite 21·51 1·001030 0·1008 0·511747 0·1420 0·284776 Apatite 0·00018 0·702593 0·2088 0·512450 77·01 1·705015 Monazite 0·0561 0·703369 0·1122 0·511821 34·14 0·913047 Zircon 20·87 0·992148 0·6049 0·515033 0·00320 0·282212 Allanite 0·00013 0·702593 0·0529 0·511434 6·816 0·408093 Ilmenite — — 0·2351 0·512622 0·00095 0·282170 Magnetite — — 0·0496 0·511413 0·1262 0·284485 High Lu, Hf and Zr Plagioclase 0·0396 0·703140 0·0919 0·511689 0·00254 0·282199 Amphibole 0·908 0·715182 0·1804 0·512266 0·02163 0·282552 Clinopyroxene 0·324 0·707086 0·1991 0·512388 0·01212 0·282376 Titanite 0·0455 0·703221 0·1462 0·512043 0·03282 0·282759 Orthopyroxene 0·677 0·711986 0·3347 0·513271 0·2124 0·286077 Ilmenite — — 0·2351 0·512622 0·00042 0·282160 Magnetite — — 0·0496 0·511413 0·01012 0·282339 Table 3: Isotope compositions of minerals, corresponding to the trace element compositions of Table 2 Phase 87Rb/86Sr 87Sr/86Sr 147Sm/144Nd 143Nd/144Nd 176Lu/177Hf 176Hf/177Hf Mean values Plagioclase 0·0396 0·703140 0·0919 0·511689 0·00572 0·282258 K-feldspar 1·463 0·722891 0·0875 0·511660 0·00378 0·282222 Amphibole 0·908 0·715182 0·1804 0·512266 0·02460 0·282607 Clinopyroxene 0·324 0·707086 0·1991 0·512388 0·02388 0·282594 Titanite 0·0455 0·703221 0·1462 0·512043 0·04465 0·282978 Orthopyroxene 0·677 0·711986 0·3347 0·513271 0·2192 0·286202 Biotite 61·14 1·550829 0·1416 0·512013 0·03156 0·282736 Apatite 0·00152 0·702612 0·2088 0·512450 77·01 1·705015 Monazite 0·0561 0·703369 0·1122 0·511821 34·14 0·913047 Zircon 20·87 0·992148 0·6049 0·515033 0·00105 0·282172 Allanite 0·00027 0·702594 0·0766 0·511589 4·244 0·360567 Xenotime 7·310 0·804001 0·7034 0·515675 5·995 0·392919 Ilmenite — — 0·2351 0·512622 0·00095 0·282170 Magnetite — — 0·0496 0·511413 0·01127 0·282361 Modified 1 Plagioclase 0·0396 0·703140 0·0212 0·511228 0·1033 0·284061 Amphibole 2·766 0·740965 0·1804 0·512266 0·02460 0·282607 Clinopyroxene 2·304 0·734548 0·1991 0·512388 0·02388 0·282594 Titanite 0·103 0·704023 0·1057 0·511779 0·1791 0·285462 Orthopyroxene 1·224 0·719568 0·1696 0·512195 0·6859 0·294827 Apatite 0·00425 0·702650 0·2088 0·512450 77·01 1·705015 Monazite 0·0561 0·703369 0·0514 0·511425 34·14 0·913047 Zircon 20·87 0·992148 0·1661 0·512172 0·00320 0·282212 Allanite 0·00230 0·702623 0·0344 0·511314 6·816 0·408093 Xenotime 8·670 0·822868 0·2047 0·512424 3·191 0·341106 Ilmenite — — 0·2351 0·512622 0·00945 0·282327 Magnetite — — 0·0274 0·511268 0·1262 0·284485 Modified 2 Plagioclase 0·0396 0·703140 0·0212 0·511228 0·1033 0·284061 K-feldspar 1·258 0·720039 0·0889 0·511669 0·00546 0·282253 Amphibole 0·0905 0·703846 0·1804 0·512266 0·02460 0·282607 Clinopyroxene 0·00301 0·702632 0·1991 0·512388 0·02388 0·282594 Titanite 0·0151 0·702800 0·1057 0·511779 0·1791 0·285462 Orthopyroxene 0·194 0·705287 0·1696 0·512195 0·6859 0·294827 Biotite 21·51 1·001030 0·1008 0·511747 0·1420 0·284776 Apatite 0·00018 0·702593 0·2088 0·512450 77·01 1·705015 Monazite 0·0561 0·703369 0·1122 0·511821 34·14 0·913047 Zircon 20·87 0·992148 0·6049 0·515033 0·00320 0·282212 Allanite 0·00013 0·702593 0·0529 0·511434 6·816 0·408093 Ilmenite — — 0·2351 0·512622 0·00095 0·282170 Magnetite — — 0·0496 0·511413 0·1262 0·284485 High Lu, Hf and Zr Plagioclase 0·0396 0·703140 0·0919 0·511689 0·00254 0·282199 Amphibole 0·908 0·715182 0·1804 0·512266 0·02163 0·282552 Clinopyroxene 0·324 0·707086 0·1991 0·512388 0·01212 0·282376 Titanite 0·0455 0·703221 0·1462 0·512043 0·03282 0·282759 Orthopyroxene 0·677 0·711986 0·3347 0·513271 0·2124 0·286077 Ilmenite — — 0·2351 0·512622 0·00042 0·282160 Magnetite — — 0·0496 0·511413 0·01012 0·282339 Phase 87Rb/86Sr 87Sr/86Sr 147Sm/144Nd 143Nd/144Nd 176Lu/177Hf 176Hf/177Hf Mean values Plagioclase 0·0396 0·703140 0·0919 0·511689 0·00572 0·282258 K-feldspar 1·463 0·722891 0·0875 0·511660 0·00378 0·282222 Amphibole 0·908 0·715182 0·1804 0·512266 0·02460 0·282607 Clinopyroxene 0·324 0·707086 0·1991 0·512388 0·02388 0·282594 Titanite 0·0455 0·703221 0·1462 0·512043 0·04465 0·282978 Orthopyroxene 0·677 0·711986 0·3347 0·513271 0·2192 0·286202 Biotite 61·14 1·550829 0·1416 0·512013 0·03156 0·282736 Apatite 0·00152 0·702612 0·2088 0·512450 77·01 1·705015 Monazite 0·0561 0·703369 0·1122 0·511821 34·14 0·913047 Zircon 20·87 0·992148 0·6049 0·515033 0·00105 0·282172 Allanite 0·00027 0·702594 0·0766 0·511589 4·244 0·360567 Xenotime 7·310 0·804001 0·7034 0·515675 5·995 0·392919 Ilmenite — — 0·2351 0·512622 0·00095 0·282170 Magnetite — — 0·0496 0·511413 0·01127 0·282361 Modified 1 Plagioclase 0·0396 0·703140 0·0212 0·511228 0·1033 0·284061 Amphibole 2·766 0·740965 0·1804 0·512266 0·02460 0·282607 Clinopyroxene 2·304 0·734548 0·1991 0·512388 0·02388 0·282594 Titanite 0·103 0·704023 0·1057 0·511779 0·1791 0·285462 Orthopyroxene 1·224 0·719568 0·1696 0·512195 0·6859 0·294827 Apatite 0·00425 0·702650 0·2088 0·512450 77·01 1·705015 Monazite 0·0561 0·703369 0·0514 0·511425 34·14 0·913047 Zircon 20·87 0·992148 0·1661 0·512172 0·00320 0·282212 Allanite 0·00230 0·702623 0·0344 0·511314 6·816 0·408093 Xenotime 8·670 0·822868 0·2047 0·512424 3·191 0·341106 Ilmenite — — 0·2351 0·512622 0·00945 0·282327 Magnetite — — 0·0274 0·511268 0·1262 0·284485 Modified 2 Plagioclase 0·0396 0·703140 0·0212 0·511228 0·1033 0·284061 K-feldspar 1·258 0·720039 0·0889 0·511669 0·00546 0·282253 Amphibole 0·0905 0·703846 0·1804 0·512266 0·02460 0·282607 Clinopyroxene 0·00301 0·702632 0·1991 0·512388 0·02388 0·282594 Titanite 0·0151 0·702800 0·1057 0·511779 0·1791 0·285462 Orthopyroxene 0·194 0·705287 0·1696 0·512195 0·6859 0·294827 Biotite 21·51 1·001030 0·1008 0·511747 0·1420 0·284776 Apatite 0·00018 0·702593 0·2088 0·512450 77·01 1·705015 Monazite 0·0561 0·703369 0·1122 0·511821 34·14 0·913047 Zircon 20·87 0·992148 0·6049 0·515033 0·00320 0·282212 Allanite 0·00013 0·702593 0·0529 0·511434 6·816 0·408093 Ilmenite — — 0·2351 0·512622 0·00095 0·282170 Magnetite — — 0·0496 0·511413 0·1262 0·284485 High Lu, Hf and Zr Plagioclase 0·0396 0·703140 0·0919 0·511689 0·00254 0·282199 Amphibole 0·908 0·715182 0·1804 0·512266 0·02163 0·282552 Clinopyroxene 0·324 0·707086 0·1991 0·512388 0·01212 0·282376 Titanite 0·0455 0·703221 0·1462 0·512043 0·03282 0·282759 Orthopyroxene 0·677 0·711986 0·3347 0·513271 0·2124 0·286077 Ilmenite — — 0·2351 0·512622 0·00042 0·282160 Magnetite — — 0·0496 0·511413 0·01012 0·282339 Of course, in natural samples heterogeneity can be produced in other ways. An initially isotopically homogeneous igneous rock may develop heterogeneity over time until this process is disrupted by some tectono-thermal event that induces a set of metamorphic reactions. Unless it involves complete equilibration of all phases (and the entirety of the grains, not just rims) metamorphism may not eliminate heterogeneity, but rather redistribute it, so that the systematic isotope variability generated by radiogenic decay over time (compositions along an isochron) becomes scattered and less predictable. An igneous source rock could alternatively have an isotopically heterogeneous mineral assemblage as a result of open-system processes in its formation and crystallization, which would inevitably be modified by production of radiogenic Sr, Nd and Hf over the time between crystallization of the source and melting to generate granite. Alternatives such as these could potentially be highly complex, and similarly complex to incorporate into a numerical model; however, although they are not considered further here, such alternative distributions of isotopic heterogeneity could be assembled as model inputs for further studies. The Hf isotope composition (Rmelt) of the melt (and any peritectic phase that formed with it) is calculated from the Hf isotope compositions (Ri) and relative contributions of the phases that produced it, according to the formula Rmelt=∑(Ri×CHfi×mi)/∑(CHfi×mi) where CHfi is the Hf concentration of phase i and mi is the mass of i entering the melt. An equation of the same form can be used to combine the compositions of all restitic phases (unmelted original crystals and peritectic crystals) to calculate a bulk restite Hf isotope composition (Rrest). The composition of the partially melted protolith (Rproto, which could represent a restite-rich magma) is given by Rproto=(Rmelt×CHfmelt×mmelt)+(Rrest×CHfrest×mrest)/(CHfmelt×mmelt)+(CHfrest×mrest)CHfrest=∑(CHfu×mu)+∑(CHfp×mp)/∑mu+∑mp where mu denotes the mass of an unmelted phase and CHfu is its Hf concentration; mp and CHfp are the equivalent terms for the peritectic phases and ∑mu + ∑mp = mrest. The modelling can be checked by comparing the value of Rproto calculated as shown with the value it would have based on all of the components present before melting. Equivalent equations are used for the calculation of Sr and Nd isotope compositions. Model results Using the assumptions and modelling approach explained above, 23 protoliths (unique combinations of modal proportions and mineral compositions) have been used to model 64 melt–source–restite sets (specified in Table 4 by the combination of protolith and melting regime), the Sr–Nd–Hf isotope compositions of which are provided in Table 5. An example of the modelling is provided in the Supplementary Data, illustrating how the equations and phase relations described above are implemented in a spreadsheet to output the data in Table 5. Table 4: Melting scenarios, defined by varying protolith compositions (mineral assemblage and chemistry) and melting regimes (some in two stages, A and B) Identifier Protolith (accessories) Reaction (soluble accessories) Temperature (°C) M A/CNK SiO2 (wt %) 1A S&D amphibolite (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 1B* S&D amphibolite (ap, mon, zrc) S&D2 (ap, mon, zrc) 950 1·54 1·04 68·0 1B S&D amphibolite (ap, mon, zrc) S&D2 (ap, mon, zrc) 950 1·54 1·04 68·0 2A B&L 557, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 3A B&L 555, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 4A B&L 478, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 5A B&L 466, hornfels (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 6A B&L 571, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 7A B&L 557, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·20 1·12 76·2 8A B&L 555, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·05 1·29 75·8 8B B&L 555, greenschist (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·18 1·20 72·6 9A B&L 478, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·14 1·17 76·6 9B B&L 478, greenschist (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·26 1·09 73·1 10A B&L 466, hornfels (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·24 1·11 73·6 10B B&L 466, hornfels (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·26 1·09 72·8 11A B&L 571, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·20 1·18 73·6 11B B&L 571, greenschist (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 12A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 12B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 13A B&L average modes1 (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 13B B&L average modes1 (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 14A B&L average modes (ap, mon, zrc, aln) B&L1 (ap, mon, zrc, aln) 875 1·17 1·17 75·1 14B B&L average modes (ap, mon, zrc, aln) B&L2 (ap, mon, zrc, aln) 950 1·22 1·15 72·8 15A B&L average modes (ap, mon, zrc, aln) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 15B B&L average modes (ap, mon, zrc, aln) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 16A B&L average modes1 (ap, mon, zrc, aln) B&L1 (ap, mon, zrc, aln) 875 1·17 1·17 75·1 16B B&L average modes1 (ap, mon, zrc, aln) B&L2 (ap, mon, zrc, aln) 950 1·22 1·15 72·8 17A B&L average modes1 (ap, mon, zrc, aln) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 17B B&L average modes1 (ap, mon, zrc, aln) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 18A B&L average modes (ap, mon, zrc, aln)2 B&L1 (ap, mon, zrc, aln) 875 1·17 1·17 75·1 18B B&L average modes (ap, mon, zrc, aln)2 B&L2 (ap, mon, zrc, aln) 950 1·22 1·15 72·8 19A P&G, tonalite (ap, zrc, aln) P&G1 (ap, zrc, aln) 925 1·36 1·00 71·8 19B P&G, tonalite (ap, zrc, aln) P&G2 (ap, zrc, aln) 950 1·62 0·90 66·9 20A P&G, tonalite3 (ap, zrc, aln) P&G1 (ap, zrc, aln) 925 1·36 1·00 71·8 20B P&G, tonalite3 (ap, zrc, aln) P&G2 (ap, zrc, aln) 950 1·62 0·90 66·9 21A P&G, tonalite3 (ap, zrc, aln)2 P&G1 (ap, zrc, aln) 925 1·36 1·00 71·8 21B P&G, tonalite3 (ap, zrc, aln)2 P&G2 (ap, zrc, aln) 950 1·62 0·90 66·9 22A B&L average modes (ap, mon, zrc, aln, xen) B&L1 (ap, mon, zrc, aln, xen) 875 1·17 1·17 75·1 22B* B&L average modes (ap, mon, zrc, aln, xen) B&L2 (ap, mon, zrc, aln, xen) 950 1·22 1·15 72·8 22B B&L average modes (ap, mon, zrc, aln, xen) B&L2 (ap, mon, zrc, aln, xen) 950 1·22 1·15 72·8 23A B&L average modes1 (ap, mon, zrc, aln, xen) B&L1 (ap, mon, zrc, aln, xen) 875 1·17 1·17 75·1 23B B&L average modes1 (ap, mon, zrc, aln, xen) B&L2 (ap, mon, zrc, aln, xen) 950 1·22 1·15 72·8 24A R2013, orthogneiss (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 25A R2013, orthogneiss4 (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 25B R2013, orthogneiss4 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 26A R2013, orthogneiss3,4 (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 26B* R2013, orthogneiss3,4 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 26B R2013, orthogneiss3,4 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 27A A2008, monzodiorite3 (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 27B A2008, monzodiorite3 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 28A B&L average modes (ap, mon) B&L1 (ap, mon) 875 1·17 1·17 75·1 28B B&L average modes (ap, mon) B&L2 (ap, mon) 950 1·22 1·15 72·8 29A B&L average modes5 (ap, mon) B&L1 (ap, mon) 875 1·17 1·17 75·1 29B B&L average modes5 (ap, mon) B&L2 (ap, mon) 950 1·22 1·15 72·8 30A B&L average modes (ap) B&L1 (ap) 875 1·17 1·17 75·1 30B B&L average modes (ap) B&L2 (ap) 950 1·22 1·15 72·8 31A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc)6 875 1·17 1·17 75·1 31B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc)7 950 1·22 1·15 72·8 32A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc)8 875 1·17 1·17 75·1 32B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc)6 950 1·22 1·15 72·8 33A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc)7 875 1·17 1·17 75·1 33B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc)7 950 1·22 1·15 72·8 34A P&G, tonalite (ap, zrc, aln) P&G1 (ap, zrc, aln)7 925 1·36 1·00 71·8 34B P&G, tonalite (ap, zrc, aln) P&G2 (ap, zrc, aln)7 950 1·62 0·90 66·9 Identifier Protolith (accessories) Reaction (soluble accessories) Temperature (°C) M A/CNK SiO2 (wt %) 1A S&D amphibolite (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 1B* S&D amphibolite (ap, mon, zrc) S&D2 (ap, mon, zrc) 950 1·54 1·04 68·0 1B S&D amphibolite (ap, mon, zrc) S&D2 (ap, mon, zrc) 950 1·54 1·04 68·0 2A B&L 557, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 3A B&L 555, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 4A B&L 478, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 5A B&L 466, hornfels (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 6A B&L 571, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 7A B&L 557, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·20 1·12 76·2 8A B&L 555, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·05 1·29 75·8 8B B&L 555, greenschist (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·18 1·20 72·6 9A B&L 478, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·14 1·17 76·6 9B B&L 478, greenschist (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·26 1·09 73·1 10A B&L 466, hornfels (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·24 1·11 73·6 10B B&L 466, hornfels (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·26 1·09 72·8 11A B&L 571, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·20 1·18 73·6 11B B&L 571, greenschist (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 12A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 12B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 13A B&L average modes1 (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 13B B&L average modes1 (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 14A B&L average modes (ap, mon, zrc, aln) B&L1 (ap, mon, zrc, aln) 875 1·17 1·17 75·1 14B B&L average modes (ap, mon, zrc, aln) B&L2 (ap, mon, zrc, aln) 950 1·22 1·15 72·8 15A B&L average modes (ap, mon, zrc, aln) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 15B B&L average modes (ap, mon, zrc, aln) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 16A B&L average modes1 (ap, mon, zrc, aln) B&L1 (ap, mon, zrc, aln) 875 1·17 1·17 75·1 16B B&L average modes1 (ap, mon, zrc, aln) B&L2 (ap, mon, zrc, aln) 950 1·22 1·15 72·8 17A B&L average modes1 (ap, mon, zrc, aln) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 17B B&L average modes1 (ap, mon, zrc, aln) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 18A B&L average modes (ap, mon, zrc, aln)2 B&L1 (ap, mon, zrc, aln) 875 1·17 1·17 75·1 18B B&L average modes (ap, mon, zrc, aln)2 B&L2 (ap, mon, zrc, aln) 950 1·22 1·15 72·8 19A P&G, tonalite (ap, zrc, aln) P&G1 (ap, zrc, aln) 925 1·36 1·00 71·8 19B P&G, tonalite (ap, zrc, aln) P&G2 (ap, zrc, aln) 950 1·62 0·90 66·9 20A P&G, tonalite3 (ap, zrc, aln) P&G1 (ap, zrc, aln) 925 1·36 1·00 71·8 20B P&G, tonalite3 (ap, zrc, aln) P&G2 (ap, zrc, aln) 950 1·62 0·90 66·9 21A P&G, tonalite3 (ap, zrc, aln)2 P&G1 (ap, zrc, aln) 925 1·36 1·00 71·8 21B P&G, tonalite3 (ap, zrc, aln)2 P&G2 (ap, zrc, aln) 950 1·62 0·90 66·9 22A B&L average modes (ap, mon, zrc, aln, xen) B&L1 (ap, mon, zrc, aln, xen) 875 1·17 1·17 75·1 22B* B&L average modes (ap, mon, zrc, aln, xen) B&L2 (ap, mon, zrc, aln, xen) 950 1·22 1·15 72·8 22B B&L average modes (ap, mon, zrc, aln, xen) B&L2 (ap, mon, zrc, aln, xen) 950 1·22 1·15 72·8 23A B&L average modes1 (ap, mon, zrc, aln, xen) B&L1 (ap, mon, zrc, aln, xen) 875 1·17 1·17 75·1 23B B&L average modes1 (ap, mon, zrc, aln, xen) B&L2 (ap, mon, zrc, aln, xen) 950 1·22 1·15 72·8 24A R2013, orthogneiss (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 25A R2013, orthogneiss4 (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 25B R2013, orthogneiss4 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 26A R2013, orthogneiss3,4 (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 26B* R2013, orthogneiss3,4 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 26B R2013, orthogneiss3,4 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 27A A2008, monzodiorite3 (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 27B A2008, monzodiorite3 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 28A B&L average modes (ap, mon) B&L1 (ap, mon) 875 1·17 1·17 75·1 28B B&L average modes (ap, mon) B&L2 (ap, mon) 950 1·22 1·15 72·8 29A B&L average modes5 (ap, mon) B&L1 (ap, mon) 875 1·17 1·17 75·1 29B B&L average modes5 (ap, mon) B&L2 (ap, mon) 950 1·22 1·15 72·8 30A B&L average modes (ap) B&L1 (ap) 875 1·17 1·17 75·1 30B B&L average modes (ap) B&L2 (ap) 950 1·22 1·15 72·8 31A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc)6 875 1·17 1·17 75·1 31B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc)7 950 1·22 1·15 72·8 32A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc)8 875 1·17 1·17 75·1 32B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc)6 950 1·22 1·15 72·8 33A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc)7 875 1·17 1·17 75·1 33B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc)7 950 1·22 1·15 72·8 34A P&G, tonalite (ap, zrc, aln) P&G1 (ap, zrc, aln)7 925 1·36 1·00 71·8 34B P&G, tonalite (ap, zrc, aln) P&G2 (ap, zrc, aln)7 950 1·62 0·90 66·9 For an identifier with a given number, A and B indicate the first and second stages of melting. Scenarios with the B* identifier represent melting after the extraction of the melt produced in the first reaction. Protoliths and reactions from the literature have been listed as S&D for Sen & Dunn (1994), B&L for Beard & Lofgren (1991), P&G for Petcovic & Grunder (2003), R2013 for Rajesh et al. (2013) and A2008 for Årebäck et al. (2008). ap, apatite; mon, monazite; zrc, zircon; aln, allanite; xen, xenotime. Differences in melt-producing reactions, the accessory phases dissolved, temperature and melt compositions define the melting regimes. It should be noted that many scenarios use the same regime but different protoliths. 1 The first set of alternative mineral trace element compositions were used (‘Modified 1’ in Table 2). 2 The amount of zircon present in the protolith has been halved and the other phases have been adjusted to bring the total mode to 100%. 3 The second set of alternative mineral trace element compositions were used (‘Modified 2’ in Table 2). 4 The mineral modes have been modified to ensure biotite and amphibole are exhausted at the same time. 5 The protolith has no zircon and the other phases have been adjusted to bring the total mode to 100%. The major minerals have been assigned higher Lu, Hf and Zr concentrations to compensate (see Table 2). 6 Half of the titanite dissolves. 7 All of the titanite dissolves. 8 A quarter of the titanite dissolves. Table 4: Melting scenarios, defined by varying protolith compositions (mineral assemblage and chemistry) and melting regimes (some in two stages, A and B) Identifier Protolith (accessories) Reaction (soluble accessories) Temperature (°C) M A/CNK SiO2 (wt %) 1A S&D amphibolite (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 1B* S&D amphibolite (ap, mon, zrc) S&D2 (ap, mon, zrc) 950 1·54 1·04 68·0 1B S&D amphibolite (ap, mon, zrc) S&D2 (ap, mon, zrc) 950 1·54 1·04 68·0 2A B&L 557, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 3A B&L 555, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 4A B&L 478, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 5A B&L 466, hornfels (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 6A B&L 571, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 7A B&L 557, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·20 1·12 76·2 8A B&L 555, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·05 1·29 75·8 8B B&L 555, greenschist (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·18 1·20 72·6 9A B&L 478, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·14 1·17 76·6 9B B&L 478, greenschist (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·26 1·09 73·1 10A B&L 466, hornfels (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·24 1·11 73·6 10B B&L 466, hornfels (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·26 1·09 72·8 11A B&L 571, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·20 1·18 73·6 11B B&L 571, greenschist (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 12A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 12B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 13A B&L average modes1 (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 13B B&L average modes1 (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 14A B&L average modes (ap, mon, zrc, aln) B&L1 (ap, mon, zrc, aln) 875 1·17 1·17 75·1 14B B&L average modes (ap, mon, zrc, aln) B&L2 (ap, mon, zrc, aln) 950 1·22 1·15 72·8 15A B&L average modes (ap, mon, zrc, aln) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 15B B&L average modes (ap, mon, zrc, aln) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 16A B&L average modes1 (ap, mon, zrc, aln) B&L1 (ap, mon, zrc, aln) 875 1·17 1·17 75·1 16B B&L average modes1 (ap, mon, zrc, aln) B&L2 (ap, mon, zrc, aln) 950 1·22 1·15 72·8 17A B&L average modes1 (ap, mon, zrc, aln) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 17B B&L average modes1 (ap, mon, zrc, aln) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 18A B&L average modes (ap, mon, zrc, aln)2 B&L1 (ap, mon, zrc, aln) 875 1·17 1·17 75·1 18B B&L average modes (ap, mon, zrc, aln)2 B&L2 (ap, mon, zrc, aln) 950 1·22 1·15 72·8 19A P&G, tonalite (ap, zrc, aln) P&G1 (ap, zrc, aln) 925 1·36 1·00 71·8 19B P&G, tonalite (ap, zrc, aln) P&G2 (ap, zrc, aln) 950 1·62 0·90 66·9 20A P&G, tonalite3 (ap, zrc, aln) P&G1 (ap, zrc, aln) 925 1·36 1·00 71·8 20B P&G, tonalite3 (ap, zrc, aln) P&G2 (ap, zrc, aln) 950 1·62 0·90 66·9 21A P&G, tonalite3 (ap, zrc, aln)2 P&G1 (ap, zrc, aln) 925 1·36 1·00 71·8 21B P&G, tonalite3 (ap, zrc, aln)2 P&G2 (ap, zrc, aln) 950 1·62 0·90 66·9 22A B&L average modes (ap, mon, zrc, aln, xen) B&L1 (ap, mon, zrc, aln, xen) 875 1·17 1·17 75·1 22B* B&L average modes (ap, mon, zrc, aln, xen) B&L2 (ap, mon, zrc, aln, xen) 950 1·22 1·15 72·8 22B B&L average modes (ap, mon, zrc, aln, xen) B&L2 (ap, mon, zrc, aln, xen) 950 1·22 1·15 72·8 23A B&L average modes1 (ap, mon, zrc, aln, xen) B&L1 (ap, mon, zrc, aln, xen) 875 1·17 1·17 75·1 23B B&L average modes1 (ap, mon, zrc, aln, xen) B&L2 (ap, mon, zrc, aln, xen) 950 1·22 1·15 72·8 24A R2013, orthogneiss (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 25A R2013, orthogneiss4 (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 25B R2013, orthogneiss4 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 26A R2013, orthogneiss3,4 (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 26B* R2013, orthogneiss3,4 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 26B R2013, orthogneiss3,4 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 27A A2008, monzodiorite3 (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 27B A2008, monzodiorite3 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 28A B&L average modes (ap, mon) B&L1 (ap, mon) 875 1·17 1·17 75·1 28B B&L average modes (ap, mon) B&L2 (ap, mon) 950 1·22 1·15 72·8 29A B&L average modes5 (ap, mon) B&L1 (ap, mon) 875 1·17 1·17 75·1 29B B&L average modes5 (ap, mon) B&L2 (ap, mon) 950 1·22 1·15 72·8 30A B&L average modes (ap) B&L1 (ap) 875 1·17 1·17 75·1 30B B&L average modes (ap) B&L2 (ap) 950 1·22 1·15 72·8 31A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc)6 875 1·17 1·17 75·1 31B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc)7 950 1·22 1·15 72·8 32A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc)8 875 1·17 1·17 75·1 32B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc)6 950 1·22 1·15 72·8 33A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc)7 875 1·17 1·17 75·1 33B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc)7 950 1·22 1·15 72·8 34A P&G, tonalite (ap, zrc, aln) P&G1 (ap, zrc, aln)7 925 1·36 1·00 71·8 34B P&G, tonalite (ap, zrc, aln) P&G2 (ap, zrc, aln)7 950 1·62 0·90 66·9 Identifier Protolith (accessories) Reaction (soluble accessories) Temperature (°C) M A/CNK SiO2 (wt %) 1A S&D amphibolite (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 1B* S&D amphibolite (ap, mon, zrc) S&D2 (ap, mon, zrc) 950 1·54 1·04 68·0 1B S&D amphibolite (ap, mon, zrc) S&D2 (ap, mon, zrc) 950 1·54 1·04 68·0 2A B&L 557, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 3A B&L 555, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 4A B&L 478, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 5A B&L 466, hornfels (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 6A B&L 571, greenschist (ap, mon, zrc) S&D1 (ap, mon, zrc) 925 1·54 1·01 69·5 7A B&L 557, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·20 1·12 76·2 8A B&L 555, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·05 1·29 75·8 8B B&L 555, greenschist (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·18 1·20 72·6 9A B&L 478, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·14 1·17 76·6 9B B&L 478, greenschist (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·26 1·09 73·1 10A B&L 466, hornfels (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·24 1·11 73·6 10B B&L 466, hornfels (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·26 1·09 72·8 11A B&L 571, greenschist (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·20 1·18 73·6 11B B&L 571, greenschist (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 12A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 12B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 13A B&L average modes1 (ap, mon, zrc) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 13B B&L average modes1 (ap, mon, zrc) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 14A B&L average modes (ap, mon, zrc, aln) B&L1 (ap, mon, zrc, aln) 875 1·17 1·17 75·1 14B B&L average modes (ap, mon, zrc, aln) B&L2 (ap, mon, zrc, aln) 950 1·22 1·15 72·8 15A B&L average modes (ap, mon, zrc, aln) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 15B B&L average modes (ap, mon, zrc, aln) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 16A B&L average modes1 (ap, mon, zrc, aln) B&L1 (ap, mon, zrc, aln) 875 1·17 1·17 75·1 16B B&L average modes1 (ap, mon, zrc, aln) B&L2 (ap, mon, zrc, aln) 950 1·22 1·15 72·8 17A B&L average modes1 (ap, mon, zrc, aln) B&L1 (ap, mon, zrc) 875 1·17 1·17 75·1 17B B&L average modes1 (ap, mon, zrc, aln) B&L2 (ap, mon, zrc) 950 1·22 1·15 72·8 18A B&L average modes (ap, mon, zrc, aln)2 B&L1 (ap, mon, zrc, aln) 875 1·17 1·17 75·1 18B B&L average modes (ap, mon, zrc, aln)2 B&L2 (ap, mon, zrc, aln) 950 1·22 1·15 72·8 19A P&G, tonalite (ap, zrc, aln) P&G1 (ap, zrc, aln) 925 1·36 1·00 71·8 19B P&G, tonalite (ap, zrc, aln) P&G2 (ap, zrc, aln) 950 1·62 0·90 66·9 20A P&G, tonalite3 (ap, zrc, aln) P&G1 (ap, zrc, aln) 925 1·36 1·00 71·8 20B P&G, tonalite3 (ap, zrc, aln) P&G2 (ap, zrc, aln) 950 1·62 0·90 66·9 21A P&G, tonalite3 (ap, zrc, aln)2 P&G1 (ap, zrc, aln) 925 1·36 1·00 71·8 21B P&G, tonalite3 (ap, zrc, aln)2 P&G2 (ap, zrc, aln) 950 1·62 0·90 66·9 22A B&L average modes (ap, mon, zrc, aln, xen) B&L1 (ap, mon, zrc, aln, xen) 875 1·17 1·17 75·1 22B* B&L average modes (ap, mon, zrc, aln, xen) B&L2 (ap, mon, zrc, aln, xen) 950 1·22 1·15 72·8 22B B&L average modes (ap, mon, zrc, aln, xen) B&L2 (ap, mon, zrc, aln, xen) 950 1·22 1·15 72·8 23A B&L average modes1 (ap, mon, zrc, aln, xen) B&L1 (ap, mon, zrc, aln, xen) 875 1·17 1·17 75·1 23B B&L average modes1 (ap, mon, zrc, aln, xen) B&L2 (ap, mon, zrc, aln, xen) 950 1·22 1·15 72·8 24A R2013, orthogneiss (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 25A R2013, orthogneiss4 (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 25B R2013, orthogneiss4 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 26A R2013, orthogneiss3,4 (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 26B* R2013, orthogneiss3,4 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 26B R2013, orthogneiss3,4 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 27A A2008, monzodiorite3 (ap, mon, zrc, aln) P&G1 (ap, mon, zrc, aln) 925 1·36 1·00 71·8 27B A2008, monzodiorite3 (ap, mon, zrc, aln) P&G2 (ap, mon, zrc, aln) 950 1·62 0·90 66·9 28A B&L average modes (ap, mon) B&L1 (ap, mon) 875 1·17 1·17 75·1 28B B&L average modes (ap, mon) B&L2 (ap, mon) 950 1·22 1·15 72·8 29A B&L average modes5 (ap, mon) B&L1 (ap, mon) 875 1·17 1·17 75·1 29B B&L average modes5 (ap, mon) B&L2 (ap, mon) 950 1·22 1·15 72·8 30A B&L average modes (ap) B&L1 (ap) 875 1·17 1·17 75·1 30B B&L average modes (ap) B&L2 (ap) 950 1·22 1·15 72·8 31A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc)6 875 1·17 1·17 75·1 31B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc)7 950 1·22 1·15 72·8 32A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc)8 875 1·17 1·17 75·1 32B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc)6 950 1·22 1·15 72·8 33A B&L average modes (ap, mon, zrc) B&L1 (ap, mon, zrc)7 875 1·17 1·17 75·1 33B B&L average modes (ap, mon, zrc) B&L2 (ap, mon, zrc)7 950 1·22 1·15 72·8 34A P&G, tonalite (ap, zrc, aln) P&G1 (ap, zrc, aln)7 925 1·36 1·00 71·8 34B P&G, tonalite (ap, zrc, aln) P&G2 (ap, zrc, aln)7 950 1·62 0·90 66·9 For an identifier with a given number, A and B indicate the first and second stages of melting. Scenarios with the B* identifier represent melting after the extraction of the melt produced in the first reaction. Protoliths and reactions from the literature have been listed as S&D for Sen & Dunn (1994), B&L for Beard & Lofgren (1991), P&G for Petcovic & Grunder (2003), R2013 for Rajesh et al. (2013) and A2008 for Årebäck et al. (2008). ap, apatite; mon, monazite; zrc, zircon; aln, allanite; xen, xenotime. Differences in melt-producing reactions, the accessory phases dissolved, temperature and melt compositions define the melting regimes. It should be noted that many scenarios use the same regime but different protoliths. 1 The first set of alternative mineral trace element compositions were used (‘Modified 1’ in Table 2). 2 The amount of zircon present in the protolith has been halved and the other phases have been adjusted to bring the total mode to 100%. 3 The second set of alternative mineral trace element compositions were used (‘Modified 2’ in Table 2). 4 The mineral modes have been modified to ensure biotite and amphibole are exhausted at the same time. 5 The protolith has no zircon and the other phases have been adjusted to bring the total mode to 100%. The major minerals have been assigned higher Lu, Hf and Zr concentrations to compensate (see Table 2). 6 Half of the titanite dissolves. 7 All of the titanite dissolves. 8 A quarter of the titanite dissolves. Table 5: Melt and source Sr, Nd and Hf isotope compositions produced by modelling Identifier Melt % Melt 87Sr/86Sr Melt 143Nd/144Nd Melt Nd Melt 176Hf/177Hf Melt εHf Source 87Sr/86Sr Source 143Nd/144Nd Source εNd Source 176Hf/177Hf Source εHf Δ87Sr/86Sr (source–melt) ΔεNd (source–melt) ΔεHf (source–melt) 1A 9·4 0·706056 0·511965 –2·50 0·282262 –9·16 0·706116 0·512091 –0·04 0·282408 –4·00 0·000061 2·46 5·16 1B* 14·6 0·706046 0·512274 3·54 0·282511 –0·35 0·706135 0·512124 0·60 0·282453 –2·41 0·000090 –2·93 –2·06 1B 23·9 0·706048 0·512154 1·20 0·282414 –3·77 0·706116 0·512091 –0·04 0·282408 –4·00 0·000068 –1·24 –0·23 2A 18·4 0·706054 0·512037 –1·09 0·282300 –7·83 0·704033 0·512044 –0·95 0·282319 –7·13 –0·002021 0·14 0·70 3A 11·2 0·706056 0·511982 –2·16 0·282262 –9·17 0·703594 0·512004 –1·74 0·282297 –7·91 –0·002462 0·42 1·27 4A 15·9 0·706054 0·512021 –1·41 0·282287 –8·29 0·703924 0·512032 –1·19 0·282291 –8·12 –0·002130 0·22 0·17 5A 14·9 0·706055 0·512014 –1·55 0·282281 –8·47 0·703828 0·512018 –1·47 0·282295 –8·01 –0·002227 0·08 0·46 6A 11·8 0·706055 0·511988 –2·05 0·282263 –9·11 0·703688 0·512019 –1·44 0·282343 –6·29 –0·002367 0·61 2·82 7A 23·6 0·707521 0·512055 –0·73 0·282328 –6·81 0·704034 0·512044 –0·95 0·282319 –7·13 –0·003487 –0·21 –0·32 8A 14·4 0·707466 0·512014 –1·55 0·282370 –5·32 0·703595 0·512004 –1·74 0·282297 –7·91 –0·003871 –0·20 –2·59 8B 57·4 0·703810 0·511997 –1·88 0·282251 –9·56 0·703595 0·512004 –1·74 0·282297 –7·91 –0·000215 0·14 1·65 9A 20·4 0·707507 0·512043 –0·98 0·282342 –6·34 0·703924 0·512032 –1·19 0·282291 –8·12 –0·003583 –0·20 –1·78 9B 52·8 0·704251 0·512031 –1·20 0·282276 –8·65 0·703924 0·512032 –1·19 0·282291 –8·12 –0·000327 0·01 0·53 10A 19·1 0·707502 0·512037 –1·09 0·282328 –6·83 0·703828 0·512018 –1·47 0·282295 –8·01 –0·003674 –0·38 –1·18 10B 29·7 0·705302 0·512034 –1·14 0·282276 –8·67 0·703828 0·512018 –1·47 0·282295 –8·01 –0·001474 –0·33 0·66 11A 15·2 0·707474 0·512018 –1·46 0·282342 –6·33 0·703688 0·512019 –1·44 0·282343 –6·29 –0·003786 0·02 0·04 11B 37·3 0·704318 0·512010 –1·61 0·282256 –9·38 0·703688 0·512019 –1·44 0·282343 –6·29 –0·000630 0·17 3·09 12A 18·5 0·707498 0·512034 –1·14 0·282340 –6·41 0·703804 0·512023 –1·36 0·282310 –7·48 –0·003694 –0·22 –1·07 12B 52·9 0·704127 0·512022 –1·39 0·282270 –8·89 0·703804 0·512023 –1·36 0·282310 –7·48 –0·000323 0·03 1·41 13A 18·5 0·713077 0·511789 –5·94 0·282393 –4·54 0·704477 0·511776 –6·18 0·282406 –4·08 –0·008600 –0·24 0·46 13B 52·9 0·705124 0·511777 –6·17 0·282337 –6·52 0·704477 0·511776 –6·18 0·282406 –4·08 –0·000647 –0·02 2·44 14A 18·5 0·707464 0·512021 –1·40 0·282340 –6·41 0·703803 0·512012 –1·57 0·282310 –7·48 –0·003661 –0·18 –1·07 14B 52·9 0·704125 0·512009 –1·64 0·282270 –8·89 0·703803 0·512012 –1·57 0·282310 –7·48 –0·000322 0·07 1·41 15A 18·5 0·707498 0·512064 –0·56 0·282339 –6·43 0·703803 0·512012 –1·57 0·282310 –7·48 –0·003695 –1·02 –1·05 15B 52·9 0·704127 0·512049 –0·86 0·282269 –8·90 0·703803 0·512012 –1·57 0·282310 –7·48 –0·000325 –0·72 1·43 16A 18·5 0·713057 0·511799 –5·74 0·282392 –4·56 0·704477 0·511785 –6·01 0·282405 –4·09 –0·008580 –0·28 0·47 16B 52·9 0·705123 0·511787 –5·98 0·282336 –6·53 0·704477 0·511785 –6·01 0·282405 –4·09 –0·000647 –0·04 2·44 17A 18·5 0·713078 0·511843 –4·88 0·282392 –4·57 0·704477 0·511785 –6·01 0·282405 –4·09 –0·008601 –1·13 0·48 17B 52·9 0·705124 0·511829 –5·16 0·282336 –6·54 0·704477 0·511785 –6·01 0·282405 –4·09 –0·000648 –0·85 2·44 18A 18·5 0·707433 0·512016 –1·50 0·282368 –5·39 0·703801 0·512007 –1·67 0·282380 –4·98 –0·003631 –0·17 0·41 18B 52·9 0·704122 0·512003 –1·76 0·282346 –6·19 0·703801 0·512007 –1·67 0·282380 –4·98 –0·000321 0·09 1·20 19A 18·3 0·750564 0·511839 –4·96 0·282233 –10·20 0·718803 0·511912 –3·53 0·282264 –9·09 –0·031761 1·43 1·11 19B 46·4 0·728108 0·511906 –3·65 0·282253 –9·46 0·718803 0·511912 –3·53 0·282264 –9·09 –0·009305 0·11 0·38 20A 18·3 0·735332 0·511705 –7·57 0·282280 –8·54 0·713082 0·511766 –6·38 0·282335 –6·57 –0·022250 1·19 1·97 20B 46·4 0·719671 0·511781 –6·09 0·282305 –7·63 0·713082 0·511766 –6·38 0·282335 –6·57 –0·006589 –0·28 1·06 21A 18·3 0·735331 0·511705 –7·57 0·282330 –6·76 0·713082 0·511766 –6·38 0·282424 –3·41 –0·022250 1·19 3·35 21B 46·4 0·719669 0·511781 –6·09 0·282374 –5·19 0·713082 0·511766 –6·38 0·282424 –3·41 –0·006588 –0·28 1·78 22A 18·5 0·707434 0·512048 –0·88 0·282579 2·06 0·703802 0·512033 –1·17 0·282461 –2·10 –0·003632 –0·29 –4·17 22B* 34·4 0·703151 0·511936 –3·07 0·282233 –10·20 0·703205 0·512019 –1·44 0·282401 –4·23 0·000053 1·63 5·97 22B 52·9 0·704123 0·512033 –1·16 0·282403 –4·18 0·703802 0·512033 –1·17 0·282461 –2·10 –0·000321 –0·01 2·07 23A 18·5 0·713039 0·511833 –5·07 0·282511 –0·36 0·704476 0·511814 –5·45 0·282490 –1·10 –0·008563 –0·39 –0·74 23B 52·9 0·705123 0·511819 –5·35 0·282410 –3·92 0·704476 0·511814 –5·45 0·282490 –1·10 –0·000646 –0·11 2·82 24A 12·4 0·750298 0·511795 –5·82 0·282195 –11·52 0·717381 0·512128 0·69 0·282326 –6·90 –0·032917 6·51 4·62 25A 13·8 0·750386 0·511805 –5·63 0·282198 –11·43 0·716278 0·512130 0·72 0·282327 –6·84 –0·034107 6·35 4·59 25B 49·2 0·726622 0·511871 –4·33 0·282213 –10·88 0·716278 0·512130 0·72 0·282327 –6·84 –0·010344 5·06 4·04 26A 13·8 0·735124 0·511711 –7·46 0·282274 –8·73 0·711198 0·512073 –0·39 0·282400 –4·27 –0·023926 7·06 4·46 26B* 35·3 0·716973 0·511885 –4·07 0·282249 –9·61 0·708319 0·512266 3·38 0·282453 –2·41 –0·008654 7·45 7·20 26B 49·2 0·718586 0·511782 –6·06 0·282260 –9·25 0·711198 0·512073 –0·39 0·282400 –4·27 –0·007388 5·67 4·98 27A 7·2 0·7