Mineral equilibria modelling method
A powerful way to show the relationship between multivariant assemblages over a P-T range for a particular whole-rock composition is the analysis of P-T pseudosections (e.g. Powell et al. 1998; White et al. 2007; Vernon & Clarke 2008). Pseudosections provide accurate P-T estimates and can be used to relate partial melting processes to the preserved metamorphic assemblages in order to gain a quantitative view of which conditions the key reactions took place. Based on the internally-consistent thermodynamic dataset ds55 (Holland & Powell, 1998 and recent updates) and Thermocalc version 3.33 (Powell & Holland, 1988) it was possible to calculate four pseudosections. The dataset consists of end members and, in combination with activity models for minerals, allowed the calculations to be undertaken in the system Na2O-CaO-K2O-FeO-MgO-Al2O3-SiO2-H2O-TiO2-O2 (NCKFMASHTO). The KFMASHTO system also takes into account Ti and Fe3+. Minor components of Ti and Fe3+ were estimated before the calculations began. With a realisitc estimate of this minor component the system can model large and complex chemical systems. The system also needs an effective bulk rock constraint that controls the metamorphic assemblages in pelitic and semipelitic rocks. A composition (SiO2 = 69.46 , Al2O3 = 8.87 , CaO = 0.28 , MgO = 3.61, FeO = 7.07, K2O = 2.84 , Na2O = 0.56 , TiO2 = 0.62 , O = 0.10 H2O = 6.60 ) was used from White et al. (2007) at subsolidus and suprasolidus conditions. MnO is not considered in the calculations because, for high-temperature pseudosections, the most recent a-x models have not yet been calibrated for Mn (e.g. White et al. 2007; Zirkler et al. 2012). The internally-consistent thermodynamic dataset used in this study contains a-x models for amphibole (Diener et al. 2007), biotite, garnet and silicate melt (White et al. 2007), cordierite, epidote, staurolite (Holland & Powell 1998), orthopyroxene (White et al. 2002), chlorite (Holland et al. 1998), chloritoid and ilmenite/hematite/magnetite (White et al. 2000), muscovite and paragonite (Coggon & Holland 2002), plagioclase and K-feldspar (Holland & Powell 2003), osumilite (Holland et al. 1996) and spinel and magnetite (White et al. 2002). The XRF data (Table S1) were converted to molar percentages of the oxides. Loss on ignition (LOI) was treated as H2O for samples AGC 417 and 419 which is not exactly correct (minor amounts of CO2 are normally present) but close enough. Samples AGC 221 and 415 have negative LOI which indicates that the weight increase arising from oxidation of Fe2+ to Fe3+ (FeO to Fe2O3) is higher than the weight loss caused by removing volatiles from the mineral structures. The method for calculating the lowest possible bulk-H2O content to fully hydrate the assemblage below the wet solidus is decribed in White et al. (2001, 2003).

Table S1
Major element compositions of AGC 221, AGC 415, AGC 417 and AGC 419
Sample AGC415   AGC221   AGC 417   AGC 419

SiO2	62.45	66.54	73.49       76.25
TiO2	0.65	0.63	0.67          0.66
Al2O3	10.65	10.37	8.71         11.06
Fe2O3	19.73	15.73	10.73        4.51
FeO	17.76*	14.16*	9.66          4.06
MnO	0.25	0.19	0.12          0.04
MgO	4.18	4.53	4.04          1.25
CaO	0.96	1.00	0.55          1.25
Na2O	0.02	0.54	0.43          3.05
K2O	1.97	2.14	1.93          1.79
P2O5	0.1	0.11	0.01          0.06
LOI	- 0.75	-0.30	0.25          0.33
Total	100.61	101.82	101.57     100.3
	
*FeO content was not determined and multiplied with factor 0.8999

Coggon, R. & Holland, T. J. B. 2002. Mixing properties of phengitic micas and revised garnet-phengite thermobarometers. Journal of Metamorphic Geology, 20, 683–696.
Diener, J. F. A., Powell, R., White, R. W. & Holland, T. J. B. 2007. A new thermodynamic model for clino- and orthoamphiboles in the system Na2O–CaO–FeO–MgO–Al2O3–SiO2–H2O–O. Journal of Metamorphic Geology, 25, 631–656.
Holland, T. J. B., Babu, E. V. S. S . K. & Waters, D. J. 1996. Phase relations of Osumilite and dehydration melting in pelitic rocks: a simple thermodynamic model for the KFMASH system. Contributions to Mineralogy and Petrology, 124, 383–394.
Holland, T. J. B., Baker & J. M. Powell, R. 1998. Mixing properties and activity-composition relationships of chlorites in the system MgO-FeO-Al2O3-SiO2-H2O. European Journal of Mineralogy, 10, 395–406.
Holland, T. J. B. & Powell, R. 1998. An internally-consistent thermodynamic dataset for phases of petrological interest. Journal of Metamorphic Geology, 16, 309–344.
Holland, T. J. B & Powell, R. 2003. Activity-composition relations for phases in petrological calculations: an asymmetric multicomponent formulation. Contributions to Mineralogy and Petrology, 145, 492–501.
Powell, R. & Holland, T.  J.  B. 1988. An internally consistent dataset with uncertainties and correlations; 3, Applications to geobarometry, worked examples and a computer program. Journal of Metamorphic Geology, 6, 173–204.
Powell, R., Holland, T. & Worley, B. 1998. Calculating phase diagrams involving solid solutions via non-linear equations, with examples using THERMOCALC. Journal of Metamorphic Geology, 16, 577–588.
Vernon, R. H. & Clarke, G. L., 2008. Principles of Metamorphic Petrology. Cambridge University Press,  Cambridge.
White, R. W., Powell, R., Holland, T. J. B. & Worley, B. A. 2000. The effect of TiO2 and Fe2O3 on metapelitic assemblages at greenschist and amphibolite facies conditions: mineral equilibria calculations in the system K2O-FeO-MgO-Al2O3-SiO2-H2O-TiO2-Fe2O3. Journal of Metamorphic Geology, 18, 497–511.
White, R. W., Powell, R. & Holland, T. J. B. 2001. Calculation of partial melting equilibria in the system Na2O- CaO-K2O-FeO-MgO-Al2O3-SiO2-H2O (NCKFMASH). Journal of Metamorphic Geology, 19, 139–153.
White, R. W., Powell, R. & Clarke, G. L., 2002. The interpretation of reaction textures in Fe-rich metapelitic granulites of the Musgrave Block, central Australia: constraints from mineral equilibria calculations in the system K2O-FeO-MgO-Al2O3-SiO2-H2O-TiO2-Fe2O3. Journal of Metamorphic Geology, 20, 41–55.
White, R. W., Powell, R. & Phillips, G. N. 2003. A mineral equilibria study of hydrothermal alteration in mafic greenschist facies rock at Kalgoorlie, Western Australia. Journal of Metamorphic Geology, 21, 455–468.
White, R. W., Powell, R. & Holland, T. J. B. 2007. Progress relating to calculations of partial melting equilibria for Metapelites. Journal of Metamorphic Geology, 25, 511–527.
Zirkler, A., Johnson, T. E., White, R. W. & Zack, T. 2012. Polymetamorphism in the mainland Lewsian complex, NW Scotland – phase equilibria and geochronological constraints from the Cnoc ant’Sidhean suite. Journal of Metamorphic Geology, 30, 865–885.