The processes that lead to the fourfold variation in arc-averaged compositions of 11 mafic arc lavas remain controversial. Control by the mantle-wedge thermal structure 12 is supported by chemical correlations with the thickness of the underlying arc crust 1-3 , 13 which affects the thermal state of the wedge. Control by down-going slab 14 temperature is supported by correlations with the slab thermal parameter 3-7. The 15 Chilean Southern Volcanic Zone (SVZ, Figure 1) provides a test of these hypotheses. 16 Our chemical data demonstrate that the SVZ and global arc averages define the same 17 chemical trends, both among elements and between elements and crustal thickness. 18 But in contrast to the global arc system, the SVZ is built on crust of variable thickness 19 with a constant slab thermal parameter. This natural experiment, along with a set of 20 numerical simulations, shows that global arc compositional variability is dominated by 21 different extents of melting that are controlled by the thermal structure of the mantle 22 wedge. Slab temperatures play a subordinate role. Variations in the subducting slab's 23 fluid flux and sediment compositions as well as mantle-wedge heterogeneities 24 produce second-order effects that are manifested as trace element and isotopic 25 signatures; these can be more clearly elucidated once the importance of wedge 26 thermal structure is recognized. 27 28 The chemical compositions of arc-front stratovolcanoes, averaged for individual 29 arcs and normalized for differentiation, display coherent systematics 1,2 (Figure 2a-f). 30 Incompatible elements correlate well with one another over fourfold concentration 31 ranges. More compatible elements, such as Ca and Sc, correlate negatively with 32 incompatible elements 2,8 , while heavy rare-earth elements vary little. Correlations 33 among incompatible elements transcend standard geochemical groupings associated 34 with slab processes. Elements believed to be immobile (e.g high-field-strength Nb, Zr), 35 or concentrated in subducting sediments 9,10 (e.g. Th, La), or "fluid-mobile" (e.g. K, Pb, U, 36 Sr), are all mutually correlated. Magma compositions also correlate with the sub-arc 37 Moho depth (Figure 2f-g), and a proxy for the thermal structure of the down-going slab 3-38 6 , the slab "thermal parameter" [Φ=slab age*convergence rate*sin(dip angle)] 11 , but not 39 with the depth of the slab beneath the arc or calculated sub-arc slab-surface 40 temperatures 12. Successful models of arc volcanism must account for these first-order 41 relationships. 42 These relationships are not dependent on the index used to represent arc 43 compositions. Here we use values normalized to 6% MgO ("6-values"), but the chemical 44 relationships persist to Mg#s (Mg#=atomic Mg/(Mg+Fe)) in equilibrium with the mantle 45 (Figure S1a), and are independent of filtering choices 2. The Ce/H 2 O ratio in olivine-46 hosted melt inclusions 4-6 has also been used to represent compositional variability 47 among volcanic arcs. Averaged melt inclusion H 2 O conc...