1. Research School of Earth Sciences, The Australian National University, Canberra, Australian Capital Territory 0200, Australia
2. School of Mathematical Sciences, Monash University, Melbourne, Victoria 3800, Australia

Correspondence to: W. P. Schellart¹ Correspondence and requests for materials should be addressed to W.P.S. (Email: wouter.schellart@anu.edu.au).

Subducting slabs provide the main driving force for plate motion and flow in the Earth's mantle^{1, 2, 3, 4}, and geodynamic, seismic and geochemical studies offer insight into slab dynamics and subduction-induced flow^{3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}. Most previous geodynamic studies treat subduction zones as either infinite in trench-parallel extent^{3, 5, 6} (that is, two-dimensional) or finite in width but fixed in space^{7, 16}. Subduction zones and their associated slabs are, however, limited in lateral extent (250–7,400 km) and their three-dimensional geometry evolves over time. Here we show that slab width controls two first-order features of plate tectonics—the curvature of subduction zones and their tendency to retreat backwards with time. Using three-dimensional numerical simulations of free subduction, we show that trench migration rate is inversely related to slab width and depends on proximity to a lateral slab edge. These results are consistent with retreat velocities observed globally, with maximum velocities (6–16 cm yr^-1) only observed close to slab edges (<1,200 km), whereas far from edges (>2,000 km) retreat velocities are always slow (<2.0 cm yr^-1). Models with narrow slabs (1,500 km) retreat fast and develop a curved geometry, concave towards the mantle wedge side. Models with slabs intermediate in width (2,000–3,000 km) are sublinear and retreat more slowly. Models with wide slabs (4,000 km) are nearly stationary in the centre and develop a convex geometry, whereas trench retreat increases towards concave-shaped edges. Additionally, we identify periods (5–10 Myr) of slow trench advance at the centre of wide slabs. Such wide-slab behaviour may explain mountain building in the central Andes, as being a consequence of its tectonic setting, far from slab edges.

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