We investigate the origin of the spatial regularity of arrays of InAs quantum dots (QDs) grown on GaAs(001). The Hopkins-Skellam index (HSI) is used with a newly developed calculation algorithm to quantify the spatial regularity both of QDs and of nm-sized surface reconstruction territories (SRTs) present in the InxGa1- xAs wetting layer prior to QD nucleation. The SRT is the minimum extent of a surface reconstruction region needed for one QD to nucleate. By computing the evolving HSI of SRTs from sequences of in situ scanning tunnelling microscopy images during growth, we find that the spatial regularity of QDs is traced back to that of the (n × 3) SRTs as early as 0.6 monolayers of InAs coverage. This regularity is disturbed by the (n × 4) SRTs which appear at higher coverage. The SRT approach is discussed in comparison to conventional capture zone theories of surface growth.