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Atomic force microscopy and photoluminescence spectroscopy (PL) has been used to study asymmetric bilayer InAs quantum dot (QD) structures grow by molecular-beam epitaxy on GaAs (001) substrates. The two InAs layers were separated by a 7-nm-thick GaAs spacer layer and were grown at different substrate temperature. We took advantage of the intrinsic nonuniformity of the molecular beams to grow the seed layer with an average InAs coverage of 2.0 ML. Then the seed layer thickness could be divided into three areas: below, around and above the critical thickness of the 2D-3D transition along the  direction of the substrate. Correspondingly, the nucleation mechanisms of the upper InAs layer (IT1L) could be also divided into three areas: temperature-controlled, competition between temperature-controlled and strain-induced, and strain-induced (template-controlled) nucleation. Small quantum dots (QDs) with a large density around 5 times 1010 cm-2 are found in the temperature-controlled nucleation area. The QD size distributions undergo a bimodal to a unimodal transition with decreasing QD densities in the strain-induced nucleation area, where the QD densities vary following that of the seed layer (templating effect). The optimum QD density with the IIII. thickness fixed at 2.4 ML is shown to be around 1.5 times 1010 cm-2 , for which the QD size distribution is unimodal and PL emission peaks at the longest wavelength. The QDs in the in-between area exhibit a broad size distribution with small QDs and strain-induced large QDs coexisting.