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tokens: of observing a region as empty as the Local Void (Section 4.2.2). The simulated Local Volumes have lower number density by up to a factor of 2 at the faint end of the luminosity function in the WDM model (Fig. 8 ). The probability of a region as empty as the observed Local Void is as high as 34 per cent in the WDM model, five times higher than that in the CDM model (Fig. 9 ). A more complete Local Volume galaxy census (e.g. the Dark Energy Spectroscopic Instruments Bright Galaxy Survey; DESI Collaboration 2016 ) should therefore provide a way to constrain the nature of dark matter. APPENDIX A: HALO MASS FUNCTIONS IN SIMULATIONS Fig. A1 shows the FOF halo mass functions at different redshifts in the COLOR and COLOR-WARM simulations as described in Section 2.1 . WDM halo mass functions flatten towards the low-mass end compared to those in CDM. As first indicated by Wang White ( 2007 ), spurious haloes form due to a numerical discreetness effect in warm and hot dark matter simulations. The mass limit of dark matter haloes below which spurious haloes form depends on the N -body particle mass of the simulation and the WDM particle mass assumed. In COLOR-WARM, the N -body mass resolution is m dm 6.2010 6 h 1 M , and the WDM particle mass is m x 1.5keV. This corresponds to a mass limit of M lim 2.4210 9 h 1 M and M min 0.5 M lim given by equations derived by Wang White ( 2007 ) and Lovell etal. ( 2014 ), respectively. These limits are indicated by dashed and dotted vertical lines in Fig. A1 . Below these mass limits, the halo mass functions steepen significantly due to the emergence of spurious haloes. Figure A1. FOF group mass (total particle mass) function at three redshifts in the simulations. Solid lines denote the COLOR simulation and dashed lines COLOR-WARM. The vertical dashed and dotted lines are the limiting masses below which spurious haloes form in COLOR-WARM, given by Wang White ( 2007 ) and Lovell etal. ( 2014 ). APPENDIX B: BOX AND RESOLUTION EFFECTS In this study, the simulation boxes we use are much smaller than the MS-W7 simulation that the GP14 model was calibrated with. In addition, the mass resolution of our simulations is about 100times higher than that of MS-W7. Fig. B1 shows the galaxy SMFs at z 0 of six COLOR-sized regions extracted from the MR-W7 simulation. We find that variations of up to 0.3 dex in galaxy abundance are expected due to cosmic variance. Figure B1. Left-hand panel: six random COLOR-sized regions (small coloured boxes) are extracted from MR-W7 (black dots denote the whole box). Right-hand panel: the galaxy stellar mass functions of the selected COLOR-sized regions (line colour corresponds to the box colour in the left-hand panel) combined with GP14 model. The black line is the stellar mass function of MR-W7 combined with the GP14 model. Fig. B2 shows the SMFs of the GP14 model combined with MR-W7 and COLOR, while the dotted line is the SMF when COLOR trees have all the branches below the resolution of