Upper left panel: the H i MF in the four simulations used in this work, and as observed by ALFALFA. The solid curves show the counts of all galaxies in the mock survey cones, while points include only those that would be detected by an ALFALFA-like survey. The colour coding (legend in upper right panel) is as in Fig. 3. The ‘bump’ feature (solid curves) at low H i mass (⁠|$M_\mathrm{HI}\lesssim 10^{7}\, \mathrm{M}_\odot$|⁠) has a numerical origin (see Section 4.2). The green crosses show the number counts from the ALFALFA extragalactic source catalogue. The bins in |$M_\mathrm{HI}$| have a width of |$0.1\, \mathrm{dex}$|⁠. Lower left panel: ratio of the curves and points from the upper-left panel to the corresponding EAGLE (CDM) curve or points. Upper right panel: as upper left panel, but for the H i WF. The bins in |$w_{50}$| have a width of |$0.1\, \mathrm{dex}$|⁠. The suppression of number counts seen at low |$v_\mathrm{max}$| in WDM cosmogonies is not evident at low |$w_{50}$| – in fact, the survey of the simulation with the ‘warmest’ DM (EAGLE with |$1.5\, \mathrm{keV}$| thermal relic) has a factor of |$\approx 2$| more detections at |$w_{50}\approx 70\, \mathrm{km}\, \mathrm{s}^{-1}$| than the surveys of CDM simulations. Lower right panel: as lower right panel, but with ratios relative to EAGLE (CDM) corresponding to points and curves in the upper right panel.