Local space densities of single M3–T9 dwarfs as a function of effective temperature used in the simulation described in Section 2.2. The top axis is given as a function of spectral type, the values of which were determined using the M dwarf temperature scale of Rajpurohit et al. (2013) for temperatures above 2800 K and the temperature scale for field M6–T9 dwarfs of Faherty et al. (2016) for temperatures below 2800 K. W21 densities are shown in blue and have been converted from a mass scale to a temperature scale using the 10 Gyr isochrone of Baraffe et al. (2015). K21 densities are shown in red. The densities of M6–M9.5 dwarfs are indicated in orange and were assumed to connect the W21 and K21 densities linearly. The linear fit that was used to generate these estimates is shown as a black dashed line. Error bars indicate the 1σ uncertainty on each bin, which were taken to be Poissonian. The 2100–2250 K bin is a lower limit and is indicated with an upward arrow.