We calculate in detail the expected properties of low redshift DLAs under the assumption that they arise in the gaseous disks of galaxies like those in the $z\approx 0$ population. A sample of 355 nearby galaxies were analysed, for which high quality H I 21-cm emission line maps are available as part of an extensive survey with the Westerbork telescope (WHISP). We find that expected luminosities, impact parameters between quasars and DLA host galaxies, and metal abundances are in good agreement with the observed properties of DLAs and DLA galaxies. The measured redshift number density of $z=0$ gas above the DLA limit is $dN/dz=0.045\pm 0.006$, which compared to higher $z$ measurements implies that there is no evolution in the co-moving density of DLAs along a line of sight between $z\sim 1.5$ and $z=0$, and a decrease of only a factor of two from $z\sim 4$ to the present time. We conclude that the local galaxy population can explain all properties of low redshift DLAs.