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 is 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 comoving 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 .