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The determination of the incidence of damped Ly$\alpha$ systems in the redshift interval $0\!\!<\!\!z\!\!<\!\!1.65$ is crucial for constraining the evolution of neutral gas in galaxies. This redshift interval corresponds to a time interval of 62\% of the age of the Universe for $q_0=0$ (77\% for $q_0=0.5$). However, because damped Ly$\alpha$ systems are relatively rare in spectra, a sensitive UV spectroscopic survey of the Ly$\alpha$ line at low redhsifts would consume considerable telescope time. We have therefore undertaken a new approach to study the evolutionary properties of damped Ly$\alpha$ systems at $z\!\!<\!\!1.65$ that takes advantage of the fact that all damped Ly$\alpha$ systems studied so far are found to have corresponding MgII metal-line absorption. From known MgII absorption-line statistics, we determine an upper limit to the number density of damped Ly$\alpha$ systems along the line of sight, $n_{\rm DLy\alpha}(z)$, at $<\!\!z\!\!> \approx 0.8$ that is consistent with the trend at higher redshift as well as the number density at the current epoch inferred from H\,I cross-sections of nearby disk galaxies. The result that $n(z)$ at low redshift conforms to a trend established by three different observing techniques over three redshift regimes provides evidence that this trend actually traces the evolution of neutral gas in galaxies. Implications for the evolution of $n_{\rm DLy\alpha}(z)$ and $\Omega_{\rm HI}(z)$, the cosmological mass density of neutral hydrogen, are discussed.
