  Reverberation mapping (RM) is a widely-used method for probing the physics of
broad-line regions (BLRs) in active galactic nuclei (AGNs). There are
increasing preliminary evidences that the RM behaviors of broad emission lines
are influenced by BLR densities, however, the influences have not been
investigated systematically from theoretical perspective. In the present paper,
we adopt locally optimally emitting cloud model and use CLOUDY to obtain the
one-dimensional transfer functions of the prominent UV and optical emission
lines for different BLR densities. We find that the influences of BLR densities
to RM behaviors have mainly three aspects. First, rarefied BLRs (with low gas
densities) may show anomalous responses in RM observations. Their emission-line
light curves inversely response the variations of continuum light curves, which
may have been observed in some UV RM campaigns. Second, the different BLR
densities in AGNs may result in correlations between the time lags and
equivalent widths of emission lines, and may contribute to the scatters of the
radius-luminosity relationships. Third, the variations of BLR densities may
explain the changes of time lags in individual objects in different years. Some
weak emission-line quasars (WLQs) are probably extreme cases of rarefied BLRs.
We predict that their RM observations may show the anomalous responses.
