  Radiative transfer models of multi-transition observations are used to
determine molecular abundances as functions of position in pre- and
protostellar cores. The data require a "drop" abundance profile with radius,
with high abundances in the outermost regions probed by low excitation 3 mm
lines, and much lower abundances at intermediate zones probed by higher
frequency lines. The results are illustrated by detailed analysis of CO and
HCO+ lines for a subset of objects. We propose a scenario in which the
molecules are frozen out in a region of the envelope where the temperature is
low enough (<= 40 K) to prevent immediate desorption, but where the density is
high enough (> 10^4-10^5 cm^{-3}) that the freeze-out timescales are shorter
than the lifetime of the core. The size of the freeze-out zone is thereby a
record of the thermal and dynamical evolution of the cores. Fits to CO data for
a sample of 16 objects indicate that the size of the freeze-out zone decreases
significantly between Class 0 and I objects, explaining the variations in, for
example, CO abundances with envelope masses. However, the corresponding
timescales are 10^{5+/-0.5} years, with no significant difference between Class
0 and I objects. These timescales suggest that the dense pre-stellar phase with
heavy depletions lasts only a short time, of order 10^5 yr, in agreement with
recent chemical-dynamical models.
