  We propose an evolutionary path for prestellar cores on the radius-mass
diagram, which is analogous to stellar evolutionary paths on the
Hertzsprung-Russell Diagram. Using James Clerk Maxwell Telescope (JCMT)
observations of L1688 in the Ophiuchus star-forming complex, we analyse the
HCO+ (J=4\rightarrow3) spectral line profiles of prestellar cores. We find that
of the 58 cores observed, 14 show signs of infall in the form of a
blue-asymmetric double-peaked line profile. These 14 cores all lie beyond the
Jeans mass line for the region on a radius-mass plot. Furthermore another 10
cores showing tentative signs of infall, in their spectral line profile shapes,
appear on or just over the Jeans mass line. We therefore propose the manner in
which a prestellar core evolves across this diagram. We hypothesise that a core
is formed in the low-mass, low-radius region of the plot. It then accretes
quasistatically, increasing in both mass and radius. When it crosses the limit
of gravitational instability it begins to collapse, decreasing in radius,
towards the region of the diagram where protostellar cores are seen.
