  We propose an analytical model for the quasistatic evolution of starless
cores confined by a constant external pressure, assuming that cores are
isothermal and obey a spherically-symmetric density distribution. We model core
evolution for Plummer-like and Gaussian density distributions in the adiabatic
and isothermal limits, assuming Larson-like dissipation of turbulence. We model
the variation in the terms in the virial equation as a function of core
characteristic radius, and determine whether cores are evolving toward virial
equilibrium or gravitational collapse. We ignore accretion onto cores in the
current study. We discuss the different behaviours predicted by the isothermal
and adiabatic cases, and by our choice of index for the size-linewidth
relation, and suggest a means of parameterising the magnetic energy term in the
virial equation. We model the evolution of the set of cores observed by Pattle
et al. (2015) in the L1688 region of Ophiuchus in the 'virial plane'. We find
that not all virially-bound and pressure-confined cores will evolve to become
gravitationally bound, with many instead contracting to virial equilibrium with
their surroundings, and find an absence of gravitationally-dominated and
virially-unbound cores. We hypothesise a 'starless core desert' in this
quadrant of the virial plane, which may result from cores initially forming as
pressure-confined objects. We conclude that a virially-bound and
pressure-confined core will not necessarily evolve to become gravitationally
bound, and thus cannot be considered prestellar. A core can only be
definitively considered prestellar (collapsing to form an individual stellar
system) if it is gravitationally unstable.
