  The fragmentation of filaments in molecular clouds has attracted a lot of
attention as there seems to be a relation between the evolution of filaments
and star formation. The study of the fragmentation process has been motivated
by simple analytical models. However, only a few comprehensive studies have
analysed the evolution of filaments using numerical simulations where the
filaments form self-consistently as part of molecular clouds. We address the
early evolution of pc-scale filaments that form within individual clouds. We
focus on three questions: How do the line masses of filaments evolve? How and
when do the filaments fragment? How does the fragmentation relate to the line
masses of the filaments? We examine three simulated molecular clouds formed in
kpc-scale numerical simulations performed with the FLASH code. We compare the
properties of the identified filaments with the predictions of analytic
filament stability models. The line masses and mass fraction enclosed in the
identified filaments increase continuously after the onset of self-gravity. The
first fragments appear early when the line masses lie well below the critical
line mass of Ostriker's hydrostatic equilibrium solution. The average line
masses of filaments identified in 3D density cubes increases far more quickly
than those identified in 2D column density maps. Our results suggest that
hydrostatic or dynamic compression from the surrounding cloud has a significant
impact on the early dynamical evolution of filaments. A simple model of an
isolated, isothermal cylinder may not provide a good approach for fragmentation
analysis. Caution must be exercised in interpreting distributions of properties
of filaments identified in column density maps, especially in the case of
low-mass filaments. Comparing or combining results from studies that use
different filament finding techniques is strongly discouraged.
