  Context: High-resolution images of circumstellar debris discs reveal
off-centred rings that indicate past or ongoing perturbation, possibly caused
by secular gravitational interaction with unseen stellar or substellar
companions. The purely dynamical aspects of this departure from radial symmetry
are well understood. However, the observed dust is subject to additional forces
and effects, most notably collisions and drag. Aims: To complement the studies
of dynamics, we therefore aim to understand how new asymmetries are created by
the addition of collisional evolution and drag forces, and existing ones
strengthened or overridden. Methods: We augmented our existing numerical code
"Analysis of Collisional Evolution" (ACE) by an azimuthal dimension, the
longitude of periapse. A set of fiducial discs with global eccentricities
ranging from 0 to 0.4 is evolved over giga-year timescales. Size distribution
and spatial variation of dust are analysed and interpreted. The basic impact of
belt eccentricity on spectral energy distributions (SEDs) and images is
discussed.
  Results: We find features imposed on characteristic timescales. First,
radiation pressure defines size cutoffs that differ between periapse and
apoapse, resulting in an asymmetric halo. The differences in size distribution
make the observable asymmetry of the halo depend on wavelength. Second,
collisional equilibrium prefers smaller grains on the apastron side of the
parent belt, reducing the effect of pericentre glow and the overall asymmetry.
Third, Poynting-Robertson drag fills the region interior to an eccentric belt
such that the apastron side is more tenuous. Interpretation and prediction of
the appearance in scattered light is problematic when spatial and size
distribution are coupled.
