  We present new Hubble Space Telescope imaging of the outer regions of M87 in
order to study its globular cluster (GC) population out to large galactocentric
distances. We discuss particularly the relationship between GC effective radii
$r_h$ and projected galactocentric distance $R_{gc}$. The observations suggest
a shallow trend $r_h \propto R_{gc}^{0.14}$ out to $R_{gc} \sim 100$ kpc, in
agreement with studies of other giant elliptical galaxies. To theoretically
reproduce this relationship we simulate GC populations with various
distributions of orbits. For an isotropic distribution of cluster orbits we
find a steeper trend of $r_h \propto R_{gc}^{0.4}$. Instead we suggest that (a)
if the cluster system has an orbital anisotropy profile, where orbits become
preferentially radial with increasing galactocentric distance, AND (b) if
clusters become more tidally under-filling with galactocentric distance, the
observed relationship can be recovered. We also apply this approach to the red
and blue GC populations separately and predict that red clusters are
preferentially under-filling at large $R_{gc}$ and have a more isotropic
distribution of orbits than blue clusters.
