  In most models of collective motion in animal groups each individual updates
its heading based on the current positions and headings of its neighbors.
Several authors have investigated the effects of including anticipation into
models of this type, and have found that anticipation inhibits polarized
collective motion in alignment based models and promotes milling and swarming
in the one attraction-repulsion model studied. However, it was recently
reported that polarized collective motion does emerge in an alignment based
asynchronous lattice model with mutual anticipation. To our knowledge this is
the only reported case where polarized collective motion has been observed in a
model with anticipation. Here we show that including anticipation induces
polarized collective motion in a synchronous, off lattice, attraction based
model. This establishes that neither asynchrony, mutual anticipation nor motion
restricted to a lattice environment are strict requirements for anticipation to
promote polarized collective motion. In addition, unlike alignment based models
the attraction based model used here does not produce any type of polarized
collective motion in the absence of anticipation. Here anticipation is a direct
polarization inducing mechanism. We believe that utilizing anticipation instead
of frequently used alternatives such as explicit alignment terms, asynchronous
updates and asymmetric interactions to generate polarized collective motion may
be advantageous in some cases.
