  In order to keep their cohesiveness during locomotion gregarious animals must
make collective decisions. Many species boast complex societies with multiple
levels of communities. A common case is when two dominant levels exist, one
corresponding to leaders and the other consisting of followers. In this paper
we study the collective motion of such two-level assemblies of self-propelled
particles. We present a model adapted from one originally proposed to describe
the movement of cells resulting in a smoothly varying coherent motion. We shall
use the terminology corresponding to large groups of some mammals where leaders
and followers form a group called a harem. We study the emergence
(self-organization) of sub-groups within a herd during locomotion by computer
simulations. The resulting processes are compared with our prior observations
of a Przewalski horse herd (Hortob\'agy, Hungary) which we use as results from
a published case study. We find that the model reproduces key features of a
herd composed of harems moving on open ground, including fights for followers
between leaders and bachelor groups (group of leaders without followers). One
of our findings, however, does not agree with the observations. While in our
model the emerging group size distribution is normal, the group size
distribution of the observed herd based on historical data have been found to
follow lognormal distribution. We argue that this indicates that the formation
(and the size) of the harems must involve a more complex social topology than
simple spatial-distance based interactions.
