Gregarious animals need to make collective decisions in order to keep their
cohesiveness. Several species of them live in multilevel societies, and form
herds composed of smaller communities. We present a model for the development
of a leadership hierarchy in a herd consisting of loosely connected sub-groups
(e.g. harems) by combining self organization and social dynamics. It starts
from unfamiliar individuals without relationships and reproduces the emergence
of a hierarchical and modular leadership network that promotes an effective
spreading of the decisions from more capable individuals to the others, and
thus gives rise to a beneficial collective decision. Our results stemming from
the model are in a good agreement with our observations of a Przewalski horse
herd (Hortob\'agy, Hungary). We find that the harem-leader to harem-member
ratio observed in Przewalski horses corresponds to an optimal network in this
approach regarding common success, and that the observed and modeled harem size
distributions are close to a lognormal.Comment: 18 pages, 7 figures, J. Stat. Phys. (2014
