  We translate a coagulation-framentation model, describing the dynamics of
animal group size distributions, into a model for the population distribution
and associate the \blue{nonlinear} evolution equation with a Markov jump
process of a type introduced in classic work of H.~McKean. In particular this
formalizes a model suggested by H.-S. Niwa [J.~Theo.~Biol.~224 (2003)] with
simple coagulation and fragmentation rates. Based on the jump process, we
develop a numerical scheme that allows us to approximate the equilibrium for
the Niwa model, validated by comparison to analytical results by Degond et al.
[J.~Nonlinear Sci.~27 (2017)], and study the population and size distributions
for more complicated rates. Furthermore, the simulations are used to describe
statistical properties of the underlying jump process. We additionally discuss
the relation of the jump process to models expressed in stochastic differential
equations and demonstrate that such a connection is justified in the case of
nearest-neighbour interactions, as opposed to global interactions as in the
Niwa model.
