  We consider certain analytical features of a stochastic model that can
explain among other things competition among species and simultaneous predation
on the competing species from a geometric perspective which allows for a
systematic description of models admitting singular Lagrangians. The model
equations are shown to admit a Jacobi Last Multiplier which in turn allows for
the construction of a Lagrangian. The Lagrangian is of singular nature so that
construction of the Hamiltonian via a Legendre transformation is not possible.
A Hamiltonian description of the model therefore requires the introduction of
Dirac brackets. Explicit results are presented for the "Kill the winner" model
and its reductions.
