  The evolution of an infinite system of interacting point entities with traits
$x\in \mathds{R}^d$ is studied. The elementary acts of the evolution are
state-dependent death of an entity with rate that includes a competition term
and independent fission in the course of which an entity gives birth to two new
entities and simultaneously disappears. The states of the system are
probability measures on the corresponding configuration space and the main
result of the paper is the construction of the evolution $\mu_0\to \mu_t$,
$t>0$, of states in the class of sub-Poissonian measures.
