  We consider a dynamic version of the Neyman contagious point process that can
be used for modelling the spacial dynamics of biological populations, including
species invasion scenarios. Starting with an arbitrary finite initial
configuration of points in ${\bf R}^d$ with nonnegative weights, at each time
step a point is chosen at random from the process according to the distribution
with probabilities proportional to the points' weights. Then a finite random
number of new points is added to the process, each displaced from the location
of the chosen "mother" point by a random vector and assigned a random weight.
Under broad conditions on the sequences of the numbers of newly added points,
their weights and displacement vectors (which include a random environments
setup), we derive the asymptotic behaviour of the locations of the points added
to the process at time step $n$ and also that of the scaled mean measure of the
point process after time step $n\to\infty$.
