  A two-type two-sex branching process is introduced with the aim of describing
the interaction of predator and prey populations with sexual reproduction and
promiscuous mating. In each generation and in each species the total number of
individuals which mate and produce offspring is controlled by a binomial
distribution with size given by this number of individuals and probability of
success depending on the density of preys per predator. The resulting model
enables us to depict the typical cyclic behaviour of predator-prey systems
under some mild assumptions on the shape of the function that characterises the
probability of survival of the previous binomial distribution. We present some
basic results about fixation and extinction of both species as well as
conditions for the coexistence of both of them. We also analyse the suitability
of the process to model real ecosystems comparing our model with a real
dataset.
