Two interacting particle systems that serve as probabilistic models for population dynamics are studied in this work. The quadratic contact process is a stochastic spatial model for a population in which each individual has two parents and the dynamics are governed by random birth and death rates and an offspring distribution kernel. Another population model, due to Bolker and Pacala, models competition of different species in a forest. In both cases, we are interested in proving the existence of nontrivial stationary distributions.