  We study a Markov birth-and-death process on a space of locally finite
configurations, which describes an ecological model with a density dependent
fecundity regulation mechanism. We establish existence and uniqueness of this
process and analyze its properties. In particular, we show global time-space
boundedness of the population density and, using a constructed
Foster-Lyapunov-type function, we study return times to certain level sets of
tempered configurations. We find also sufficient conditions that the degenerate
invariant distribution is unique for the considered process.

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