To assess the number of life-bearing worlds in astrophysical environments, it is necessary to take the intertwined processes of abiogenesis (birth), extinction (death), and transfer of life (migration) into account. We construct a mathematical model that incorporates this trio of mechanisms and accordingly derive the probability distribution function and other statistical properties (e.g. mean) for the number of worlds with biospheres. We show that a given astrophysical setting may become eventually saturated with life if the rate of successful transfers of organisms is higher than the extinction rate of biospheres. Based on the available data, we suggest that this criterion might be fulfilled for star-forming clusters (and perhaps the Galactic bulge under optimal circumstances), thereby indicating that such regions could constitute promising abodes for hosting and detecting life.