  We carry out a comprehensive theoretical examination of the relationship
between the spatial distribution of optical transients and the properties of
their progenitor stars. By constructing analytic models of star-forming
galaxies and the evolution of stellar populations within them, we are able to
place constraints on candidate progenitors for core-collapse supernovae (SNe),
long-duration gamma ray bursts, and supernovae Ia. In particular we first
construct models of spiral galaxies that reproduce observations of
core-collapse SNe, and we use these models to constrain the minimum mass for
SNe Ic progenitors to approximately 25 solar masses. Secondly, we lay out the
parameters of a dwarf irregular galaxy model, which we use to show that the
progenitors of long-duration gamma-ray bursts are likely to have masses above
approximately 43 solar masses. Finally, we introduce a new method for
constraining the time scale associated with SNe Ia and apply it to our spiral
galaxy models to show how observations can better be analyzed to discriminate
between the leading progenitor models for these objects.
