  In an attempt to constrain evolutionary models of the asymptotic giant branch
(AGB) phase at the limit of low masses and low metallicities, we have examined
the luminosity functions and number ratio between AGB and red giant branch
(RGB) stars from a sample of resolved galaxies from the ACS Nearby Galaxy
Survey Treasury (ANGST). This database provides HST optical photometry together
with maps of completeness, photometric errors, and star formation histories for
dozens of galaxies within 4 Mpc. We select 12 galaxies characterized by
predominantly metal-poor populations as indicated by a very steep and blue RGB,
and which do not present any indication of recent star formation in their
color--magnitude diagrams. Thousands of AGB stars brighter than the tip of the
RGB (TRGB) are present in the sample (between 60 and 400 per galaxy), hence the
Poisson noise has little impact in our measurements of the AGB/RGB ratio. We
model the photometric data with a few sets of thermally pulsing AGB (TP-AGB)
evolutionary models with different prescriptions for the mass loss. This
technique allows us to set stringent constraints to the TP-AGB models of
low-mass metal-poor stars (with M<1.5 Msun, [Fe/H]<~-1.0). Indeed, those which
satisfactorily reproduce the observed AGB/RGB ratios have TP-AGB lifetimes
between 1.2 and 1.8 Myr, and finish their nuclear burning lives with masses
between 0.51 and 0.55 Msun. This is also in good agreement with recent
observations of white dwarf masses in the M4 old globular cluster. These
constraints can be added to those already derived from Magellanic Cloud star
clusters as important mileposts in the arduous process of calibrating AGB
evolutionary models.
