  We use the Panchromatic Hubble Andromeda Treasury (PHAT) survey dataset to
perform spatially resolved measurements of star cluster formation efficiency
($\Gamma$), the fraction of stellar mass formed in long-lived star clusters. We
use robust star formation history and cluster parameter constraints, obtained
through color-magnitude diagram analysis of resolved stellar populations, to
study Andromeda's cluster and field populations over the last $\sim$300 Myr. We
measure $\Gamma$ of 4-8% for young, 10-100 Myr old populations in M31. We find
that cluster formation efficiency varies systematically across the M31 disk,
consistent with variations in mid-plane pressure. These $\Gamma$ measurements
expand the range of well-studied galactic environments, providing precise
constraints in an HI-dominated, low intensity star formation environment.
Spatially resolved results from M31 are broadly consistent with previous trends
observed on galaxy-integrated scales, where $\Gamma$ increases with increasing
star formation rate surface density ($\Sigma_{\mathrm{SFR}}$). However, we can
explain observed scatter in the relation and attain better agreement between
observations and theoretical models if we account for environmental variations
in gas depletion time ($\tau_{\mathrm{dep}}$) when modeling $\Gamma$,
accounting for the qualitative shift in star formation behavior when
transitioning from a H$_2$-dominated to a HI-dominated interstellar medium. We
also demonstrate that $\Gamma$ measurements in high $\Sigma_{\mathrm{SFR}}$
starburst systems are well-explained by $\tau_{\mathrm{dep}}$-dependent
fiducial $\Gamma$ models.
